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\section{Introduction}
During last few years very exiting experimental results are obtained
in the charm and beauty meson and baryon spectroscopies \cite{Amsler}.
Recent CLEO measurements on the two-photon decay rates of the even-parity,
scalar $0^{++}, \chi_{b(c)0}$ and tensor $2^{++}, \chi_{b(c)2}$
states (\cite{Amsler,Ecklund} and references therein) were
motivation to investigate the properties of these mesons and their
radiative decays.
In the present work, we calculate the mass and decay constants of the
ground state heavy bottomonium, $\chi_{b2}(1P)$ and charmonium,
$\chi_{c2}(1P)$ tensor mesons with $I^G(J^{PC})=0^+(2^{++})$ in the framework
of the QCD sum rules approach.
QCD sum rules approach as a non-perturbative approach is one of the most
powerful and applicable tools to hadron physics and can play an important role
in calculation of the characteristic parameters of the hadrons (for details
about this method and some applications see \cite{svz,colangelo}).
Note that the mass and decay constant of the strange tensor
$K_2^*(1430)$ with quantum numbers $I(J^P)=1/2(2^+)$ have been calculated in
\cite{kazem1} in the same framework. These parameters for
light unflavored tensor mesons have also been calculated in \cite{aliev}.
The obtained results for the masses and decay constants are used in calculation
of the magnetic dipole moments of the light tensor mesons
using the QCD sum rules method in \cite{kazem2}.
The paper is organized as follows: in next section, sum rules for the
mass and decay constant of the ground state heavy quarkonia, $\chi_{Q2}$
tensor mesons are derived in the context of the QCD sum rules method.
Section 3 is devoted to the numerical analysis of the mass and decay constants
as well as the comparison of the obtained results on the mass with the
experimental values.
\section{Theoretical Framework}
In this section, we obtain the sum rules for the mass and decay constant of the heavy
$\chi_{Q2}(1P)$ tensor meson in the framework of the QCD sum rules approach.
For this aim we consider the following correlation function
\begin{eqnarray}\label{correl.func.101}
\Pi _{\mu\nu,\alpha\beta}=i\int
d^{4}xe^{iq(x-y)}{\langle}0\mid {\cal T}[j _{\mu\nu}(x)
\bar j_{\alpha\beta}(y)]\mid 0{\rangle},
\end{eqnarray}
where, $j_{\mu\nu}$ is the interpolating current of the $\chi_{Q2}(1P)$
tensor meson and ${\cal T}$ is the time ordering operator.
The explicit form of the current $j_{\mu\nu}$ creating the ground state
heavy tensor $\chi_{Q2}(1P)$ state with quantum numbers
$I^G(J^{PC})=0^+(2^{++})$ from the vacuum can be written in the following
form:
\begin{eqnarray}\label{tensorcurrent}
j _{\mu\nu}(x)=\frac{i}{2}\left[\bar Q(x) \gamma_{\mu} \olra{\cal D}_{\nu}(x)
Q(x)+\bar Q(x) \gamma_{\nu} \olra{\cal D}_{\mu}(x) Q(x)\right],
\end{eqnarray}
where $Q$ stands for heavy b or c quark and the $ \olra{\cal D}_{\mu}(x)$
represents the derivative with respect to four-x acting on left and right,
simultaneously. This two-side covariant derivative is defined as:
\begin{eqnarray}\label{derivative}
\olra{\cal D}_{\mu}(x)=\frac{1}{2}\left[\ora{\cal D}_{\mu}(x)-
\ola{\cal D}_{\mu}(x)\right],
\end{eqnarray}
where,
\begin{eqnarray}\label{derivative2}
\overrightarrow{{\cal D}}_{\mu}(x)=\overrightarrow{\partial}_{\mu}(x)-i
\frac{g}{2}\lambda^aA^a_\mu(x),\nonumber\\
\overleftarrow{{\cal D}}_{\mu}(x)=\overleftarrow{\partial}_{\mu}(x)+
i\frac{g}{2}\lambda^aA^a_\mu(x).
\end{eqnarray}
In the above relations, the $\lambda^a$ are the Gell-Mann matrices and
$A^a_\mu(x)$ are the external (vacuum) gluon fields , which can be
expressed directly in terms of the gluon field strength tensor
using the Fock-Schwinger gauge, $x^\mu A^a_\mu(x)=0$, as the following way:
\begin{eqnarray}\label{gluonfield}
A^{a}_{\mu}(x)=\int_{0}^{1}d\alpha \alpha x_{\beta} G_{\beta\mu}^{a}(\alpha x)=
\frac{1}{2}x_{\beta} G_{\beta\mu}^{a}(0)+\frac{1}{3}x_\eta x_\beta {\cal D}_\eta
G_{\beta\mu}^{a}(0)+...
\end{eqnarray}
Since the
current contains derivatives with respect to the space-time so we will
consider the two currents at points x and y. After doing calculations and applying the derivatives, we will set $y=0$.
It is well known that in the QCD sum rules approach, the correlation function
in Eq. (\ref{correl.func.101}) is calculated in two different ways.
The physical or phenomenological part, which is obtained in terms of the
hadronic parameters such as mass and decay constant inserting a complete set of
the states owing the same
quantum numbers as the interpolating current $j_{\mu\nu}$.
The theoretical or QCD part, which is calculated in terms of the QCD
parameters such as quark masses, quark condensates and quark-gluon coupling
constants etc. The correlation function in this part
is calculated in deep Euclidean region, $q^2\ll0$, via operator product
expansion (OPE). The short distance effects are calculated via the perturbation
theory, whereas the long distance contributions,
which are non-perturbative effects
are parameterized in terms of the quark-quark, gluon-gluon and quark-gluon
condensates. The sum rules for the observables (masses and decay constants)
of the ground state $\chi_{Q2}(1P)$ meson are obtained
equating both representations of the correlation function, isolating the ground
state and applying Borel transformation to suppress the contribution of the higher
states and continuum through the dispersion relation.
To proceed first we calculate the phenomenological part. Inserting a complete set
of intermediate state, $\chi_{Q2}(1P)$ to time ordering product in
Eq. (\ref{correl.func.101}), and performing integral over x we get:
\begin{eqnarray}\label{phen1}
\Pi _{\mu\nu,\alpha\beta}=\frac{{\langle}0\mid j _{\mu\nu}(0) \mid
\chi_{Q2}\rangle \langle \chi_{Q2}\mid j_{\alpha\beta}(0)\mid
0\rangle}{m_{\chi_{Q2}}^2-q^2}
&+& \cdots,
\end{eqnarray}
where $\cdots$ denotes the contribution of the higher states and continuum.
From the above relation, it is clear that we need to know the matrix element,
$\langle 0 \mid j_{\mu\nu}(0)\mid \chi_{Q2}\rangle$, which can be
parameterized in terms of the decay constant, $f_{\chi_{Q2}}$:
\begin{eqnarray}\label{lep}
\langle 0 \mid j_{\mu\nu}(0)\mid \chi_{Q2}\rangle=f_{\chi_{Q2}}
m_{\chi_{Q2}}^3\varepsilon_{\mu\nu},
\end{eqnarray}
where $\varepsilon_{\mu\nu}$ is the polarization tensor of $\chi_{Q2}$ meson.
Using Eq. (\ref{lep}) in Eq. (\ref{phen1}), we obtain the following final
representation of the correlation function
in phenomenological side:
\begin{eqnarray}\label{phen2}
\Pi _{\mu\nu,\alpha\beta}=\frac{f^2_{\chi_{Q2}}m_{\chi_{Q2}}^6}{m_{\chi_{Q2}}^2-q^2}
\left\{\frac{1}{2}(g_{\mu\alpha}g_{\nu\beta}+g_{\mu\beta}g_{\nu\alpha})\right\}+
\mbox{other structures}+...,
\end{eqnarray}
where, the only structure which contains a contribution of the tensor meson has
been kept. In calculations,
we have performed summation over the polarization tensor using
\begin{eqnarray}\label{polarizationt1}
\varepsilon_{\mu\nu}\varepsilon_{\alpha\beta}^*=\frac{1}{2}T_{\mu\alpha}T_{\nu\beta}+
\frac{1}{2}T_{\mu\beta}T_{\nu\alpha}
-\frac{1}{3}T_{\mu\nu}T_{\alpha\beta},
\end{eqnarray}
where,
\begin{eqnarray}\label{polarizationt2}
T_{\mu\nu}=-g_{\mu\nu}+\frac{q_\mu q_\nu}{m_{\chi_{Q2}}^2}.
\end{eqnarray}
The next step is to calculate the theoretical or QCD side of the correlation
function in deep Euclidean region, $q^2\ll0$ . Using the explicit expression for
the tensor current presented in
Eq. (\ref{tensorcurrent}) inside the correlation function shown in
Eq. (\ref{correl.func.101}) and contracting out all quark pairs using the
Wick's theorem, we obtain the following expression for the QCD side:
\begin{eqnarray}\label{correl.func.2}
\Pi _{\mu\nu,\alpha\beta}&=&\frac{i}{4}\int
d^{4}xe^{iq(x-y)} \Bigg\{Tr\left[S_Q(y-x)\gamma_\mu\olra{\cal D}_{\nu}(x)
\olra{\cal D}_{\beta}(y)S_Q(x-y)\gamma_\alpha\right]\nonumber \\
&&+\left[\beta\leftrightarrow\alpha\right]
+\left[\nu\leftrightarrow\mu\right]+\left[\beta\leftrightarrow\alpha,
\nu\leftrightarrow\mu\right]\Bigg\}.
\end{eqnarray}
To proceed we need to know the heavy quark propagator, $S_Q(x-y)$.
This propagator has been calculated in \cite{22Balitsky}:
\bea\label{heavylightguy}
S_Q (x-y)& =& S_b^{free} (x-y) - i g_s \int \frac{d^4 k}{(2\pi)^4}
e^{-ik(x-y)} \int_0^1 dv \Bigg[\frac{\not\!k + m_Q}{( m_Q^2-k^2)^2}
G^{\mu\nu}[v(x-y)] \sigma_{\mu\nu} \nnb \\
\ar \frac{1}{m_Q^2-k^2} v (x_\mu-y_\mu)
G^{\mu\nu} \gamma_\nu \Bigg]~,
\eea
where,
\bea\label{freeprop}
S^{free}_{Q}(x-y)
\es\frac{m_{Q}^{2}}{4\pi^{2}}\frac{K_{1}(m_{Q}\sqrt{-(x-y)^2})}{\sqrt{-(x-y)^2}}-i
\frac{m_{Q}^{2}(\not\!x-\not\!y)}{4\pi^{2}(x-y)^2}K_{2}(m_{Q}\sqrt{-(x-y)^2})~,
\eea
and $K_n(z)$ being the modified Bessel function of the second kind.
The next step is to use the expression of the heavy propagators and perform the
derivatives with respect to x and y in Eq. (\ref{correl.func.2}). After
setting $y=0$,
the following final expression for the QCD side of the correlation function
in coordinate space is obtained:
\begin{eqnarray}\label{correl.func.3}
\Pi _{\mu\nu,\alpha\beta}=\frac{i}{64} \left(\frac{m_Q}{\pi}\right)^4
\int d^{4}xe^{iqx}\left\{\left[\Gamma_{\mu\nu,\alpha\beta}\right]+
\left[\beta\leftrightarrow\alpha\right]+\left[\nu\leftrightarrow\mu\right]+
\left[\beta\leftrightarrow\alpha,\nu\leftrightarrow\mu\right]\right\},
\end{eqnarray}
where,
\begin{eqnarray}\label{fonk}
\Gamma_{\mu\nu,\alpha\beta}&=&\Big\{-2 m_Q g_{\alpha\nu} g_{\beta\mu} {\cal
K}_1 {\cal K}_2 +
2 \Big( m_Q^2 x_\alpha x_\nu g_{\beta\mu} - g_{\alpha\nu} g_{\beta\mu} +
g_{\alpha\mu} g_{\beta\nu} + g_{\alpha\beta} g_{\mu\nu}\Big) {\cal K}_2^2
\nonumber \\
&-& 2 m_Q^2 x_\alpha x_\nu g_{\beta\mu} {\cal K}_1 {\cal K}_3 -
2 m_Q g_{\alpha\nu} \Big(2 x_\beta x_\mu - x^2 g_{\beta\mu}\Big) {\cal K}_2
{\cal K}_3 \nonumber \\
&+& 2 m_Q^2 x_\alpha x_\nu \Big(2 x_\beta x_\mu - x^2 g_{\beta\mu}\Big)
{\cal K}_3^2 -
2 m_Q^2 x_\alpha x_\nu \Big(2 x_\beta x_\mu - x^2 g_{\beta\mu}\Big)
{\cal K}_2 {\cal K}_4 \Big\}\nonumber \\
&+&\mbox{nonperturbative contributions} ~,
\end{eqnarray}
and
\begin{eqnarray}
{\cal K}_n = {K_n(m_Q\sqrt{-x^2}) \over (\sqrt{-x^2})^n}~.
\end{eqnarray}
In the present work, we calculate the contributions of the heavy quark and gluon
condensates in nonperturbative part of the correlation function in QCD side. After a simple calculation we obtain for the heavy quark condensate
(for the coefficient of the aforementioned structure)
\bea
\label{nolabel}
-{m_Q^3 \over 2(q^2-m_Q^2)} \lla \bar{Q}Q \rra~. \nnb
\eea
Using the well--known relation between the heavy quark and the gluon
condensates
\bea\label{nolabel}
m_Q \lla \bar{Q}Q \rra = - {1\over 12 \pi}
\lla {\alpha_s \over \pi} G^2 \rra~,\nnb
\eea
these two nonperturbative contributions can be written in terms of gluon
condensate contribution. Numerical analysis shows that, taking into account
quark condensates decreases gluon condensate contribution about 15\%.
Few words about the neglected dimension two operator in the operator
product expansion are in order. The term proportional to $1/q^2$
introduced in \cite{Chetyrkin0} is a phenomenological
parametrization of the higher order contributions to the perturbative
series. In other words, this term can
appear when considering any types of correlation functions where the
perturbative series are not zero. Obviously, this term vanishes when
considering the difference of the correlators induced by vector and axial
vector currents, VV-AA in the chiral limit, $m_q=0$ (for more details see \cite{Narison}). In the
present work, we neglect this term because we work to leading
order in $\alpha_s$.
Now, we apply the Fourier transformation to the QCD side of the correlation
function to get its expression in momentum space. The next step is to select
the structure which gives contribution to the tensor state
from both sides of the correlation function, equate the coefficient of the
selected structure from both sides and apply the Borel transformation to suppress
the contribution of the higher states and continuum. After lengthy calculations,
finally we obtain the following sum rules for the decay constant of the heavy
tensor quarkonia:
\begin{eqnarray}\label{sumrul}
f_{\chi_Q}^2e^{-m_{\chi_Q}^2/M^2} &=&\frac{N_c}{m_{\chi_Q}^6}\int_{4
m_Q^2}^{s_0} ds \int_1^\infty du \,
{e^{-s/M^2} [s-s(u)] \over 16 \pi^2 u^6}
\Big\{ - 2 m_Q^2 u^3 + [4 M^2 - s - s(u)] \nonumber \\
&-& 2 [4 M^2 - s - s(u)] u + [2 m_Q^2 + 4 M^2 - s - s(u)] u^2 \Big\} +
I(M^2) \lla {\alpha_s\over \pi} G^2 \rra,\nonumber \\
\end{eqnarray}
where,
\begin{eqnarray}\label{su}
s(u)=m_Q^2\left[u+\frac{1}{1-\frac{1}{u}}\right],
\end{eqnarray}
and the explicit expression of the function $I(M^2)$ is quite lengthy and
therefore we do not present it.
In the above sum rules, $M^2$ is the Borel mass parameter, $s_0$ is the
continuum threshold and $N_c=3$ is the color factor. The mass of the heavy
tensor meson is also obtained applying derivative with respect to
$-\frac{1}{M^2}$ to the both sides of the sum rules for the decay constant
and dividing by itself, i.e.,
\begin{eqnarray}\label{sumrul2}
m_{\chi_Q}^2&=&\Bigg(\int_{4
m_Q^2}^{s_0} ds \int_1^\infty du \,
{e^{-s/M^2} [s^2-s~s(u)] \over 16 \pi^2 u^6}
\Big\{ - 2 m_Q^2 u^3 + [4 M^2 - s - s(u)] \nonumber \\
&-& 2 [4 M^2 - s - s(u)] u + [2 m_Q^2 + 4 M^2 - s - s(u)] u^2 \Big\}\nonumber\\
&+&\int_{4 m_Q^2}^{s_0} ds \int_1^\infty du \,
{e^{-s/M^2} [s-s(u)] \over 16 \pi^2 u^6}
\Big\{ 4M^4(1-u)^2\Big\} - {d\over d(1/M^2)} I(M^2) \lla {\alpha_s \over
\pi} G^2 \rra
\Bigg)\nonumber\\&\times&\Bigg(\int_{4
m_Q^2}^{s_0} ds \int_1^\infty du \,
{e^{-s/M^2} [s-s(u)] \over 16 \pi^2 u^6}
\Big\{ - 2 m_Q^2 u^3 + [4 M^2 - s - s(u)] \nonumber \\
&-& 2 [4 M^2 - s - s(u)] u + [2 m_Q^2 + 4 M^2 - s - s(u)] u^2 \Big\}
+ I(M^2) \lla {\alpha_s \over\pi} G^2 \rra \Bigg)^{-1}.\nonumber \\
\end{eqnarray}
\section{Numerical analysis}
In this section, we numerically analyze the sum rules for the mass and decay
constant of the ground state tensor quarkonia. Some input parameters entering
the sum rules are quark masses, $m_b=(4.8\pm 0.1)~GeV$, $m_c=(1.46 \pm 0.05)~GeV$
\cite{colangelo} and gluon condensate, $\langle 0|\frac{1}{\pi}\alpha_{s}G^{2}|0\rangle=(0.012
\pm 0.004)~ GeV^{4}$. It should be noted that recent analysis of experimental data leads to the
$\langle 0|\frac{1}{\pi}\alpha_{s}G^{2}|0\rangle=(0.005
\pm 0.004)~ GeV^{4}$ for the gluon condensate \cite{Ioffeb}. For conservative estimation in numerical analysis, we also take into account the value
of gluon condensate $\langle 0|\frac{1}{\pi}\alpha_{s}G^{2}|0\rangle=(2.16\pm0.38)\times 10^{-2}~GeV^4$ which follows
from sum rules of $e^{+}e^{-} \rightarrow I=1~ hadrons$ \cite{12} and heavy quarkonia \cite{13,14,15}. Few words about quark mass are in order. The aforementioned masses are the pole masses for the quarks. Using the four loop results for
the vacuum polarization operator in \cite{Chetyrkin}, the running masses of the charm and
beauty quarks, $m_c(3GeV)=(0.986\pm0.013)~GeV$ and $m_b(m_b)=(4.163\pm0.016)~GeV$ are obtained. These improved values of the running masses of charm and
beauty quarks as well as wide range of gluon
condensate are used in numerical calculations. To obtain more reliable results for the mass and decay constant of the heavy tensor meson, we will also take into account
a more realistic error coming from
the range spanned by the pole and
running quark masses as well as the range for the value of the gluon condensate.
From the sum
rules for the decay constant and mass it is clear that they contain also two
auxiliary parameters, continuum threshold $s_0$
and Borel mass parameter $M^2$. The standard criteria in QCD sum rules is that
the physical quantities should be independent of these mathematical objects,
so we should look for working regions for these parameters
at which the masses and decay constants practically remain unchanged. To determine the working
region for the Borel mass parameter
the procedure is as follows: the lower limit of $M^2$ is obtained requiring
that the higher states and continuum contributions constitute, say,
30\% of the total dispersion integral. The upper limit of $M^2$ is chosen demanding
that the sum rules for the decay constants and masses should be convergent, i.e.,
contribution of the operators with higher dimensions is small. As a result, we
choose the regions: $ 8~ GeV^2 \leq
M^2_ {\chi_{b2}}\leq 20~ GeV^2 $ and $ 4~ GeV^2 \leq
M^2_ {\chi_{c2}}\leq 7~ GeV^2 $ for the Borel mass parameter. The continuum threshold $s_0$ is not completely arbitrary but it is correlated to the energy of the first exited
state with quantum numbers of the interpolating current. Our numerical results are in consistency with this point and show that in the interval $(m_{\chi_{Q2}}+0.4)^2\leq
s_0^{\chi_{Q2}}\leq (m_{\chi_{Q2}}+0.7)^2$, the results are practically insensitive to the variation of this parameter.
Here we would like to make the following
remark. It is shown in \cite{Lucha2} that the continuum
threshold $s_{0}$ can depend
on the Borel mass parameter. Therefore, the standard criteria,
namely, weak dependence of the results on variation of the auxiliary parameters
does not provide us realistic errors, and in fact the actual
error should be large. Following \cite{Lucha2}, in the present work we will
add also the systematic errors to the numerical values.
Our numerical analysis on the masses and decay constants leads to the results presented in Table 1.
\begin{table}[h] \centering
\begin{tabular}{|c||c|c|c|c|} \hline &
Present Work&Experiment \cite{Amsler}
\\\cline{1-3}\hline\hline
$m_{\chi_{b2}}$& $(9.90\pm2.48)~GeV $ &$(9.91221\pm0.00057)~GeV$\\
\cline{1-3} $m_{\chi_{c2}}$& $(3.47\pm0.95)~GeV $ &$(3.55620\pm0.00009)~GeV$\\
\cline{1-3} $f_{\chi_{b2}}$& $0.0122\pm0.0072 $ &-\\
\cline{1-3}$f_{\chi_{c2}}$& $0.0111\pm0.0062 $ &-\\
\cline{1-3}\hline\hline
\end{tabular}
\vspace{0.8cm} \caption{Values for the masses and decay constants of the tensor
mesons $\chi_{Q_2}$.} \label{tab:27}
\end{table}
The quoted errors in our predictions are due to the variations in the continuum
threshold and Borel parameter, uncertainties in quark masses and wide range of the gluon condensates presented at the beginning of this section as well as the systematic errors. The results presented in Table 1 show a good consistency between our predictions
and the experimental values \cite{Amsler} on the masses of the ground state
heavy, $\chi_{b2}$ and, $\chi_{c2}$ tensor mesons.
Our predictions on the
decay constants can be verified in the future experiments.
\section{Acknowledgment}
We thank A. Ozpineci for his useful discussions.
|
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Can you name that album? Hint: It's played on SiriusXM Lithium
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{"url":"https:\/\/socratic.org\/questions\/how-do-you-graph-two-cycles-of-y-2tan-4theta","text":"# How do you graph two cycles of y=-2tan(4theta)?\n\nJul 11, 2017\n\n$-$ sign signifies an inverse graph of tangent graph\n\n2 signifies the graph amplitude or the $y$ values are of two times larger than a normal tangent graph\n\n$4 \\theta$ signifies 4 repeats of the normal tangent graph in a $2 \\pi$ or 360degrees cycle\n\nIn your case, you need to plot 2 cycle of y.\nSince 4 cycle in 2$\\pi$\n1 complete cycle in $2 \\frac{\\pi}{4} = \\frac{\\pi}{2}$\n\ndivide $\\frac{\\pi}{2}$ into four parts for each of the four parts of graph which starts at 0.\n\n#### Explanation:\n\ngraph{y=-2tan (4x) [-10, 10, -5, 5]}","date":"2019-01-18 17:39:45","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 7, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.47126978635787964, \"perplexity\": 1690.6191672345938}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2019-04\/segments\/1547583660258.36\/warc\/CC-MAIN-20190118172438-20190118194438-00510.warc.gz\"}"}
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{"url":"https:\/\/eepower.com\/news\/increased-european-interest-reveals-continued-growth-in-u-s-wind-energy-market\/","text":"News\n\n# Increased European Interest Reveals Continued Growth in U.S. Wind Energy Market\n\nMay 03, 2007 by Jeff Shepard\n\nThe recent announcement by Acciona (which claims to be the world\u2019s largest wind power developer) that it will develop its first wind turbine production plant in the United States has brought renewed attention to the continued growth of the American wind energy market. The project, to be located in Iowa, represents an investment of nearly $23 million and will produce approximately 250 wind turbines in 2008, a figure that is expected to rise over the next few years. Acciona\u2019s plant will supply wind turbines for wind farms located throughout North America and will provide the company, when it is operating at full capacity, with worldwide production capacity of approximately 1,740 wind turbines for a total of 2,610MW per year. As the continued concern over the environment, coupled with technological advances and government initiated tax incentives, \"empowers\" more Americans to consider \"alternative\" energy options, European wind energy companies are entering the U.S. market with increased confidence. Besides the latest announcement by Acciona, EDP Energieas de Portugal SA recently announced an agreement to purchase Horizon Wind Energy LLC (based in Houston, Texas) for$2.15 billion, which would be the Portuguese utility\u2019s first entry into the U.S. market. Vestas Wind Systems of Denmark, the world\u2019s largest wind-turbine maker, announced that it would build a $60 million wind-turbine factory in Colorado, which will be the company\u2019s first manufacturing plant in the United States. In its evaluation of the domestic market, the American Wind Energy Association (AWEA) reports that wind power generating capacity increased by 27% in 2006 and is expected to increase an additional 26% in 2007, proving wind is now a mainstream option for new power generation. The U.S. wind energy industry installed 2,454MW of new generating capacity in 2006, an investment of approximately$4 billion, billing wind as one of the largest sources of new power generation in the country \u2013 second only to natural gas \u2013 for the second year in a row. New wind farms boosted cumulative U.S. installed wind energy capacity by 27% to 11,603MW, well above the 10,000MW milestone reached in August 2006. One megawatt of wind power produces enough electricity to serve 250 to 300 homes on average each day.\n\nWind energy facilities currently installed in the U.S. are expected to produce an estimated 31 billion kilowatt-hours annually or enough electricity to serve 2.9 million American homes. It is claimed that this source of electricity will displace approximately 23 million tons of carbon dioxide \u2013 the leading greenhouse gas \u2013 each year, which would otherwise be emitted by coal, natural gas, oil and other traditional energy sources.\n\nWind power has also attracted the support of state and federal government legislatures. The U.S. Congress recently extended the federal production tax credit (PTC) through December 2008 to further expand the number of wind farms throughout the U.S. Furthermore, legislation was put forward in the Senate in February that would allow purchasers of a small wind system to receive a credit on their taxes for a portion of the turbine\u2019s cost. The \"Rural Wind Energy Development Act\" (S. 673) would provide a federal tax credit of \\$1,500 per 1\/2kW of capacity to purchasers of small wind systems nationwide. This five-year credit would apply to all wind systems with capacities of under 100kW used to power individual homes, farms, or small businesses.\n\nThe bill would also allow the credit to be carried over \u2013 meaning that in the event that using the credit reduces the consumer\u2019s taxable income below the minimum threshold, the unusable excess credit would be carried over to the next tax year. This provision essentially allows a consumer with a low annual income to take full advantage of the credit. The bill would also provide for an accelerated depreciation of three years for small wind turbines.\n\nAccording to the Global Wind Energy Council (GWEC), the United States (11,603MW) ranks third in total installed capacity behind German (20,621) and Spain (11,615), and the U.S. was the global leader in new installed capacity at 2,454MW (ahead of second-place Germany\u2019s total of 2,233.","date":"2021-10-25 17:46:10","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.21930642426013947, \"perplexity\": 3332.096662654933}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2021-43\/segments\/1634323587719.64\/warc\/CC-MAIN-20211025154225-20211025184225-00579.warc.gz\"}"}
| null | null |
Massacre var et amerikansk dødsmetalband. De blev dannet i 1983 af Allen West og Bill Andrews. Kort tid efter sluttede Kam Lee sig til dem (bedst kendt for sine vokalbidrag til de tidlige Death demoer) og derefter Rick Rozz.
Medlemmer
Medlemmer inden opbrud
Kam Lee – Vokal
Steve Swanson – Guitar
Terry Butler – Bas
Sam Williams – Guitar
Curtis Beeson – Trommer
Tidligere medlemmer
Michael Borders- Bas
Bill Andrews – Trommer
Pete Sison – Bas
Syrus Peters – Trommer
Allen West – Guitar
Joe Cangelosi – Trommer
Rick Rozz – Guitar
Rob Goodwin – live guitar
Butch Gonzales – bass
Walt Thrashler – Midlertidig guitarist
Diskografi
1986: Aggressive Tyrant (Demo)
1987: Chambers of Ages (Demo)
1990: Second Coming (Demo)
1991: "Provoked Accurser" (Single)
1991: From Beyond
1992: Inhuman Condition (EP)
1994: Infestation of Death (Opsamlingsalbum)
1996: Promise
2006: ''Tyrants of Death (Livedemo fra 1986)
Fodnoter
Dødsmetalgrupper
Musikgrupper fra 1983
|
{
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| 6,435
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Tiny Algae, Surprising Findings
On board the research vessel Roger Revelle in 2012, BIOS researcher Becky Garley helped to bring onboard a CTD instrument (used to collect measurements of seawater temperature and conductivity, a measure of salinity, at various depths). Garley helped collect data in the Southern Ocean used by researcher Nick Bates back at BIOS labs for their carbon dioxide research. She arrived at BIOS as an intern in 2010 after earning undergraduate and graduate degrees from universities in Britain. Photo by Rebecca Fowler.
Chemical oceanographer Nick Bates's ongoing study of the ocean-atmosphere interface sheds light on a group of tiny, beautiful marine plants called coccolithophores, which have been found to release carbon dioxide into the atmosphere in regions near Antarctica.
A paper published in January in Earth & Space Science News reported that coccolithophores show a net release of carbon dioxide into seawater during plant growth as they produce minuscule structures of calcium carbonate. This differs from another common phytoplankton group in the Southern Ocean, called diatoms, that act as carbon dioxide sinks, or reservoirs, during photosynthesis.
Bates and fellow scientists found that this balance in the release of carbon dioxide seems to shift at high coccolithophore concentrations, when sufficient carbon dioxide gas builds up then escapes into the atmosphere.
Coccolithophore image by NOAA-Pacific Marine Environment Laboratory.
The start of the research was a 2008 project that looked at coccolithophores around the Falkland Islands in the South Atlantic. In subsequent years, their work grew to include the study of a phenomenon in the Southern Ocean known as the Great Calcite Belt, which appears in satellite images as an enormous band of milky water surrounding Antarctica. Coocolithophores, sphere-shaped algae covered in plates of the mineral calcite, bloom in this region near the sea surface in austral summertime.
"We found really interesting scientific issues with the coccolithophores in the Great Calcite Belt, including the issue of this bloom producing carbon dioxide," Bates said. He was surprised to find that, in places, this actually reversed the direction of air-sea carbon dioxide exchange, turning parts of the Southern Ocean into sources of carbon dioxide flowing into the atmosphere, rather than the large carbon dioxide sink that is usually observed across the Southern Ocean.
Bates said he hopes the findings will lead to other work in the Southern Ocean. Colleagues on the project included BIOS research specialist Becky Garley; marine chemist Phoebe Lam of Woods Hole Oceanographic Institution; and the project's principal investigator, biological oceanographer Barney Balch, and oceanographer Ben Twining, both at the Bigelow Laboratory for Ocean Sciences in Maine.
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
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| 7,881
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Coccophagus flavoscutellum is een vliesvleugelig insect uit de familie Aphelinidae. De wetenschappelijke naam is voor het eerst geldig gepubliceerd in 1881 door Ashmead.
Aphelinidae
|
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| 5,173
|
Q: Angular 1.5 component router sibling components Is there a way with the new component router for Angular 1.5 to keep the sibling component rendered in the ng-outlet directive?
I want to show the Detail View in parallel with the sibling List View.
As far as I understand the official Docs (https://docs.angularjs.org/guide/component-router) it should be possible with the $$router and bind it to the child component.
Here is what I tried to do:
http://plnkr.co/edit/KzW8fLAxrte9jSg5jhEg?p=preview
<ng-outlet><crisis-detail $router="$$router"></crisis-detail>
There i a similiar post on this binding topic:
Angular 1.5 component $router binding
A: There is no ability to show siblings simultaneously with Angular 1.5 Component Router as far as I know.
However, workaround is to make sibling to be actually child, and then use empty component to show with default, "no details" route.
Workaround:
First, we need some root component to activate list itself:
.component('listRoot', {
template: '<ng-outlet></ng-outlet>', //just ng-outlet, to render List inside
$routeConfig: [
{path: '/...', name: 'ListRoot',component: 'list' },
]
})
Then we need to add components for list, detail, and noDetail mode.
.component('list', {
template: 'List ... <ng-outlet></ng-outlet>',
$routeConfig: [
{path: '/', name: 'List',component: 'noDetails', useAsDefault: true },
{path: '/:id',name: 'Details',component: 'details'}
],
bindings: {
$router: '<'
},
controller: function () {
var ctrl = this
$routerOnActivate = function(route) {
ctrl.router = this.$router;
}
this.goToDetails = function(id) {
ctrl.$router.navigate(['Details', {id: id}])
}
}
})
.component('detail', {
template: 'Details: <a ng-link="[\'List\']">Go Back</a>'
})
.component('noDetails', {
template: '' //just empty template
})
Accessing parent:
Also, to be able to notify parent (in your example - sibling Detail component telling it ID to List, and List marking it as selected after) you can use require component option, to be able to access parent component scope.
.component('detail', {
template: 'Details: <a ng-link="[\'List\']">Go Back</a>',
require: {
parent: '^list'
},
controller: {
this.goBackWithNotify = function(data) {
ctrl.parent.someParentComponentProperty = data;
}
}
})
Edited plunker with example.
PS: I used more recent version of router.
|
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| 9,077
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La grotte de Tchertovy Vorota () est un site archéologique datant du Néolithique situé dans les monts Sikhote-Aline, à environ de la ville de Dalnegorsk dans le kraï du Primorié, en Russie. Cette grotte de roche karstique, située sur une falaise en calcaire, se trouve à environ de la rivière Krivaïa, un affluent de la Roudnaïa. On a retrouvé à Tchertovy Vorota des restes de textiles parmi les plus anciens du monde.
Description
La grotte est formée d'une chambre principale, mesurant environ de long, prolongée de plusieurs galeries plus petites. Le site a été pillé plusieurs fois avant les premières fouilles archéologiques en 1973. Environ 600 artefacts en pierre, en os ou en coquille, 700 fragments de poterie et plus de 700 os d'animaux ont été trouvés sur le site. Un disque de jade brun-vert de d'épaisseur et de diamètre y a également été trouvé.
Parmi les ossements d'animaux, on note la présence de restes de chiens viverrins, d'ours bruns et noirs d'Asie, de sangliers, de blaireaux, de cerfs élaphes, de poissons ainsi que de coquilles de mollusques.
Anciens textiles
Des fragments de textile carbonisés, provenant de cordes, filets et textiles tissés, ont été retrouvés dans la grotte sous les restes d'une structure en bois ayant pris feu et s'étant effondrée. Les fibres étaient probablement issues de l'espèce Carex sordida, de la famille des Cyperaceae. Ces fragments de textile ont été directement datés à environ 9 400 - 8 400 calBP, soit environ 7 400 - 6 400 , ce qui constitue la trace de textiles la plus ancienne dans les vestiges archéologiques d'Asie orientale. Aucune fusaïole n'ayant été identifiée dans la grotte, qu'on trouve par ailleurs rarement dans les sites archéologiques contemporains d'Asie orientale, les archéologues ont émis l'hypothèse que les individus de Tchertovy Vorota produisaient leurs textiles soit à la main, soit à l'aide d'un métier à tisser.
Restes humains
Les restes de sept individus ont été découverts dans la grotte. Parmi eux, les crânes de deux individus désignés (PD 1) et Porte du Diable 2 (PD 2) ont été datés autour de 5 726 - 5 622 .
Archéogénétique
Les restes de cinq individus ont été soumis à une analyse génétique. PD 1 et PD 5 (pour ce dernier, contrairement à ce qui avait été originellement déduit) sont des femmes. PD 1 appartient à l'haplogroupe d'ADN mitochondrial D4, alors que PD 2 appartient à l'haplogroupe M.
Une comparaison avec l'ensemble des populations humaines, anciennes et modernes, présentes dans les bases de données indique que les individus de Tchertovy Vorota sont proches génétiquement des Oultches, puis des Oroqen et des Hezhen, tous des peuples locuteurs de langues toungouses du bassin de l'Amour. La distance génétique entre les individus retrouvés à Tchertovy Vorota et l'enfant de la culture de Malta-Buret est cependant la même qu'entre ce même enfant et les populations modernes d'Asie orientale.
À l'exception de PD 1, la quantité d'ADN extraite est insuffisante pour permettre une analyse des traits phénotypiques. PD 1 ne possède pas l'allèle dérivé des gènes ou associé à une couleur de peau claire, du gène HERC2 associé aux yeux bleus, du gène LT associé à la persistance de la lactase ou du gène ALDH2 associé au syndrome du rougissement asiatique. Il possède cependant probablement les allèles dérivés de deux gènes souvent trouvés dans les populations d'Asie orientale modernes : celui du gène et du gène , ce dernier étant associé à un cérumen sec et à une réduction des odeurs corporelles. Il possède également l'allèle dérivé du gène associé à un risque augmenté d'hypertension artérielle.
Régime alimentaire
L'analyse isotopique des ossements humains retrouvés à Tchertovy Vorota suggère que les protéines de leur régime alimentaire proviennent à la fois de sources terrestres et marines. En effet, près de 25 % de leurs apports en protéines semblent provenir de sources marines, très probablement de saumon anadrome. Par ailleurs, ils chassaient probablement des mammifères terrestres et collectaient des noix.
Notes et références
Voir aussi
Bibliographie
Liens externes
Grotte en Sibérie
Site préhistorique en Sibérie
Site mésolithique en Russie
Histoire du kraï du Primorié
|
{
"redpajama_set_name": "RedPajamaWikipedia"
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| 568
|
\section{Introduction}
Deparameterization has become a popular method to circumvent the problem of
time in canonical quantum gravity. Since coordinate time is observer-dependent
and does not have a corresponding operator after quantization, one instead
selects one of the phase-space degrees of freedom as a measure of change for
other variables \cite{GenHamDyn1,BergmannTime}. Popular examples of internal
times are a free massless scalar field or a variable that quantifies dust.
These variables are turned into operators when the theory is quantized and
therefore appear in the state equations. They are of such a form that
constraint equations can be rewritten as familiar evolution equations, for
instance of Schr\"odinger or Klein--Gordon type. However, as part of the
general problem of time \cite{KucharTime,Isham:Time,AndersonTime} there is
some arbitrariness involved in the choice of a particular internal time. Just
as with coordinate time in classical general relativity or its cosmological
models, one would therefore like to show that the choice of internal time does
not affect predictions made from a quantum cosmological model. Only then can
the model and its underlying theory be considered covariant.
The question of covariance in internal-time formulations has rarely been
studied, but some results are available \cite{MultChoice,ClocksDyn}. In this
paper, we use semiclassical methods developed for effective constraints
\cite{EffCons,EffConsRel,EffTime,EffTimeLong,EffTimeCosmo} in order to study
this quation. We analyze an explicit model which permits two different choices
of internal time. At a semiclassical level, the methods of effective
constraints will be used to demonstrate covariance of moment corrections in
the two internal-time formulations. However, the introduction of a proper-time
parameter turns out to be a more complicated step than usually
appreciated. Such a parameter is important in order to relate evolution
equations to observer frames, and it is often used in quantum cosmology in
order to reformulate quantum evolution equations as effective or modified
Friedmann equations.
In usual treatments of this question, it seems to be assumed implicitly that
time reparameterization invariance is always guaranteed in homogeneous models
of quantum cosmology because they are subject to just one constraint, the
Hamiltonian constraint $C$ with spatially constant lapse function. A single
constraint always commutes with itself and therefore remains first class even
if it is modified by quantum effects or fully quantized.
The last statement is correct, but it cannot always be applied to homogeneous
quantum cosmology. In a Dirac quantization of a homogeneous cosmological model
one replaces the classical constraint equation $C=0$ by an equation
$\hat{C}\psi=0$ for physical states $\psi$. Since solving the state equation
and constructing a suitable physical Hilbert space are complicated tasks, one
often takes a shortcut and computes an ``effective'' equation which can more
easily be analyzed, and which one expects to take the form of the classical
Friedmann equation plus quantum corrections. There are different procedures
for deriving such equations, but in some way they all make use of the
expectation value $\langle\hat{C}\rangle$ of the constraint operator in a
certain class of states. (The most systematic procedure of this type is the
canonical effective one already mentioned; see for instance
\cite{BounceSqueezed} for cosmological effective equations.)
The effective constraint equation $\langle\hat{C}\rangle=0$ then resembles the
Friedmann equation, as desired. But it does not imply that the state $\psi$
used in it is a physical state satisfying $\hat{C}\psi=0$. The quantum
constraint equation amounts to more than one independent expectation-value
equation, as systematically described in the formalism of effective
constraints. For instance, if $\hat{O}$ is some operator not equal to a number
times the identity, the equation $\langle\hat{O}\hat{C}\rangle=0$ is,
generically, independent of the equation $\langle\hat{C}\rangle=0$. The
premise in the tacit assumption that time reparameterization invariance is
always respected in homogeneous quantum cosmology because there is just a
single constraint is therefore violated. Making sure that time
reparameterization invariance, or more generally covariance, is still realized
after quantization, or under which conditions it can be broken, is then an
important task of quantum cosmology.
We will perform this task in the present paper for a specific model, and
confirm that covariance cannot be taken for granted in deparameterized
constructions. We then use the framework of effective constraints in order to
compare different deparameterizations within the same setting, which is made
possible by an analysis of the underlying gauge structure of quantum
constraints. This discussion will lead us to a general definition of
proper-time evolution in effective equations such that time reparameterization
invariance is realized in moment corrections. Our new definition leads to
proper-time evolution equations with moment corrections which are obtained
from those in deparameterized evolution by a change of gauge. Compared with
traditional derivations of proper-time evolution from deparameterized
evolution, however, the covariant formulation predicts different quantum
corrections for effective equations. A proper investigation of time
reparameterization invariance is therefore crucial for a reliable
determination of fluctuation corrections in quantum cosmological models.
In addition to moment corrections, different choices of internal or proper
time may give rise to different factor ordering corrections. In contrast to
moment corrections, these terms cannot be related by gauge transformations
because effective constraints and the gauge they generate are computed for a
fixed factor ordering. Factor ordering corrections therefore break covariance
of internal-time formulations. In our specific model, all three time choices
require different factor orderings of the constraint operator for real
evolution generators. Time reparameterization invariance is therefore broken
in internal-time quantum cosmology if all relevant corrections are taken into
account, a result which makes the outcome of \cite{MultChoice} more
specific. However, the new proper-time evolution introduced here is time
reparameterization invariant when compared with other choices of internal
time. This evolution is unique in realizing the same type of covariance as in
classical cosmological models, which is broken in internal-time evolution.
\section{The model}
Our cosmological model is isotropic, spatially flat, and has a cosmological
constant $\Lambda$ as well as a free, massless scalar field
$\tilde{\phi}$. Its classical description is therefore given by the Friedmann
equation
\begin{equation} \label{Friedmann}
H^2= \frac{8\pi G}{3} \frac{\tilde{p}_{\tilde{\phi}}^2}{2a^6}+ \Lambda
\end{equation}
for the scale factor $a$ in $H=\dot{a}/a$ in terms of proper
time.
We introduce the following canonical variables. (See \cite{ROPP} for a review
of quantum cosmology and of the notation used here.) The Hubble parameter $H$
is canonically conjugate to the ``volume''
\begin{equation}
V:= \frac{a^3}{4\pi G}
\end{equation}
such that $\{H,V\}=1$. The scalar field $\tilde{\phi}$ is canonically
conjugate to the momentum $p_{\tilde{\phi}}$, such that
$\{\tilde{\phi},p_{\tilde{\phi}}\}=1$. The cosmological constant
$\Lambda$ is canonically conjugate to a variable which we call
$T$, such that $\{T,\Lambda\}=1$.
The last statement may be unexpected. The cosmological constant is usually
treated as just that, a constant that appears in Einstein's equation much like
a fundamental constant such as $G$. However, it is mathematically consistent
to treat it as the momentum of a variable $T$ which does not appear in
the action or Hamiltonian constraint of the theory. The momentum
$\Lambda$ of any such quantity is conserved in time, and therefore
appears just as a constant in the field equations. We are not modifying the
dynamics by introducing this new canonical pair $(T,\Lambda)$,
nor are we trying to derive a mechanism for dark energy. We are merely using a
mathematically equivalent formulation of the usual theory, as will be clear
from the equations derived below. The new parameter $T$ then presents
to us a new option of a global internal time, which we can compare with the
more standard global internal time $\tilde{\phi}$.
We note that we do not intend $T$ to have physical meaning or to be
measurable. This might be taken as a disadvantage of the formulation, but it
is not that much different from the free scalar field $\tilde{\phi}$ for which
no physical explanation is known. Both fields are introduced primarily for the
purpose of serving as a global internal time. The variable $T$ in fact
has an advantage compared with $\tilde{\phi}$ because the energy density
associated with it is just the cosmological constant, for which there is
observational support. The energy density of a free scalar field, by contrast,
has not been observed.
We have put tildes on the scalar symbols used so far. We now rescale these
quantities so as to remove most numerical factors from our equations, just for
the sake of convenience and in order not to distract from the important
terms. We introduce
\begin{equation}
p_{\phi}:= \frac{p_{\tilde{\phi}}}{\sqrt{12\pi G}}
\end{equation}
and its canonical momentum $\phi$. It is straightforward to confirm that the
Friedmann equation (\ref{Friedmann}) is equivalent to the constraint equation
\begin{equation} \label{C}
C=-VH^2+\frac{p_{\phi}^2}{V}+V\Lambda=0
\end{equation}
in these new variables. We have multiplied the terms in the Friedmann equation
with $V$ in order to have energies rather than energy densities.
If we use this constraint to generate evolution equations with respect to
proper time, we should remember the factor of $(4\pi G)^{-1}$ in the
definition of $V$. The usual generator of proper-time evolution equations is
\begin{equation}
\tilde{C}=\frac{3}{8\pi G} \frac{a^3}{V}C= \frac{3}{2}C\,.
\end{equation}
Our proper-time equations therefore differ by a factor of $3/2$ from the usual
ones, for instance
\begin{equation}
\frac{{\rm d}V}{{\rm d}\tau}= \{V,C\}= 2VH
\end{equation}
which implies
\begin{equation}
H=\frac{1}{2V} \frac{{\rm d}V}{{\rm d}\tau}= \frac{3}{2a}\frac{{\rm d}a}{{\rm
d}\tau}
\end{equation}
with the promised factor of $3/2$ compared with the usual $H=\dot{a}/a$. For
completeness, we note the second classical evolution equation
\begin{equation}
\frac{{\rm d}H}{{\rm d}\tau} = -H^2-\frac{p_{\phi}^2}{V^2}+\Lambda \approx
-2(H^2-\Lambda) \approx -2 \frac{p_{\phi}^2}{V^2}
\end{equation}
with the last two weak equalities indicating that the constraint (\ref{C}) has
been used.
\section{Deparameterization}
\label{s:Deparam}
We deparameterize the model in two different ways, using the global internal
times $\phi$ and $T$, respectively. We begin with the more familiar choice
$\phi$, solving $C=0$ for the momentum
\begin{equation}
p_{\phi}(V,H,\Lambda) = -V\sqrt{H^2-\Lambda}\,.
\end{equation}
\subsection{Scalar time}
In this section, we quantize the model after deparameterization, so that there
is an operator $\hat{p}_{\phi}$ acting on a (physical) Hilbert space of wave
functions that do not depend on $\phi$, for instance $\psi(V,T)$. All we
assume about this operator for our semiclassical analysis is that it is Weyl
ordered. The methods of \cite{EffAc,Karpacz} then allow us to compute an
effective Hamiltonian by formally expanding the expectation value
\begin{eqnarray}
H_{\phi}&:=&\langle p_{\phi}(\hat{V},\hat{H},\hat{\Lambda})\rangle = \langle
p_{\phi}(V+(\hat{V}-V),H+(\hat{H}-H),\Lambda+(\hat{\Lambda}-\Lambda))\rangle\\
&=& p_{\phi}(V,H,\Lambda)+\sum_{a_1,a_2,a_3=2}^{\infty} \frac{1}{a_1!a_2!a_3!}
\frac{\partial^{a_1+a_2+a_3} p_{\phi}(V,H,\Lambda)}{\partial V^{a_1}\partial
H^{a_2}\partial\Lambda^{a_3}} \Delta(V^{a_1}H^{a_2}\Lambda^{a_3})
\end{eqnarray}
in $\hat{V}-V$, $\hat{H}-H$ and $\hat{\Lambda}-\Lambda$.
Although we use the same symbols $V$, $H$ and $\Lambda$ for our basic
variables, they now refer to expectation values of the corresponding
operators. In the expanded expression, in addition to expectation values, we
have the moments
\begin{equation}
\Delta(O_1^{a_1}\cdots O_n^{a_n}) = \langle
(\hat{O}_1-O_1)^{a_1}\cdots
(\hat{O}_n-O_n)^{a_n}\rangle_{\rm symm}
\end{equation}
(with totally symmetric or Weyl ordering) as independent variables. For
instance, $\Delta(H^2)=(\Delta H)^2$ is the square of the $H$-fluctuation. If
the cosmological constant is just a constant, the quantum state is an
eigenstate of $\Lambda$, such that all moments including $\Lambda$
vanish. However, we keep these moments in our equations for full
generality. We will work exclusively with semiclassical approximations of the
order $\hbar$, which includes corrections linear in second-order moments or
terms with an explicit linear dependence on $\hbar$. We will ignore all
higher-order moments as well as products of second-order moments. The
elimination of higher-order terms will not always be indicated explicitly but
holds throughout the paper. In our specific example, we have
\begin{eqnarray} \label{Hphi}
H_{\phi} &=& -V\sqrt{H^2-\Lambda}- \frac{H}{\sqrt{H^2-\Lambda}} \Delta(VH)+
\frac{1}{2} \frac{V\Lambda}{(H^2-\Lambda)^{3/2}} \Delta(H^2)\\
&&+
\frac{1}{2\sqrt{H^2-\Lambda}} \Delta(V\Lambda)- \frac{1}{2}
\frac{VH}{(H^2-\Lambda)^{3/2}} \Delta(H\Lambda)+ \frac{1}{8}
\frac{V}{(H^2-\Lambda)^{3/2}} \Delta(\Lambda^2)\,. \nonumber
\end{eqnarray}
The commutator of operators induces a Poisson bracket on expectation values
and moments, seen as functions on the space of states. They can be derived
from the definition
\begin{equation} \label{AB}
\{A,B\} = \frac{\langle[\hat{A},\hat{B}]\rangle}{i\hbar}
\end{equation}
and the Leibniz rule. In particular, the classical bracket $\{H,V\}=1$ still
holds true for the expectation values, and expectation values have zero
Poisson brackets with the moments. For Poisson brackets of two moments there
are general equations \cite{EffAc,HigherMoments}, but for small orders it is
usually more convenient to compute brackets directly from (\ref{AB}). For
instance,
\begin{eqnarray}
\{\Delta(H^2),\Delta(V^2)\} &=& 4\Delta(VH)\,,\\
\{\Delta(H^2),\Delta(VH)\}&=& 2\Delta(H^2)\,,\\
\{\Delta(V^2),\Delta(VH)\}&=&-2\Delta(V^2)\,.
\end{eqnarray}
These Poisson brackets give rise to the equations of motion
\begin{eqnarray}
\frac{{\rm d}V}{{\rm d}\phi} &=& \{V,H_{\phi}\} =
\frac{VH}{\sqrt{H^2-\Lambda}}- \frac{\Lambda}{(H^2-\Lambda)^{3/2}} \Delta(VH)
+\frac{3}{2} \frac{VH\Lambda}{(H^2-\Lambda)^{3/2}} \Delta(H^2)\\
&&+
\frac{H}{2(H^2-\Lambda)^{3/2}} \Delta(V\Lambda)- \frac{1}{2}
\frac{V(2H^2+\Lambda)}{(H^2-\Lambda)^{5/2}} \Delta(H\Lambda)+ \frac{3}{8}
\frac{VH}{(H^2-\Lambda)^{5/2}} \Delta(\Lambda^2) \nonumber
\end{eqnarray}
and
\begin{equation}
\frac{{\rm d}H}{{\rm d}\phi} = -\sqrt{H^2-\Lambda} + \frac{1}{2}
\frac{\Lambda}{(H^2-\Lambda)^{3/2}} \Delta(H^2) -\frac{1}{2}
\frac{H}{(H^2-\Lambda)^{3/2}} \Delta(H\Lambda)+ \frac{1}{8}
\frac{1}{(H^2-\Lambda)^{3/2}} \Delta(\Lambda^2)\,,
\end{equation}
accompanied by equations of motion for the moments such as
\begin{equation}
\frac{{\rm d}\Delta(V^2)}{{\rm d}\phi} = 2\frac{H}{\sqrt{H^2-\Lambda}}
\Delta(V^2)- 2\frac{V\Lambda}{(H^2-\Lambda)^{3/2}}\Delta(VH) +
\frac{VH}{(H^2-\Lambda)^{3/2}} \Delta(V\Lambda)\,.
\end{equation}
Expectation values and moments are therefore dynamically coupled.
These equations can be compared with the classical Friedmann equation if we
transform them to proper time. The usual way to do so is by using the chain
rule after computing ${\rm d}\phi/{\rm d}\tau=\{\phi,C\}$. However, within the
deparameterized setting, we do not have a quantum-corrected expression for $C$
since we quantized $p_{\phi}$ after solving $C=0$. The introduction of proper
time in a deparameterized setting is therefore ambiguous. We will present two
different alternatives in this section, none of which will turn out to be
consistent by our general analysis in the next section.
The term in the constraint relevant for $\{\phi,C\}$ is $p_{\phi}^2/V$, while
the other two terms have zero Poisson brackets with $\phi$. We tentatively
introduce quantum corrections of this term by using the same methods that gave
us the quantum corrected $p_{\phi}(V,H,\Lambda)$. The new term is then
\begin{equation}
C_{\phi}:= \frac{p_{\phi}^2}{V} - 2\frac{p_{\phi}}{V^2}
\Delta(Vp_{\phi})+ \frac{p_{\phi}^2}{V^3} \Delta(V^2) +
\frac{1}{V}\Delta(p_{\phi}^2) \,,
\end{equation}
leading to
\begin{eqnarray}
\frac{{\rm d}\phi}{{\rm d}\tau} &=& \{\phi,-C_{\phi}\} = -2\frac{p_{\phi}}{V} +
\frac{2}{V^2} \Delta(Vp_{\phi})-\frac{2p_{\phi}}{V^3} \Delta(V^2)\\
&=& 2\sqrt{H^2-\Lambda}+ 2\frac{\sqrt{H^2-\Lambda}}{V^2}\Delta(V^2)+
\frac{2H}{V\sqrt{H^2-\Lambda}}\Delta(VH)-
\frac{\Lambda}{(H^2-\Lambda)^{3/2}} \Delta(H^2)\\
&& - \frac{1}{V\sqrt{H^2-\Lambda}} \Delta(V\Lambda)+
\frac{H}{(H^2-\Lambda)^{3/2}} \Delta(H\Lambda)-
\frac{1}{4}\frac{1}{(H^2-\Lambda)^{3/2}} \Delta(\Lambda^2) + \frac{2}{V^2}
\Delta(Vp_{\phi}) \,. \nonumber
\end{eqnarray}
(We use $-C_{\phi}$ in order to align forward motion of $\phi$ with forward
motion of $\tau$.) The chain rule then gives the proper-time equations
\begin{eqnarray}
\frac{{\rm d}V}{{\rm d}\tau} &=& \frac{{\rm d}V}{{\rm d}\phi} \frac{{\rm
d}\phi}{{\rm d}\tau} = 2VH+ 2 \Delta(VH)+
2\frac{VH\Lambda}{(H^2-\Lambda)^2} \Delta(H^2) \\
&& - 2\frac{Hp_{\phi}}{V^2\sqrt{H^2-\Lambda}} \Delta(V^2) +
2\frac{H}{V\sqrt{H^2-\Lambda}} \Delta(Vp_{\phi}) \\
&& -\frac{V(H^2+\Lambda)}{(H^2-\Lambda)^2} \Delta(H\Lambda)+ \frac{1}{2}
\frac{VH}{(H^2-\Lambda)^2} \Delta(\Lambda^2)
\end{eqnarray}
and
\begin{eqnarray}
\frac{{\rm d}H}{{\rm d}\tau} &=& -2(H^2-\Lambda) - 2\frac{H}{V} \Delta(VH)+
\frac{2\Lambda}{H^2-\Lambda} \Delta(H^2)\\
&& + 2 \frac{p_{\phi}\sqrt{H^2-\Lambda}}{V^3} \Delta(V^2)-
2\frac{\sqrt{H^2-\Lambda}}{V^2} \Delta(Vp_{\phi})\\
&& + \frac{1}{V}\Delta(V\Lambda)- 2\frac{H}{H^2-\Lambda} \Delta(H\Lambda)+
\frac{1}{2} \frac{1}{H^2-\Lambda} \Delta(\Lambda^2)\,.
\end{eqnarray}
Alternatively, we could square the deparameterized quantum Hamiltonian
(\ref{Hphi}) and rearrange terms so as to make the expression look like the
classical constraint plus moment terms. We obtain
\begin{eqnarray} \label{HphiSquared}
0 &=& \frac{H_{\phi}^2}{V}-V^2(H^2-\Lambda)-2H \Delta(VH)+
\frac{V\Lambda}{H^2-\Lambda} \Delta(H^2)\\
&&+ \Delta(V\Lambda)-
\frac{VH}{H^2-\Lambda} \Delta(H\Lambda)+ \frac{1}{4}
\frac{V}{H^2-\Lambda} \Delta(\Lambda^2)\,. \nonumber
\end{eqnarray}
It is then possible to treat $H_{\phi}=\langle\hat{p}_{\phi}\rangle$ as the
momentum of $\phi$ because, kinematically, $\{\phi,H_{\phi}\}= -i\hbar^{-1}
\langle[\hat{\phi},\hat{p}_{\phi}]\rangle=1$ in the effective framework. This
gives
\begin{eqnarray}
\frac{{\rm d}\phi}{{\rm d}\tau} &=& -2\frac{H_{\phi}}{V} =
2\sqrt{H^2-\Lambda}+ \frac{2H}{V\sqrt{H^2-\Lambda}}\Delta(VH)-
\frac{\Lambda}{(H^2-\Lambda)^{3/2}} \Delta(H^2)\\
&& - \frac{1}{V\sqrt{H^2-\Lambda}} \Delta(V\Lambda)+
\frac{H}{(H^2-\Lambda)^{3/2}} \Delta(H\Lambda)-
\frac{1}{4}\frac{1}{(H^2-\Lambda)^{3/2}} \Delta(\Lambda^2)
\end{eqnarray}
and
\begin{eqnarray}
\frac{{\rm d}V}{{\rm d}\tau} &=& 2VH+ 2 \Delta(VH)+
2\frac{VH\Lambda}{(H^2-\Lambda)^2} \Delta(H^2) \\
&& -\frac{V(H^2+\Lambda)}{(H^2-\Lambda)^2} \Delta(H\Lambda)+ \frac{1}{2}
\frac{VH}{(H^2-\Lambda)^2} \Delta(\Lambda^2)\,,\\
\frac{{\rm d}H}{{\rm d}\tau} &=& -2(H^2-\Lambda) - 2\frac{H}{V} \Delta(VH)+
\frac{2\Lambda}{H^2-\Lambda} \Delta(H^2)\\
&& + \frac{1}{V}\Delta(V\Lambda)- 2\frac{H}{H^2-\Lambda} \Delta(H\Lambda)+
\frac{1}{2} \frac{1}{H^2-\Lambda} \Delta(\Lambda^2)\,.
\end{eqnarray}
These equations are different than what we obtained with the first choice of
$C$.
\subsection{Cosmological time}
For internal time $T$, we solve the constraint $C=0$ for the momentum
\begin{equation}
\Lambda(V,H,p_{\phi}) = H^2-\frac{p_{\phi}^2}{V^2}\,.
\end{equation}
Its semiclassical quantization gives the Hamiltonian
\begin{equation} \label{HT}
H_T = H^2-\frac{p_{\phi}^2}{V^2}+ \Delta(H^2)- \frac{3p_{\phi}^2}{V^4}
\Delta(V^2)- \frac{1}{V^2} \Delta(p_{\phi}^2)+ 4\frac{p_{\phi}}{V^3}
\Delta(Vp_{\phi})\,,
\end{equation}
generating equations of motion
\begin{equation}
\frac{{\rm d}V}{{\rm d}T} = -2H
\end{equation}
and
\begin{equation}
\frac{{\rm d}H}{{\rm d}T} = 2\frac{p_{\phi}^2}{V^3}+ 12\frac{p_{\phi}^2}{V^5}
\Delta(V^2)+ \frac{2}{V^3}\Delta(p_{\phi}^2)- 12\frac{p_{\phi}}{V^4}
\Delta(Vp_{\phi})\,.
\end{equation}
We attempt to transform to proper time using
\begin{equation}
\frac{{\rm d}T}{{\rm d}\tau} = \{T,-C\}=-V\,.
\end{equation}
No quantum corrections appear in this equation because the constraint is
linear in $\Lambda$. We obtain
\begin{equation}
\frac{{\rm d}V}{{\rm d}\tau} = 2VH
\end{equation}
and
\begin{eqnarray}
\frac{{\rm d}H}{{\rm d}\tau} &=& -2\frac{p_{\phi}^2}{V^2}-
12\frac{p_{\phi}^2}{V^4} \Delta(V^2)- \frac{2}{V^2}\Delta(p_{\phi}^2)+
12\frac{p_{\phi}}{V^3} \Delta(Vp_{\phi})\\
&\approx& -2(H^2-\Lambda)- 2\Delta(H^2)- 6\frac{H^2-\Lambda}{V^2}\Delta(V^2)+
4\frac{p_{\phi}}{V^3} \Delta(Vp_{\phi})\,.
\end{eqnarray}
In the last step, we have used the constraint $H_T-\Lambda=0$ in order to
bring the equation closer to the form seen with $\phi$ as internal
time. Nevertheless, there is no obvious relationship between the two
deparameterizations (in either one of the two versions presented for the
scalar time), and covariance remains unclear.
\subsection{A new scalar time}
A formal difference between the scalar and cosmological choices of internal
times is the linear appearance of the time momentum in the former case,
compared with the quadratic appearence in the latter. In order to show that
this is not the reason for the disagreement of proper-time evolutions, we
modify the treatment of scalar time by applying a canonical transformation:
We replace $\phi$ and $p_{\phi}$ by $q:=\frac{1}{2}\phi/p_{\phi}$ and
$p:=p_{\phi}^2$. The constraint
\begin{equation}
C=-VH^2+\frac{p}{V}+V\lambda=0
\end{equation}
is then linear in $p$ which we now use as the momentum of internal time $q$.
Proceeding as before, we have the quantum Hamiltonian
\begin{equation}
H_q=V^2(H^2-\Lambda)+ (H^2-\Lambda)\Delta(V^2)+ 4VH\Delta(VH)+
V^2\Delta(H^2)- 2V\Delta(V\Lambda)
\end{equation}
and the internal-time evolution equations
\begin{eqnarray}
\frac{{\rm d}V}{{\rm d}q}&=& -2V^2H-2H\Delta(V^2)-4V\Delta(VH)\,,\\
\frac{{\rm d}H}{{\rm d}q}&=&
2V(H^2-\Lambda)+4H\Delta(VH)+2V\Delta(H^2)-2\Delta(V\Lambda)\,.
\end{eqnarray}
Internal time $q$ is tentatively related to proper time $\tau$ by
\begin{equation}
\frac{{\rm d}q}{{\rm d}\tau} = -\frac{1}{V}\,,
\end{equation}
and we obtain proper-time equations
\begin{eqnarray}
\frac{{\rm d}V}{{\rm d}\tau} &=& 2VH+2\frac{H}{V}\Delta(V^2)+4\Delta(VH)\,,\\
\frac{{\rm d}H}{{\rm d}\tau} &=& -2(H^2-\Lambda)-4\frac{H}{V}
\Delta(VH)-2\Delta(H^2)+ \frac{2}{V}\Delta(V\Lambda)
\end{eqnarray}
which agree with none of the previous versions.
\section{Gauge structure}
\label{s:Gauge}
Covariance is a property of the gauge nature of a theory. For systems with a
single Hamiltonian constraint $C$, as in our classical model,
reparameterization invariance is guaranteed by the fact that we always have
$\{C,C\}=0$ and the constraint is first class. It generates a gauge
transformation which corresponds to reparameterization invariance of the time
variable, be it proper time as the gauge parameter in ${\rm d}/{\rm
d}\tau=\{\cdot,C\}$ or internal time. Even if the classical constraint is
modified by putative quantum corrections, as a single constraint it always
commutes with itself and reparameterization invariance should be
respected. Our examples contradict this expectation.
The discrepancy is resolved if we remember that quantization introduces new
degrees of freedom, parameterized in the effective formulation by
fluctuations, covariances and higher moments of a state. If fluctuations are
included as in our examples, the system is therefore equipped with a
different, enlarged phase space.
For the same reduction of degrees of freedom to result in this enlarged
setting as in the classical theory, there must also be additional
constraints. If a canonical pair such as $(\phi,p_{\phi})$ is eliminated by
solving the classical constraint and factoring out its gauge flow, not only
the expectation values of $\phi$ and $p_{\phi}$ must be eliminated by
quantized constraints but also the moments involving $\phi$ or $p_{\phi}$. On
the quantum phase space, these latter variables are independent of the
expectation values, and therefore require new constraints in order to be
eliminated.
\subsection{Effective constraints}
Using the canonical effective description, additional constraints appear
automatically for any first-class classical constraint $C$. If $\hat{C}$ is an
operator with classical limit $C$, about which we again assume only that it is
Weyl ordered, not only the expectation value
\begin{equation}
C_1:=\langle\hat{C}\rangle=0
\end{equation}
is a constraint, but also all expressions of the form
\begin{equation}
C_f:=\langle(\hat{f}-f)\hat{C}\rangle=0
\end{equation}
where $f$ is an arbitrary classical phase-space function and $\hat{f}$ its
(Weyl-ordered) quantization. For $f\not=1$, the equation $C_f=0$ is
independent of $C_1=0$ on the quantum phase space. There are therefore
infinitely many new constraints $C_f$, which can conveniently be organized by
using for $f$ polynomials in some set of basic phase-space variables.
Just as expectation values of Hamiltonians used in the deparameterized
models, the effective constraints can be expanded in moments. We have
\begin{eqnarray}
C_1(O_1, \ldots, O_n,\Delta(\cdot)) &=&
C(O_1, \ldots, O_n)\\
&&+
\sum_{a_1,\ldots,a_n} \frac{1}{a_1!\cdots a_n!}
\frac{\partial^{a_1+\cdots+a_n} C(O_1, \ldots, O_n)}{\partial
O_1^{a_1}\cdots \partial O_n^{a_n}}
\Delta(O^{a_1}\cdots O^{a_n}) \nonumber
\end{eqnarray}
where the basic variables are called $O_1,\ldots,O_n$, $\Delta(\cdot)$ denotes
their moments, and $C$ is the classical constraint.
Similarly, any $C_f$ can be expanded in this way, but it usually requires
reordering terms because $\hat{f}\hat{C}$ is not necessarily Weyl ordered for
Weyl ordered $\hat{f}$ and $\hat{C}$. We will see this more explicitly in our
examples.
\subsection{Cosmological model}
We now compute effective constraints up to second-order moments for our
constraint (\ref{C}). This order requires us to accompany
$C_1=\langle\hat{C}\rangle$ by all constraints $C_f$ with $f$ linear in basic
variables. We obtain seven constraints
\begin{eqnarray}
C_1 &=& -VH^2+\frac{p_{\phi}^2}{V}+V\Lambda
+\frac{p_{\phi}^2}{V^3}\Delta(V^2)- 2H\Delta(VH)- V\Delta(H^2)\\
&&+
\frac{1}{V}\Delta(p_{\phi}^2)- 2\frac{p_{\phi}}{V^2} \Delta(Vp_{\phi})+
\Delta(V\Lambda)\,,\nonumber\\
C_V &=& -\left(H^2+\frac{p_{\phi}^2}{V^2}-\Lambda\right) \Delta(V^2)- 2VH
\left(\Delta(VH)-\frac{1}{2}i\hbar\right)\\
&&+
2\frac{p_{\phi}}{V}\Delta(Vp_{\phi}) +V\Delta(V\Lambda)\,,\nonumber\\
C_H &=& -2VH\Delta(H^2)- \left(H^2+\frac{p_{\phi}^2}{V^2}-\Lambda\right)
\left(\Delta(VH)+\frac{1}{2}i\hbar\right)\\
&& +2\frac{p_{\phi}}{V}
\Delta(Hp_{\phi})+ V\Delta(H\Lambda)\,,\nonumber\\
C_{\phi} &=& -\left(H^2+\frac{p_{\phi}^2}{V^2}-\Lambda\right) \Delta(V\phi)-
2VH\Delta(H\phi)\\
&&+ 2\frac{p_{\phi}}{V}\left(\Delta(\phi
p_{\phi})+\frac{1}{2}i\hbar\right) +V\Delta(\phi\Lambda)\,,\nonumber\\
C_{p_{\phi}} &=&
-\left(H^2+\frac{p_{\phi}^2}{V^2}-\Lambda\right)\Delta(Vp_{\phi})
-2VH\Delta(Hp_{\phi})+
2\frac{p_{\phi}}{V}\Delta(p_{\phi})^2+V\Delta(p_{\phi}\Lambda)\,,\\
C_T &=& -\left(H^2+\frac{p_{\phi}^2}{V^2}-\Lambda\right)
\Delta(VT)-2VH\Delta(HT) +2\frac{p_{\phi}}{V}\Delta(p_{\phi}T)\\
&&+
V\left(\Delta(\Lambda T)+\frac{1}{2}i\hbar\right)\,,\nonumber\\
C_{\Lambda} &=& -\left(H^2+\frac{p_{\phi}^2}{V^2}-\Lambda\right)
\Delta(V\Lambda)- 2VH\Delta(H\lambda)+ 2\frac{p_{\phi}}{V}
\Delta(p_{\phi}\Lambda)+ V\Delta(\Lambda^2)\,.
\end{eqnarray}
The terms of $\frac{1}{2}i\hbar$ are from reordering to Weyl ordered
moments. Some of the effective constraints are therefore complex, and so will
be some of the moments after solving the constraints. This property is not
problematic because we have not eliminated any variables yet and are therefore
still in the kinematical setting. As shown in \cite{EffCons,EffConsRel}, after
solving the constraints and factoring out their gauge flows one can impose
reality conditions on the resulting physical moments. Real-valued observables
are then obtained, corresponding to expressions taken in the physical Hilbert
space.
Also in \cite{EffCons,EffConsRel}, it has been shown that the effective
constraints form a first-class system. Therefore, they generate gauge
transformations. However, the phase space of expectation values and moments up
to a certain order is not always symplectic, and the number of constraints is
not always equal to the number of independent gauge transformations. (See
\cite{brackets} for a discussion of first-class constraints in non-symplectic
systems.) In particular, a smaller number of gauge-fixing conditions may
be required if one would like to fix the gauge of a given set of constraints
on a Poisson manifold.
\subsection{Effective deparameterization}
Deparameterization with respect to a given internal time such as $\phi$
amounts to a specific choice of gauge fixing. After deparameterization,
$\phi$, just as the usual $t$ in non-relativistic quantum mechanics, is no
longer represented by an operator but only appears as a parameter in the
theory. It is not subject to quantum fluctuations and does not have quantum
correlations with other variables. These properties are reflected in the
gauge-fixing conditions
\begin{equation} \label{phiGauge}
\Delta(\phi^2)=\Delta(V\phi)=\Delta(H\phi)= \Delta(\phi
T)=\Delta(\phi\Lambda)=0
\end{equation}
which, as shown in \cite{EffTime,EffTimeLong}, suffice to fix the
effective constraints $C_f$ with linear $f$.
The remaining covariance of $\phi$ with $p_{\phi}$ is not zero but takes the
complex value
\begin{equation} \label{Deltaphip}
\Delta(\phi p_{\phi})=-\frac{1}{2}i\hbar
\end{equation}
as a consequence of $C_{\phi}=0$ together with the gauge-fixing
conditions. This complex value plays only a formal role, but it is useful
because it means that the uncertainty relation
\begin{equation}
\Delta(\phi^2)\Delta(p_{\phi})^2-\Delta(\phi p_{\phi})^2\geq
\frac{\hbar^2}{4}
\end{equation}
is still respected even with $\Delta(\phi^2)=0$.
\subsubsection{Scalar time}
We proceed to solving the remaining effective constraints. From $C_V=0$, we
obtain
\begin{equation} \label{DeltaVp}
\Delta(Vp_{\phi}) = \frac{1}{2} \frac{V}{p_{\phi}}
\left(\left(H^2+\frac{p_{\phi}^2}{V^2}-\Lambda\right) \Delta(V^2)+ 2VH
\left(\Delta(VH)-\frac{1}{2}i\hbar\right)- V\Delta(V\Lambda)\right)\,;
\end{equation}
from $C_H=0$,
\begin{equation} \label{DeltaHp}
\Delta(Hp_{\phi}) = \frac{1}{2}\frac{p_{\phi}}{V} \left(2VH\Delta(H^2)+
\left(H^2+\frac{p_{\phi}^2}{V^2}-\Lambda\right)
\left(\Delta(VH)+\frac{1}{2}i\hbar\right)- V\Delta(H\Lambda)\right)\,;
\end{equation}
from $C_{\Lambda}=0$,
\begin{equation}
\Delta(p_{\phi}\Lambda) = \frac{1}{2}\frac{p_{\phi}}{V}
\left(\left(H^2+\frac{p_{\phi}^2}{V^2}-\Lambda\right)\Delta(V\Lambda)+
2VH\Delta(H\Lambda)- V\Delta(\Lambda^2)\right)\,;
\end{equation}
and from $C_{p_{\phi}}=0$,
\begin{eqnarray}
\Delta(p_{\phi}^2) &=& \frac{1}{2} \frac{p_{\phi}}{V}
\left(\left(H^2+\frac{p_{\phi}^2}{V^2}-\Lambda\right)
\Delta(Vp_{\phi})+2VH\Delta(Hp_{\phi}) - V\Delta(p_{\phi}\Lambda)\right)\\
&=& \frac{1}{4} \frac{V^2}{p_{\phi}^2}
\left(H^2+\frac{p_{\phi}^2}{V^2}-\Lambda\right) \Delta(V^2)+
\frac{V^4H^2}{p_{\phi}^2} \Delta(H^2)+ \frac{V^3H}{p_{\phi}^2}
\left(H^2+\frac{p_{\phi}^2}{V^2}-\Lambda\right)\Delta(VH)\nonumber\\
&&-
\frac{V^3}{p_{\phi}^2} \left(H^2+\frac{p_{\phi}^2}{V^2}-\Lambda\right)
\Delta(V\Lambda)- \frac{V^4H}{p_{\phi}^2} \Delta(H\Lambda)+ \frac{1}{4}
\frac{V^4}{p_{\phi}^2} \Delta(\Lambda^2)\,.
\end{eqnarray}
Notice again that the moments $\Delta(Vp_{\phi})$ and $\Delta(Hp_{\phi})$ are
complex. The reason is that we are in the process of deparameterizing by
$\phi$, which eliminates all moments related to the canonical pair
$(\phi,p_{\phi})$, including their covariances with other variables. In the
complex moments, $p_{\phi}$ is therefore not an independent variable
anymore. It is a function of $V$, $H$, $\Lambda$ and the moments owing to the
constraint $C_1=0$. While $\hat{V}\hat{p}_{\phi}$ is a Hermitian operator
when $V$ and $p_{\phi}$ are independent, it is no longer Hermitian in this
ordering if $p_{\phi}$ is a function of $H$ after solving $C_1=0$. The complex
contributions to $\Delta(Vp_{\phi})$ and $\Delta(Hp_{\phi})$ implicitly
describe the ordering obtained after solving the constraints. Note that
$\Delta(p_{\phi}\Lambda)$ remains real, which is consistent with the fact that
$p_{\phi}$ does not depend on $T$ after $C_1=0$ is solved. (See also
\cite{FluctEn} for a related discussion of complex moments.)
All $p_{\phi}$-moments can now be eliminated from the remaining constraint
$C_1=0$, as appropriate for a system deparameterized with respect to
$\phi$. The resulting expression can be compared with the evolution generator
on the physical Hilbert space, where no operators for $\phi$ and $p_{\phi}$
exist. However, there is one last step before such a comparison can be
done. We have introduced gauge-fixing conditions, and must therefore make sure
that the evolution generator preserves these conditions. Usually, such a
generator is not the remaining (unfixed) constraint $C_1$ but a linear
combination of all the constraints of the system. (The gauge fixing requires
us to use a specific lapse function $N$ on the quantum phase space.)
Using the methods of \cite{EffTimeLong,AlgebraicTime}, one can check that, in
the present example, the unique generator respecting the gauge-fixing
conditions is of the form
\begin{eqnarray} \label{NC}
NC &=& \frac{1}{2p_{\phi}} \left((VC)_1- \frac{1}{2p_{\phi}} (VC)_{p_{\phi}}-
\frac{1}{2p_{\phi}} \frac{\partial p_{\phi}}{\partial V} (VC)_V -
\frac{1}{2p_{\phi}} \frac{\partial p_{\phi}}{\partial H} (VC)_H\right.\\
&&\left.-
\frac{1}{2p_{\phi}} \frac{\partial p_{\phi}}{\partial \Lambda}
(VC)_{\Lambda} -
\frac{1}{2p_{\phi}} \frac{\partial p_{\phi}}{\partial T} (VC)_T\right)
\nonumber
\end{eqnarray}
where $(VC)_f$ are defined just like the previous effective constraints but
with $\hat{V}\hat{C}$ inserted instead of $\hat{C}$. The factor of $\hat{V}$
removes the $1/V$ in the quadratic kinetic term $p_{\phi}^2/V$ in
$C$. We emphasize that we are still dealing with the original system of
effective constraints because any $(VC)_f$ can be written as a linear
combination of the $C_f$ to the same order. For instance,
\begin{equation}
(VC)_1 = \langle(V+(\hat{V}-V))\hat{C}\rangle = VC_1+C_V
\end{equation}
and
\begin{equation}
(VC)_V = \langle(\hat{V}-V)(V+(\hat{V}-V))\hat{C}\rangle = VC_V+\Delta(V^2)
C_1\,.
\end{equation}
For our present purposes, it suffices to justify the combination (\ref{NC}) of
constraints by confirming that the resulting generator
\begin{eqnarray}
NC&=&\frac{p_{\phi}-V\sqrt{H^2-\Lambda}}{2p_{\phi}}
\left(p_{\phi}+V\sqrt{H^2-\Lambda}\right) + \frac{H}{\sqrt{H^2-\Lambda}}
\Delta(VH)-
\frac{1}{2} \frac{V\Lambda}{(H^2-\Lambda)^{3/2}} \Delta(H^2) \nonumber\\
&&-
\frac{1}{2\sqrt{H^2-\Lambda}} \Delta(V\Lambda)+ \frac{1}{2}
\frac{VH}{(H^2-\Lambda)^{3/2}} \Delta(H\Lambda)- \frac{1}{8}
\frac{V}{(H^2-\Lambda)^{3/2}} \Delta(\Lambda^2)
\end{eqnarray}
indeed preserves the gauge-fixing conditions: all $p_{\phi}$-moments have
cancelled out. Moreover, solving $NC=0$ for $p_{\phi}$ gives an expression
identical with the deparameterized $\phi$-Hamiltonian (\ref{Hphi}). We
therefore confirm that deparemeterization can be performed before or after
quantization, with equivalent results.
\subsubsection{Cosmological time}
Deparameterization of the effective constraints with respect to $T$ is done by
using the gauge-fixing conditions
\begin{equation} \label{TGauge}
\Delta(T^2)=\Delta(VT)=\Delta(HT)=\Delta(\phi T)=\Delta(p_{\phi}T)=0
\end{equation}
which implies $\Delta(T\Lambda)=-\frac{1}{2}i\hbar$ using $C_T=0$. As before,
we can solve all constraints for the $\Lambda$-moments, but we do not need the
explicit expressions because the relevant generator,
\begin{equation}
\left(V^{-1}C'\right)_1 = -H^2+\frac{p_{\phi}^2}{V^2}+\Lambda-
\Delta(H^2)+3\frac{p_{\phi}^2}{V^4} \Delta(V^2)- 4\frac{p_{\phi}}{V^3}
\Delta(Vp_{\phi})+ \frac{1}{V^2} \Delta(p_{\phi}^2)
\end{equation}
contains no such moments. Solving $(V^{-1}C')_1=0$ for $\Lambda=H_T$ gives an
expression for the $T$-Hamiltonian identical with (\ref{HT}).
Similarly to the scalar case, the momentum $\Lambda$
appears with a factor of $V$, which leads to the modified effective constraint
$(V^{-1}C')_1$. We have indicated by the prime on $C'$ a change of factor
ordering with respect to the original Weyl-ordered constraint operator
$\hat{C}$. In order for $(V^{-1}C')_1$ to be real, we need a symmetric ordering
of the contribution $\hat{V}^{-1} (\hat{V}\hat{H}^2)'$ with some ordering of
$\hat{V}\hat{H}^2$ again indicated by the prime. The product with
$\hat{V}^{-1}$ is not symmetric if Weyl-ordering is used for
$(\hat{V}\hat{H}^2)'$, but it is symmetric if we instead use
\begin{equation} \label{VH2}
\hat{V}\hat{H}^2 =
\frac{1}{3}(\hat{V}\hat{H}^2+\hat{H}\hat{V}\hat{H}+\hat{H}^2\hat{V})-i\hbar
\hat{H}= (\hat{V}\hat{H}^2)_{\rm Weyl}-i\hbar\hat{H}\,.
\end{equation}
Indeed, with the subtraction of $i\hbar \hat{H}$ in the reordered constraint
$\hat{C}'=\hat{C}-i\hbar\hat{H}$, we have
\begin{equation}
\left(V^{-1}C'\right)_1 =
\langle(V^{-1}-V^{-2}(\hat{V}-V))(\hat{C}-i\hbar\hat{H})\rangle=
\frac{C_1}{V}-\frac{C_V-i\hbar VH}{V^2}
\end{equation}
as a real expression of the effective constraints, where $C_V$ has imaginary
part $\hbar VH$.
Unlike the generator of deparameterized evolution in the scalar model, the
generator for cosmological time is {\em not} a linear combination of the
original effective constraints because $i\hbar H/V$ is not of such a form. The
two deparameterized models are therefore realized within the same effective
constrained system only if we ignore reordering contributions with an explicit
dependence on $\hbar$. The moment corrections in the two models are related
by a gauge transformation and therefore provide the same effects in
observables. However, $\hbar$-dependent terms are not related by gauge
transformations and lead to different effects in observables. For
semiclassical states, for which our analysis is valid, second-order moments
are generically of the order $\hbar$, and it is not possible to ignore factor
ordering corrections compared with moment corrections. The two different
internal times therefore lead to different predictions, and time
reparameterization invariance is broken.
\subsection{Proper time}
Using effective constraints, we have rederived the deparameterized
Hamiltonians (\ref{Hphi}) and (\ref{HT}) for our model with two different
choices of internal time. The agreement with derivations in deparameterized
models in the preceding Sec.~\ref{s:Deparam} demonstrates that it does not
matter whether we deparameterize the classical theory and then quantize the
internal-time Hamiltonians, or whether we quantize first using effective
constraints and then deparameterize. At least at the semiclassical level used
here, deparameterization therefore commutes with quantization.
Moreover, we have realized the two internal-time models as two different gauge
fixings of the same constrained system, up to reordering terms. Since the
constraints are first class, the observable content of the models does not
depend on the particular gauge fixing used to derive it, as long as only
moment corrections are considered. (Explicit gauge transformations of moments
relating the models can be derived as in \cite{EffTimeLong}.) We have
therefore demonstrated in our quantized cosmological model how covariance can
in principle be realized, in the sense that the two internal-time versions
derived in Sec.~\ref{s:Deparam} would be equivalent to each other. However, in
our explicit example, covariance is broken by factor ordering corrections,
which appear whenever the momenta of two internal times appear in the
constraint with different phase-space dependent factors. However, this result,
which we consider to be rather important, cannot explain the mismatch of
proper-time evolutions we found in Sec.~\ref{s:Deparam} because this mismatch
appears even for moment corrections. The existence of gauge transformations
that successfully transform the moment corrections in deparameterized
effective constraints, at first sight, makes the disagreement of their
proper-time evolutions only more puzzling.
However, supplied with the methods of effective constraints, we can now
revisit this question with a complete view on the gauge structure. Our first
attempt to derive proper-time evolution from internal-time evolution required
an expression for ${\rm d}\phi/{\rm d}\tau$ or ${\rm d}T/{\rm d}\tau$. Since
there is no $\tau$ in the deparameterized theory, such an expression can only
come from the original constraint. It may be amended by different versions of
moment corrections, as seen in the scalar example, but it is always closely
related to the original gauge generator which we have now called $C_1$.
At this point, we can see the reason for our problem of mismatched proper-time
evolutions. A deparameterized model is equivalent to a specific gauge fixing
of effective constraints. The gauge fixing must be preserved by evolution in
the model, which requires a specific combination of effective constraints as
evolution generator. If the classical constraint is not linear in the momentum
of internal time, or if there are phase-space dependent factors such as $V$ or
$1/V$ of the momentum of internal time, the evolution generator preserving the
gauge fixing is not equal to the effective constraint $C_1$ used for proper
time. The only generator consistent with the gauge-fixing conditions is the
deparameterized Hamiltonian (or this Hamiltonian multiplied with a quantum
phase-space function not depending on internal time and its momentum).
In this way, only the deparameterized evolution can be described within a
deparameterized model. It is impossible to transform this evolution to proper
time and still have reparameterization invariance or covariance. Referring to
the chain rule in order to transform from an internal time to proper time is
meaningless in this context of multiple constraints. The 1-parameter chain
rule ${\rm d}/{\rm d}\tau=({\rm d}\phi/{\rm d}\tau) {\rm d}/{\rm d}\phi$ is
valid only if evolution is described by a unique 1-dimensional
trajectory. This is the case in the classical theory, in which there is just
one constraint, but not in the quantum theory in which expectation values and
moments provide independent constraints. In order to apply the 1-parameter
chain rule, one would first have to select a unique trajectory generated by a
distinguished linear combination of the constraints. But once a specific
linear combination has been selected, it corresponds to a fixed choice of
time. Transformations between different time choices are then no longer
possible.
There is a way to obtain proper-time evolution from the effective
constraints. Proper time is not a phase-space variable, and therefore it does
not correspond to a natural gauge fixing of the effective constraints.
Instead of fixing the gauge of linear constraints $C_f$, we compute invariant
expectation values and moments, or Dirac observables of this subset of
constraints. Up to terms of higher order in $\hbar$ including products of
second-order moments, as always in this paper, we have the invariants
\begin{eqnarray}
{\cal V} &=& V-\frac{VH}{p_{\phi}} \Delta(V\phi)-
\frac{V^2}{p_{\phi}}\Delta(H\phi)+
\frac{V^3\Lambda}{2p_{\phi}^2}\Delta(\phi^2)\,,\\
{\cal H} &=& H+2\frac{VH}{p_{\phi}} \Delta(H\phi)- \frac{V}{p_{\phi}}
\Delta(\phi\Lambda)+ H\Delta(\phi^2)
\end{eqnarray}
as well as
\begin{eqnarray}
\Delta({\cal V}^2) &=& \Delta(V^2)-2\frac{V^2H}{p_{\phi}} \Delta(V\phi)+
\frac{V^4H^2}{p_{\phi}^2} \Delta(\phi^2)\,,\\
\Delta({\cal VH}) &=& \Delta(VH)+\frac{p_{\phi}}{V} \Delta(V\phi)-
\frac{V^2H}{p_{\phi}} \Delta(H\phi)- HV\Delta(\phi^2)\,,\\
\Delta({\cal H}^2) &=& \Delta(H^2)+2\frac{p_{\phi}}{V} \Delta(H\phi)+
\frac{p_{\phi}^2}{V^2} \Delta(\phi^2)\,,\\
\Delta({\cal V}p_{\phi}) &=& \Delta(Vp_{\phi})-
\frac{V^2H}{p_{\phi}} \Delta(\phi p_{\phi})\,. \label{DeltaVpObs}
\end{eqnarray}
Moreover, $p_{\phi}$, $\Lambda$, $\Delta(p_{\phi}^2)$,
$\Delta(p_{\phi}\Lambda)$ and $\Delta(\Lambda^2)$ are invariant. Note that
$\Delta({\cal V}p_{\phi})$ in (\ref{DeltaVpObs}) is real even if $\phi$ is
used as internal time because the non-zero imaginary parts of
$\Delta(Vp_{\phi})$ and $\Delta(\phi p_{\phi})$, according to (\ref{DeltaVp})
and (\ref{Deltaphip}) cancel out completely.
These combinations of expectation values and moments are invariant to
second-order moments under gauge transformations generated by effective
constraints $C_f$ with $f$ linear in basic variables. In the gauge
(\ref{phiGauge}) of a formulation deparameterized by internal time $\phi$,
they are equal to the kinematical expectation values and moments of the same
type and thus provide an invariant extension of these variables. In the gauge
of some other internal time such as $T$, with conditions (\ref{TGauge}), there
are additional non-zero moments compared with the simple kinematical
expressions $V$, $H$, $\Delta(V^2)$, $\Delta(VH)$, $\Delta(H^2)$ and
$\Delta(Vp_{\phi})$. If one analyzes a model using different internal times,
such as $\phi$ and $T$ in the present case, one should therefore not directly
compare moments of the same type, but combinations as dictated by invariant
moments. For instance, the fluctuation $\Delta(V^2)$ computed with internal
time $\phi$ represents the same observable (with respect to linear constraints
$C_f$) as $\Delta(V^2)-2(V^2H/p_{\phi}) \Delta(V\phi)+ (V^4H^2/p_{\phi}^2)
\Delta(\phi^2)$ computed with internal time $T$.
The remaining constraint $C_1$ written in terms of invariant expectation
values and moments is
\begin{equation}
{\cal C} = -{\cal V}{\cal H}^2+ \frac{p_{\phi}^2}{{\cal V}^2}+ {\cal
V}\Lambda- {\cal V}\Delta({\cal H}^2)- 2{\cal H}\Delta({\cal VH})+
\frac{p_{\phi}^2}{{\cal V}^3} \Delta({\cal V}^2) +\frac{1}{{\cal V}}
\Delta(p_{\phi}^2) -2\frac{p_{\phi}}{{\cal V}^2} \Delta({\cal V}p_{\phi})+
\Delta({\cal V}\Lambda) + i\hbar H\,.
\end{equation}
The moment corrections are of the same form that $C_1$ has in terms of the
kinematical expectation values and moments. However, the transformation to
invariant moments leads to an imaginary part $\hbar H$ which indicates that
the Weyl-ordered operator used for $C_1$ was not of the correct ordering.
Similarly to (\ref{VH2}), we have
\begin{equation} \label{H2V}
\hat{H}^2\hat{V} =
\frac{1}{3}(\hat{V}\hat{H}^2+\hat{H}\hat{V}\hat{H}+\hat{H}^2\hat{V})+i\hbar
\hat{H}= (\hat{V}\hat{H}^2)_{\rm Weyl}+i\hbar\hat{H}\,.
\end{equation}
If we use the ordering $(\hat{V}\hat{H}^2)''=\hat{H}^2\hat{V}$ in a reordered
constraint operator $\hat{C}''$, we have $\hat{C}''=\hat{C}_{\rm
Weyl}-i\hbar\hat{H}$ and the imaginary parts in $\langle\hat{C}''\rangle$
cancel out after transformation to invariant expectation values and moments:
\begin{equation}
{\cal C}'' = -{\cal V}{\cal H}^2+ \frac{p_{\phi}^2}{{\cal V}^2}+ {\cal
V}\Lambda- {\cal V}\Delta({\cal H}^2)- 2{\cal H}\Delta({\cal VH})+
\frac{p_{\phi}^2}{{\cal V}^3} \Delta({\cal V}^2) +\frac{1}{{\cal V}}
\Delta(p_{\phi}^2) -2\frac{p_{\phi}}{{\cal V}^2} \Delta({\cal V}p_{\phi})+
\Delta({\cal V}\Lambda)\,.
\end{equation}
We have not found an independent argument why the ordering of $\hat{C}''$
should be used for proper-time evolution. The appearance of this particular
ordering is therefore rather surprising, as is the fact that it is different
from the two orderings required for scalar and cosmological internal times.
With a real-valued effective constraint ${\cal C}''$ in terms of invariants,
we can finally introduce proper-time evolution. We do not introduce
gauge-fixing conditions but explicitly select the lapse function of the
generic evolution generator
\begin{equation}
NC_{\rm eff}=N_1C_1''+ \sum_f N_fC_f''= \langle (N_1 +N_f
(\hat{f}-f))\hat{C}''\rangle =\langle\hat{N}\hat{C}''\rangle
\end{equation}
by setting all $N_f=0$ for $f\not=1$ and $N_1=1$. This choice
implements the feature that proper time, in a geometrical formulation,
corresponds to a lapse function $N=1$. At the operator level, we
should then have $\hat{N}=1$ without any contributions from
$\hat{f}-f$. Proper-time evolution equations are then generated by
${\cal C}''$, which is $\langle\hat{C}''\rangle$ expressed in
invariant expectation values and moments. Just as in classical
equations, it is not necessary to compute complete Dirac observables
which are also invariant under the flow generated by ${\cal C}''$,
since we can directly interpret proper-time trajectories in
geometrical terms. The tedious constructions of physical Hilbert
spaces in standard treatments of canonical quantum cosmology are, at
the effective level, replaced by invariance conditions with respect to
the flow generated by $C_f$, combined with reality conditions on
${\cal C}''$.
Proper time can therefore be implemented within the effective
constrained system, but it amounts to a gauge fixing different from
most deparameterized models. If we consider only moment corrections,
there are gauge transformations between proper-time and all
deparameterized models within the effective constrained system and
reparameterization invariance is preserved, including proper
time. Factor-ordering corrections generically break
covariance. However, no gauge transformation to proper time exists
within a deparameterized model, in which the gauge fixing can no
longer be changed. This is the case even if factor ordering terms are
ignored, so that covariance is more strongly broken in such cases.
Other coordinate times, such as conformal time, can be implemented in the same
way by still using $N_f=0$ but $N\not=1$ a function of expectation
values. Their evolution generators are given by ${\cal N}{\cal C}''$ where
${\cal N}$ is obtained by replacing expectation values in $N$ by their
invariant analogs. No new factor ordering of $\hat{C}$ is required because we
just multiply the proper-time generator ${\cal C}''$ with a function of
invariants, which keeps the expression real. Our definition of proper-time
therefore allows the same changes of time coordinates as in the classical
theory and is, in this sense, time reparameterization invariant. This
invariance is broken only if we try to compare coordinate time with internal
time.
\section{Discussion}
We have pointed out that time reparameterization invariance of
effective equations is not guaranteed after quantization even in
systems with a single constraint, and illustrated this often
overlooked property in a specific cosmological model. Our detailed
analysis of the underlying quantum gauge system has led us to a new
procedure in which one can implement proper-time evolution at the
effective level. This new definition includes all analogs of different
classical choices of coordinate time and is time reparameterization
invariant in this sense. Moreover, our procedure unifies models with
coordinate times and internal times because they are all obtained from
the same first-class constrained system by imposing different gauge
conditions, up to factor orderings.
The last condition is important and ultimately leads to violations of
time reparameterization invariance or covariance of internal-time
formulations. The effective constrained system provides gauge
transformations that map moment corrections in an evolution generator
for one time choice to the moment corrections obtained with a
different time choice, including proper time. However, in our model,
the time choices we studied explicitly, given by scalar time,
cosmological time and proper time, all require different factor
orderings of the constraint operator for real evolution
generators. Since effective constraints are computed for a given
factor ordering of the constraint operator, they do not allow gauge
transformations that would change factor ordering corrections. Factor
ordering terms therefore generically imply that different time choices
lead to different predictions, and time reparameterization invariance
of internal-time formulations is broken. The only solution to this
important problem is to insist on one specific time choice for all
derivations. The only distinguished time choice, in our opinion, is
proper time: it refers directly to the time experienced by observers
and gives evolution equations that can be used directly in an
effective Friedmann equation of cosmological models. Moreover, it is
time-reparameterization invariant when compared with other choices of
coordinate time, while there are no complete transformations for
different choices of internal time.
We have worked entirely at an effective level up to second order in moment
corrections, corresponding to a semiclassical approximation to first order in
$\hbar$. This order suffices to demonstrate our claims because differences in
quantum corrections between the models are visible at this order. In
principle, one can extend the effective expansion to higher orders, but it
becomes more involved and is then best done using computational help. We have
not considered such an extension in the present paper because the orders we
did include already show quite dramatic differences between the models if
improper gauge conditions are used, for instance by trying to rewrite a
deparameterized model in proper time by using the 1-parameter chain rule.
Our deparameterized models could certainly be formulated with operators acting
on a physical Hilbert space without using an effective theory. However, no
general method is known that would allow one to compare physical Hilbert
spaces based on different deparameterizations, or to introduce proper time at
this level. By using an effective formulation, we have gained the advantage of
being able to embed all such models within the same constrained system, and to
transform their moment corrections by simple changes of gauge
conditions. These properties were crucial in our strict definition of
proper-time evolution at the quantum level, for which we used effective
observables such as invariant moments instead of operators on a physical
Hilbert space. Internal-time formulations based on a single physical Hilbert
space, as used for instance in loop quantum cosmology, cannot be assumed to
give correct moment terms in effective equations, strengthening the
results of \cite{MultChoice}. Investigations of internal-time formulations of
quantum cosmological models with significant quantum fluctuations are
therefore likely to be spurious.
\section*{Acknowledgements}
This work was supported in part by NSF grant PHY-1607414 and a McNair
scholarship.
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 5,138
|
\section{Introduction}
It is a fascinating idea that some of
the deep puzzles of particle physics may be attributed to the geometry
of extra space dimensions. The most discussed one is the gauge hierarchy
problem why the electroweak scale is much lower than the Planck
scale. An attractive hypothesis to explain this hierarchy was proposed
using large extra dimensions \cite{Arkani-Hamed:1998rs}.
Soon later an alternative interesting idea
was postulated by Randall and Sundrum \cite{Randall:1999ee}. In their
first model (RS1), the compact extra dimension has a size not much
larger than the Planck length, but with a warped metric. This warped
extra dimension is also interesting in the context of AdS/CFT
correspondence in string theories \cite{Maldacena:1997re}.
In fact, stringy realization of the
warped extra dimension was considered in compactifications with
non-vanishing fluxes of higher tensor fields. (See ref. \cite{Giddings:2001yu}
and references therein.)
Another puzzle which we would like to address here is the question of
fermion masses and flavor mixing. An extra-dimensional explanation to this
puzzle owes to the configuration of the wave functions of the quarks and
leptons along the extra dimensions. In a field theory approach, the
smallness of the Yukawa coupling and thus the fermion mass is due to the
small overlap of the wave functions of the relevant fields in the extra
dimensions. The idea was proposed in flat TeV$^{-1}$ size extra dimension
\cite{Arkani-Hamed:1999dc}, which was utilized to construct realistic
models of the
Yukawa sector \cite{Kaplan:2001ga,Kakizaki:2001ue,Choi:2003di,Choi:2003ff}.
The geometrical approach to the Yukawa couplings can also be applied to
the RS1 model. For this purpose, the standard model (SM) fields should
reside in the warped
bulk. Though this was recognized to be possible
\cite{Davoudiasl:1999tf,Chang:1999nh}, the electroweak (EW) precision
test restricts the RS1 bulk SM strongly since the $t$ quark is much
heavier than other quarks and can give a significant amount of shift to
the weak gauge boson mass ratio $M_W/M_Z$ from the SM prediction
due to $t$ quark and its
Kaluza-Klein (KK) mode mixing \cite{Hewett:2002fe}. Several attempts
were made to resolve this problem \cite{Hewett:2002fe, Kim:2002kk}.
Recently, Agashe {\it et al.} \cite{Agashe:2003zs} showed that the above problem of the too large
Peskin-Takeuchi $T$ parameter is due to the absence of a custodial $SU(2)$
symmetry in the bulk, as is suggested by the AdS/CFT correspondence, and
proposed a model which has the gauge symmetry $SU(3)_C \times SU(2)_L\times
SU(2)_R\times U(1)_{B-L}$. This model may be related
with the warped Higgsless model which shows a possibility of EW symmetry
breaking
without a Higgs field in the RS1 SM \cite{Csaki:2003zu, Burdman:2003ya}.
It must be stressed that the Higgs field in the model we consider
must be confined on the brane
in order not to reincarnate the gauge hierarchy problem
\cite{Chang:1999nh}. Because of this peculiar property, the Higgs field
acts as a boundary condition (BC) for the bulk field equations. If the
Higgs couples to different bulk fermions with (more or less) universal
strength at the boundary, the small masses and mixings of the SM
fermions can be induced by the suppression of the zero-mode wave
functions on the infra-red (IR) boundary \cite{Grossman:1999ra,
Gherghetta:2000qt}.
In this paper, we shall consider the fermion mass structure of quarks
and leptons (including neutrinos) in the framework of the warped bulk
fermions. Under the situation that a fundamental principle to dictate
the parameters in the 5D bulk theory is not known, it would be natural
to take the hypothesis that the 5D Yukawa couplings do not have any
particular textures. Thus we assume that the 5D Yukawa couplings are all
around unity in magnitude. Under this ``almost universal'' hypothesis,
the fermion mass structure is solely due to the configurations of the
(zero-mode) wave functions of the bulk fermions. In the case at hand,
they are controlled by bulk fermion masses. An attractive point of this
approach is that the whole bulk structure may be revealed in future
experiments to explore consequences of the Kaluza-Klein modes of the SM
particles.
The purpose of the paper is two fold: First we present a simple analytic
method which is useful to estimate the bulk fermion masses from known
experimental data under the assumption of the almost universal 5D Yukawa
couplings. Despite the fact that there are already many (numerical)
analyzes on the fermion masses in the warped extra dimension in the
literature, we believe that it is still worth presenting our analytic
results because of simplicity and accessibility. The hierarchical structure
in the quark mass matrices makes our analysis very robust. For the lepton
sector, although it may suffer from some pollution of numerical
coefficients because of its somewhat less hierarchical pattern of the
masses and mixings, it is still possible to determine generic structure.
The second purpose of the paper is to show that the $U_{e3}$ entry of
the Maki-Nakagawa-Sakata (MNS) mixing matrix in the neutrino sector is
typically close to the present experimental upper bound when the neutrino
masses are of Dirac type.
\section{The standard model in the RS1 bulk}
The basic framework of our study is a simple system where one flavor of
fermion resides in the bulk of the RS1. We extend it to the three flavor
system later in this paper.
The RS1 metric is given by
\begin{equation}
ds^2= e^{-2\sigma(y)}(dt^2-dx^2) - dy^2,
\end{equation}
where $y$ represents the warped coordinate for extra-dimension
and $\sigma(y) = k|y|$. The 5th dimension is bounded in the interval
$(0,L)$. The gravity is confined at $y=0$ boundary known as Planck (UV) brane,
whereas our world is confined on the other end ($y=L$), which is called
the TeV (IR) brane.
$y$ coordinate can be converted to a conformally flat coordinate,
$z\equiv e^\sigma/k$, where the metric becomes
\begin{equation}
ds^2= \frac{1}{(kz)^2}(dt^2-dx^2 - dz^2).
\end{equation}
The interval becomes $1/k < z <1/T$, where $T=k e^{-kL}\sim {\cal O}(1) $ TeV .
The 5D fermion action becomes
\begin{eqnarray}
S_{\rm fermion}=\int d^4x dy \left[ \overline{\hat\Psi} e^\sigma
i\gamma^\mu\partial_\mu \hat{\Psi} -\frac{1}{2}
\overline{\hat\Psi} \gamma_5\partial_y \hat{\Psi}
+\frac{1}{2}(\partial_y \overline{\hat\Psi})\gamma_5 \hat\Psi
+ m_D \overline{\hat\Psi}\hat\Psi
+ m_M \overline{\hat\Psi}\hat\Psi^c
\right]\ ,
\end{eqnarray}
where $\hat{\Psi}\equiv e^{-2\sigma}\Psi .$
The bulk
Majorana mass $m_M$ is non-zero only if the fermion is neutral.
This Lagrangian has the five-dimensional $\mathbb{Z}_2\times\mathbb{Z}_2'$ parity
on each boundary (brane),
\begin{equation}
\gamma_5 \Psi (x,-y)\,={}\pm\Psi (x,y) \, ,\hspace{6mm}
\gamma_5 \Psi (x,L-y)\,={}\pm\Psi (x,L + y) \ .
\end{equation}
$\mathbb{Z}_2$ and $\mathbb{Z}_2'$ represent UV and IR parity of bulk field and written in the
form of (UV, IR).
The bulk Dirac mass is defined by $m_D=\sigma'= kc\ {\rm sign}(y)$.
The bulk fermion can be divided into two chiral components,
$\hat{\Psi}=\hat{\Psi}_L+\hat{\Psi}_R$, for $ \gamma_5\hat{\Psi}_L= -\hat{\Psi}_L \, ,
\gamma_5\hat{\Psi}_R= \hat{\Psi}_R$.
Each chiral field can be expanded to the KK modes
\begin{equation}
\hat{\Psi}(x,y)_{L(R)} = \sqrt{k}\sum_n \psi_{L(R)}^{(n)}(x) f_{L(R)}^{(n)}(y) .\
\end{equation}
After the mode expansion, the 4D effective action for KK modes becomes
\begin{equation}
S_{\rm eff}
= \int d^4 x \sum_n\left[\overline{\psi}^{(n)}_L i \gamma^\mu \partial_\mu
\psi^{(n)}_L + \overline{\psi}^{(n)}_R i\gamma^{\mu} \partial_\mu
\psi^{(n)}_R - m^{(n)}(\overline{\psi}^{(n)}_L \psi^{(n)}_R +
\overline{\psi}^{(n)}_R \psi^{(n)}_L)
\right] \ ,
\label{eff0}
\end{equation}
where $m^{(n)}$ is a mass of nth KK excited mode.
To generate the action (\ref{eff0}), KK mode functions should
satisfy the mode equations in $z$ coordinate,
\begin{eqnarray}
\left(\partial_z \pm \frac{c}{z}\right) f_{L/R}^{(n)} = \mp m^{(n)}
f_{R/L}^{(n)}~ .
\end{eqnarray}
A generic 5D bulk fermion can have
four different forms according to the $\mathbb{Z}_2 \times \mathbb{Z}_2'$ parity,
\begin{eqnarray}
\label{eq:Psi1} \hat{\Psi}_i(x,y) & = & \sqrt{k}\sum_n [\psi^{(n)}_{iL}(x)
f^{(n)}_{iL}(y)
+ \psi^{(n)}_{iR}(x) f^{(n)}_{iR}(y) ] \, .
\end{eqnarray}
The indices $i=1,2$ represent the parallel conditions, where
$f_{iL}$ has $(\pm\pm)$ parity and $f_{iR}$ has $(\mp\mp)$, and
$i=3,4$ represent the crossed conditions, where $(\pm\mp)$ for
$f_{iL}$ and $(\mp\pm)$ for $f_{iR}$, respectively. Each mode
function except the zero modes can be written in the series of
Bessel functions. For more details, see Ref. \cite{Chang:2005vj}.
The Higgs field $\phi(x)$ is confined on the IR boundary,
\begin{eqnarray}
S
=-\int d^4 x dy \frac{\lambda_{5}}{T}
H(x)\left(\overline{\hat{\Psi}}_{1}(x,y)
\hat{\Psi}_{2}(x,y)+\overline{\hat{\Psi}}_{2}(x,y)
\hat{\Psi}_{1}(x,y)\right)\delta(y-L)~,
\end{eqnarray}
where $H=e^{- k L}\phi(x)$ is canonically normalized Higgs
scalar and $\lambda_5$ is the Yukawa coupling. When the Higgs field
get a vacuum expectation value $\langle H \rangle = v_W$,
the surviving zero modes give the SM fermion mass term,
\begin{equation}
m_f=\left.\frac{\lambda_5 v_W k}{T}f_{1L}^{(0)}f_{2R}^{(0)}\bar\psi^{(0)}_{1L}
\psi^{(0)}_{2R} \right|_{z=1/T},
\label{chiralmass}
\end{equation}
where the zero mode functions are
\begin{eqnarray}
f_{1L}^{(0)} = \frac{(kz)^{-c_1}}{N_1^{(0)}},\ \ ~~~
f_{2R}^{(0)} = \frac{(kz)^{c_2}}{N_2^{(0)}},
\end{eqnarray}
and the normalization becomes
\begin{eqnarray}
N^{(0)}_1=\sqrt{\frac{ 1- \epsilon^{2{c}_1-1}}{2{c}_1-1}} , \ \ ~~~
N^{(0)}_2=\sqrt{\frac{ \epsilon^{-2{c}_2-1}-1}{2{c}_2+1}} ,
\end{eqnarray}
with $\epsilon= T/k=e^{-kL}$. We will drop the indices
1 and 2 from this point to avoid the confusion with
family indices.
The SM requires that two $SU(2)_L$ singlet right-handed fermions
should exist for a
corresponding left-handed doublet. To match the particle content,
we set $(Q_i,U_i,D_i)$ and $(L_i,N_i,E_i)$ as bulk fields
where $i=1,2,3$ represent 3 generations.
$Q$ and $L$ include $SU(2)_L$ quark and lepton doublets.
$U,D,E,N$ include the SM fields $(u,d,e)_R$ and a right-handed neutrino $N_R$,
respectively.
If we expand the model to 3 generations, the mass term is written in $3\times 3$
matrix,
\begin{equation}
M^f_{ij}/v_W = y^f_{ij} =\lambda^f_{5ij} F_L(c_i) \times F_R(c_j) ,
\end{equation}
where $y^f_{ij}$ is a 4D effective Yukawa coupling of fermion $f$ and
$\lambda^f_{5ij}$ is a 5D boundary Yukawa coupling, and
\begin{equation}
F_{L}(c_i) = \epsilon ^{c_i-1/2} \sqrt{\frac{ 2c_i -1}{1- \epsilon^{2c_i -1}}}
,\ \ ~~~
F_{R}(c_i) = \epsilon ^{-c_i-1/2} \sqrt{\frac{ 2c_i +1}{\epsilon^{-2c_i
-1}-1}},
\label{para1}
\end{equation}
where $c_i$ represents each mass of $(Q_i,U_i,D_i)$
and $(L_i,N_i,E_i)$.
$F_{L(R)}(c_i)=1$ when bulk fermion mass is zero $c_i=0$. If we increase
$(-)c_i$,
$F_{L(R)}(c_i)$ decrease slowly until $(-)c_i=1/2$. For $(-)c_i>1/2$,
it decrease fast in power of $\epsilon ^{(-)c_i}$;
\begin{eqnarray}
F_{L(R)}(c_i) &\simeq & \epsilon ^{(-)c_i-1/2} \sqrt{(-)2 c_i -1}
\hspace{1cm} \mbox{ for } (-)c_i-1/2 \gg 1/kL
\nonumber \\
& \simeq & (kL)^{-1/2}\hspace{2.8cm} ~~~ \mbox{ for } |(-)c_i -
\frac{1}{2}| \ll 1/kL
\nonumber \\
& \simeq & \sqrt{ 1-(-)2c_i} \hspace{2.1cm} ~~~ \mbox{ for } (-)c_i -1/2
\ll -1/kL .
\end{eqnarray}
The mass difference of bulk fermion gives the natural mass
hierarchy between different SM fermions.
\section{Fermion Masses and Mixings}
The bulk SM conflicts with the electro-weak precision test without some
symmetry \cite{Hewett:2002fe,Kim:2002kk}. The $SU(2)_L\times SU(2)_R\times U(1)_{B-L}$ bulk SM is a favorable
candidate because its custodial isospin prevents the extra-contribution
from the KK fermion modes to the gauge boson self-energy \cite{Agashe:2003zs}.
Also, this model draws interests due to the connection with the Higgsless
model of electro-weak symmetry breaking \cite{Csaki:2003zu,Burdman:2003ya}.
All SM fields except the Higgs field reside in the bulk \cite{Chang:1999nh}.
There are some fields which have no SM counter part, $e.g.$ $SU(2)_R$ charged
gauge bosons. The ``crossed" BC $(\pm\mp)$ assigned to these fields eliminates
their zero modes, thus we will not see any light additional field.
Among the bulk fermions we defined in previous section,
$Q$ and $L$ fields are consisted with $(\pm\pm)$ fields only,
while $SU(2)_R$ doublet contains one component with $(\pm\mp)$ parity,
because their charged current should conserve $\mathbb{Z}_2\times\mathbb{Z}_2'$ parity.
Thus, for $U,N, D,E$ fields, only one component of the doublet
can have a zero mode.
If the SM is induced from this model, there should be at least one bulk
$SU(2)_L$ doublet and two $SU(2)_R$ doublet fermions for each family.
To establish a simple but realistic model for 4D fermion
masses,
we choose the bulk mass matrices are real and diagonal.
Also, for simplicity
we ignore CP phase in the Yukawa couplings. Inclusion of the CP
phase is straightforward.
In this paper, we use a (almost) universal Yukawa coupling model that
the Higgs scalar couples to all fermions with (almost) universal
strength.
In this model, the fermion mass hierarchy is generated only by
the bulk fermion mass structures.
For the case that the universality is exact,
$ 3\times 3$ matrix $M_{ij}=v_W F_L(c_{Qi}) F_R(c_{Aj})$ has
only one non-zero eigenvalue.
This approach is similar to the fermion mass hierarchy generation
method by Froggatt and Nielsen which was used in anomalous $U(1)$ model \cite{Froggatt:1978nt,Elwood:1997pc,
Elwood:1998kf}, and also in various bulk SM models
\cite{Agashe:2004ay,Agashe:2004cp,Huber:2003tu,Choi:2003ff,Choi:2003di,Moreau:2005kz}.
\subsection{Quark Masses and Mixings}
The bulk fields $Q_i$, $U_i$ and $D_i$
with bulk mass parameters $c_{Qi}$, $c_{Ui}$, $c_{Di}$,
contain the zero modes which can be interpreted as the SM fermions.
If we take all parameters to be real, the mass matrices can be diagonalized by
bi-orthogonal transformation,
\begin{equation}
U^T_{qL} M_q U_{qR}=M_q^{\rm diag} ~~~~~ \mbox{ for }
q=u,d. \label{bioth}
\end{equation}
The CKM matrix is defined as $K= U_{uL}^T U_{dL}$.
With simplified Wolfenstein parametrization
for $\lambda \simeq 0.22$, the CKM matrix $K$ can be written
\begin{equation}
K\simeq
\left(\begin{array}{ccc} 1 &\lambda & \lambda^3 \\
\lambda & 1 & \lambda^2 \\ \lambda^3 & \lambda^2 & 1
\end{array} \right), \label{CKM}
\end{equation}
where the numerical coefficient of each entry is of order unity. A
natural choice for $U_{u_L}$ and $U_{d_L}$ in this case is of the
similar form as (\ref{CKM}):
\begin{equation}
U_{u_L} \simeq U_{d_L} \simeq
\left(\begin{array}{ccc} 1 &\lambda & \lambda^3 \\
\lambda & 1 & \lambda^2 \\ \lambda^3 & \lambda^2 & 1
\end{array} \right). \label{mixing-quark}
\end{equation}
Here any number greater than $\lambda^{0.5}$ is replaced as unity.
The above choice of mixing is reasonable since the $u_L$ and $d_L$ has the
same bulk mass.
The fermion masses can also be expressed in terms of $\lambda$,
\begin{eqnarray}
M_u^{\rm diag} = diag(m_u, m_c, m_t) &\simeq& v_{W}\ diag(\lambda^8, \lambda^{3.5}, 1),
\nonumber\\
M_d^{\rm diag} = diag(m_d, m_s, m_b) &\simeq& v_{W}\ diag(\lambda^7, \lambda^5, \lambda^{2.5} ).
\label{quarkmass}
\end{eqnarray}
If we consider the (almost) universal coupling, the quark mass matrices become
\begin{equation}
(M_a)_{ij}\simeq v_W F_L(c_{Qi}) F_R(c_{Aj}), \label{ansatz}
\end{equation}
where $a=u,d$ and $A=U,D$.
It follows from the above that
\begin{eqnarray}
(M_aM_a^T)_{ij}= (U_{aL} (M_a^{D})^2 U_{aL}^T)_{ij}
\simeq
v_W^2 F_L(c_{Qi}) F_L(c_{Qj}) (\sum_k F_R(c_{Ak})^2)
.
\end{eqnarray}
Let us now determine the mass parameters $c$'s.
For $u$ quark, we find
\begin{eqnarray}
M_u M_u^T
\simeq (v_W C)^2\left( F_L(c_{Qi}) F_L(c_{Qj}) \right) \simeq v_W^2
\left(\begin{array}{ccc} \lambda^6 &\lambda^5 & \lambda^3 \\
\lambda^5 & \lambda^4 & \lambda^2 \\ \lambda^3 & \lambda^2 & 1
\end{array} \right),
\end{eqnarray}
where the last equality is obtained by substituting
Eqs.~(\ref{mixing-quark}) and (\ref{quarkmass}) into (\ref{bioth}).
This leads
\begin{eqnarray}
F_L(c_{Q1}) \simeq C^{-1}\lambda^3, ~~~~
F_L(c_{Q2}) \simeq C^{-1} \lambda^2, ~~~~
F_L(c_{Q3}) \simeq C^{-1},
\end{eqnarray}
where $C\simeq F_R(c_{U3})$. Notice that this procedure works because of
the hierarchical mass structure $m_t \gg m_c, m_u$. This observation is
crucial when discussing the neutrino masses. We will come back this
point shortly.
If $c_{U3}$ is too large, the mass of down sector quark from $SU(2)_R$
doublet $U_3$ becomes too small, giving too much contribution to
Peskin-Takeuchi $T$ parameter. It should be restricted, $F_R(c_{U3})
\mathrel{\raise.3ex\hbox{$<$\kern-.75em\lower1ex\hbox{$\sim$}}} 1.2$. Also the constraint from $Z\rightarrow b\bar{b}$ gives the
allowed range $F_L(c_{Q3}) \mathrel{\raise.3ex\hbox{$<$\kern-.75em\lower1ex\hbox{$\sim$}}} 0.7$ \cite{Agashe:2003zs}. Since
$m_t/v_W \simeq F_L(c_{Q3}) F_R(c_{U3})\simeq 1$, for the range of our
interest, 2 TeV $<T<$ 8 TeV and with the standard choice of curvature
scale $k\simeq M_{pl}$, the bulk top masses are almost fixed around the
values $c_{U3}\simeq 0.2$ and $c_{Q3} \simeq 0.3$. Then from
(\ref{para1}), we find
\begin{eqnarray}
c_{Q1} \simeq 0.61,\ ~~~~
c_{Q2} \simeq 0.56 ,\ ~~~~
c_{Q3} \simeq 0.3 .
\end{eqnarray}
If we assume that off-diagonal term in $U_{qR}$ is small enough, with
Eq. (\ref{bioth}) and (\ref{quarkmass}), the quark mass matrices can be written
in the following form:
\begin{eqnarray}
M_u
\simeq v_W
\left( \begin{array}{ccc}\lambda^8 &\lambda^{4.5} & \lambda^3 \\
\lambda^9 & \lambda^{3.5} & \lambda^2 \\
\lambda^{11} & \lambda^{5.5} & 1
\end{array}
\right) U_{u_R}^T
\simeq v_W
\left(\begin{array}{ccc} \lambda^8 &\lambda^{4.5} & \lambda^3 \\
& \lambda^{3.5} & \lambda^2 \\ & & 1
\end{array} \right),\
\label{uquark}
\end{eqnarray}
for the $U$ fields and,
\begin{eqnarray}
M_d
\simeq v_W
\left(\begin{array}{ccc} \lambda^7 &\lambda^6 & \lambda^{5.5} \\
\lambda^8 & \lambda^5 & \lambda^{4.5} \\
\lambda^{10}& \lambda^7 & \lambda^{2.5}
\end{array} \right) U_{d_R}^T
\simeq v_W
\left(\begin{array}{ccc} \lambda^7 &\lambda^6 & \lambda^{5.5} \\
& \lambda^5 & \lambda^{4.5} \\ & & \lambda^{2.5}
\end{array} \right),
\label{dquark}
\end{eqnarray}
for the $D$ fields.
The lower left components
depend on the details of the mixing matrices and
are redundant for the mass determination.
Our hypothesis of the almost universal 5D Yukawa couplings implies that
both of the mass matrices given above are expressed as
Eq. (\ref{ansatz}), which can be achieved if one chooses
\begin{eqnarray}
c_{U1} \simeq -0.70 ,\ ~~~~
c_{U2} \simeq -0.52 ,\ ~~~~
c_{U3} \simeq 0.2 ,
\end{eqnarray}
\begin{eqnarray}
c_{D1} \simeq -0.65 ,\ ~~~~
c_{D2} \simeq -0.60 ,\ ~~~~
c_{D3} \simeq -0.57 .
\end{eqnarray}
There can be small modification for a different choice of initial
parameter range.
The bulk masses we obtained above are approximately in agreement with
the previous calculations
\cite{ Agashe:2004cp,Huber:2003tu}.
\subsection{Lepton Masses and Mixings}
We now consider the mass matrices for charged leptons and neutrinos.
It is required to use a more cautious analysis to the lepton sector,
because the hierarchy between lepton masses and mixings is weaker than
that of quarks.
An advantage of the extra-dimensional explanation for the fermion masses
is that the small masses can easily be generated as a consequence of
the separation of the wave functions. When the fermions are in the
warped extra dimension, the zero-mode wave functions have exponential
form so that this suppression mechanism is very effective. Thus the
Dirac masses of the neutrinos can be very small, allowing us to discuss
the case where the light neutrinos are Dirac ones.
Motivated by the aforementioned argument, let us first consider the
Dirac neutrino case. We assume $SU(2)_L$ doublet bulk leptons $L_i$
with bulk mass $c_{Li}$ and $SU(2)_R$ doublets $E_i$ and $N_i$ with
masses $c_{Ni}$ and $c_{Ei}$. Each of them contains the zero mode
$l_{iL}$, $e_{iR}$ and $\nu_{iR}$, respectively. If we consider that the
SM neutrinos are Dirac particles, the MNS mixing matrix for neutrino is
equivalent to the CKM matrix, $U_{MNS}= U_e^\dagger U_\nu$, where
\begin{equation}
M_\nu^\dagger M_\nu = U_\nu (M_\nu^{\rm diag})^2U_\nu^\dagger ,\ \ ~~~
M_e^\dagger M_e = U_e (M_e^{\rm diag})^2 U_e^\dagger .
\end{equation}
for Dirac neutrino mass.
With the same approximation as the quark case,
the MNS matrix can be approximated as
\begin{eqnarray}
| U_{\rm MNS}| \sim \left(\begin{array}{ccc}
1 & 1 & \lambda^m \\
1 & 1& 1 \\
1 & 1& 1
\end{array}\right),
\label{mixing}
\end{eqnarray}
where the experimental constraint on $U_{e3}$ gives $m>1.3$.
Though the individual neutrino masses are not yet measured,
the mass differences between them are determined by the neutrino
oscillation data,
\begin{eqnarray}
\Delta m_{sol}^2 = m^2_2 - m^2_1\simeq 7.5\times
10^{-5}~\mbox{eV}^2, \ ~~~~
\Delta m_{atm}^2= |m^2_3 - m^2_2|\simeq 2.5\times
10^{-3}~\mbox{eV}^2.
\end{eqnarray}
The WMAP result suggests
that any of neutrino mass should be $m_i < 1.0$ eV. With all known data,
there exist three possible cases: (1) almost degenerate neutrinos, (2) the
normal hierarchy (NH), (3) the inverse hierarchy (IH). If the neutrino
masses are almost degenerate $m_i\lesssim 1$ eV, then with the maximal
mixing of the MNS matrix, we expect that all the left-handed mode
functions have almost the same configurations. Also the right-handed
neutrinos should have the same pattern, while the right-handed charged
lepton should have the hierarchical form. This may be possible.
However, the structure of the MNS matrix as well as the mass differences
would be a consequence of some numerology. We will not discuss this case
furthermore.
For the NH case, as $\nu_1$ is very
light or even massless, the other neutrino masses are fixed as
\begin{eqnarray}
m_1=0 ,\ ~~~
m_2=\sqrt{\Delta m_{sol}^2} ,\ ~~~
m_3=\sqrt{\Delta m_{sol}^2+\Delta m_{atm}^2}.
\end{eqnarray}
For the IH, $\nu_3$ is very light so that
\begin{eqnarray}
m_1=\sqrt{\Delta m_{atm}^2 -
\Delta m_{sol}^2} ,\ ~~~
m_2=\sqrt{\Delta m_{atm}^2},\ ~~~
m_3=0 .
\end{eqnarray}
If we allow the random cancellation during the diagonalization of mass matrix,
there can be too many possibilities. On the other hand, if we follow the first
assumption of no-cancellation strictly, the mass matrix should have either of
the following two forms
\begin{equation}
M_\nu^T M_\nu\propto
\left(\begin{array}{ccc} \lambda^{2n} &\lambda^n &
\lambda^n \\
\lambda^n & 1 & 1 \\ \lambda^n & 1 & 1
\end{array} \right)~~ \mbox{(NH)~~~~ or~~~~ }
\left(\begin{array}{ccc} \lambda^{2k} &1 &
1 \\
1& \lambda^{2l} & \lambda^{2l} \\
1& \lambda^{2l} & \lambda^{2l}
\end{array} \right)~~ \mbox{(IH) },
\label{numass}
\end{equation}
where $k$, $l$ and $n$ are some positive numbers.
The derivation of the above can be found in
Refs.~\cite{Altarelli:2002hx,Altarelli:2002sg}.
In short, we utilize the fact that $U_{\rm MNS}$ is almost tri/bi-maximal and
the neutrino masses are close to
(0,0,1) for NH and (1,-1,0) or (1,1,0) for IH.
We can derive (\ref{numass}) by adding a small perturbation to the solutions of
the approximation. For the IH case, $k\sim l\mathrel{\raise.3ex\hbox{$>$\kern-.75em\lower1ex\hbox{$\sim$}}} 1$ is favored to avoid too large
$U_{e3}$.
It is clear that the IH is not consistent with
our almost universal Yukawa coupling approach, where
the lepton mass matrices should be written as
\begin{equation}
(M_\nu)_{ij} \simeq v_W F_L(c_{Li}) F_R(c_{Nj}), \ \ ~~~~
(M_e)_{ij} \simeq v_W F_L(c_{Li}) F_R(c_{Ej}).
\end{equation}
Therefore we consider only the NH case, where the lepton masses can be written as,
\begin{eqnarray}
M_\nu^{\rm diag} = diag(m_1, m_2, m_3) &=& v_W\ diag(<\lambda^{20.5}, \lambda^{20.5}, \lambda^{19}),
\nonumber\\
M_e^{\rm diag} = diag(m_e, m_\mu, m_\tau) &=& v_W\ diag(\lambda^{8.5}, \lambda^5, \lambda^3 ).
\label{1.5}
\end{eqnarray}
Our hypothesis implies as in the quark sector
\begin{eqnarray}
(M_a^T M_a)_{ij} &\simeq& (U_a (M_a^D)^2 U_a^T)_{ij}
\simeq v_W^2 F_L(c_{Li}) F_L(c_{Lj}) \sum_k F_R(c_{Ak})^2
\label{lepton2}
\end{eqnarray}
with $a=\{\nu, e\}$ and $A= \{N, E\}$, which can accord with the NH
neutrino masses. With Eq.~(\ref{numass}), one finds
\begin{equation}
M_e^T M_e
\simeq v_W^2\lambda^{6} \left(\begin{array}{ccc} \lambda^{2n} &\lambda^n &
\lambda^n \\
\lambda^n & 1 & 1 \\ \lambda^n & 1 & 1
\end{array} \right),\ \ ~~~~
M_\nu^T M_\nu\simeq \lambda^{32} M_e^T M_e~.\label{Un}
\end{equation}
The bulk mass terms of $SU(2)_L$ doublets are
\begin{eqnarray}
F_L(c_{L1} )\simeq C_L^{-1} \lambda^{3+n},\ ~~~~
F_L(c_{L2} ) \simeq C_L^{-1} \lambda^{3} ,\ ~~~~
F_L(c_{L3} ) \simeq C_L^{-1} \lambda^{3},
\end{eqnarray}
where $C_L\sim F_R(c_{E3})$.
Unlike the quark case, we cannot simply set the mixing matrices $U_e\simeq
U_{\nu}$.
The maximal mixing between 2 and 3 flavors together with
(\ref{Un}) suggests the following left-handed mixing matrices
\begin{equation}
U_f\simeq \left(\begin{array}{ccc}
1 & \lambda^{a_f} & \lambda^n \\
\lambda^{b_f} & 1& 1 \\
\lambda^{c_f} & 1& 1
\end{array}\right), \label{Uf}
\end{equation}
with $f=e,\nu$.
Writing
\begin{equation}
(M_a^T M_a)_{ij}=m_{a3}^2 U_{ai3}U_{aj3}
+m_{a2}^2 U_{ai2}U_{aj2}+m_{a1}^2 U_{ai1}U_{aj1},
\end{equation}
with $m_{ai}$ being the $i$-th mass eigenvalue of species $a$, one finds
that the first term in the right-handed side should dominate over the
rest to reproduce (\ref{Un}). This requires that the mass eigenvalues are
more hierarchical than the mixings. In fact, one finds
\begin{equation}
1.5+a_{\nu} \gtrsim n, 2+a_{e} \gtrsim n. \label{hierarchy}
\end{equation}
Next we consider the MNS matrix.
The MNS matrix $U_{\rm MNS}=U^T_e U_\nu$ can be evaluated by using
(\ref{Uf}).
Then
Eq. (\ref{mixing}) implies
\begin{eqnarray}
\lambda^{a_{\nu}}\sim \lambda^{b_{\nu}}+\lambda^{c_{\nu}} \sim
1,\ ~~~~
\lambda^{b_{e}}+\lambda^{c_{e}} \lesssim \lambda^{m},\ ~~~~
\lambda^{n}\lesssim \lambda^{m} \label{UeUnu}.
\end{eqnarray}
Eqs. (\ref{hierarchy}) and (\ref{UeUnu}) restrict the allowed values of
$n$ and $m$ in a narrow range
\begin{equation}
1.3 \lesssim m \lesssim n \lesssim 1.5.
\end{equation}
Thus, as a representative value, we expect
\begin{equation}
U_{e3} \simeq \lambda^m \simeq 0.10-0.14,
\end{equation}
provided that the 5D Yukawa couplings are almost universal and no
accidental cancellation takes place in the determination of the mass
structure. This value is close to the present upper bound and should be
explored by near future experiments. This observation may be one of the most
important consequences of the present paper. For $m\simeq 1.5$, it is
interesting to rewrite the above as follows:
\begin{equation}
U_{e3} \simeq \sqrt{\frac{\Delta m_{sol}^2}{\Delta m_{atm}^2}}.
\label{interesting-relation}
\end{equation}
We should note that the numerical coefficient in front cannot be
determined in our framework. The actual value would depend on the range
of the 5D Yukawa couplings. We should also note that the interesting
relation (\ref{interesting-relation}) may be polluted by possible
cancellation among various contributions because of the less
hierarchical structure of the neutrino masses and mixings.
The charged lepton bulk mass can be obtained with the similar method as
the quark case. The relations,
\begin{eqnarray}
F_L(c_{L1}) F_R(c_{E1}) \simeq \lambda^{8.5},\ ~~~~
F_L(c_{L2}) F_R(c_{E2}) \simeq \lambda^5,\ ~~~~
F_L(c_{L3}) F_R(c_{E3}) \simeq \lambda^3,
\end{eqnarray}
hold approximately if the right-handed lepton mixing is chosen to be
small enough. However, there is a wider range of solution space in above
equation than that of quarks.
The lepton flavor violation
limit from $\mu \rightarrow 3e$ and other
experimental data restrict that $c_{L3}$ cannot be smaller
than $0.5$ \cite{Huber:2003tu}.
The lower bound on the bulk lepton masses are,
\begin{eqnarray}
c_{L1} \simeq 0.59,\ ~~~~~
&&c_{L2} \simeq 0.5 ,\ ~~~~~
c_{L3} \simeq 0.5 ,\nonumber\\
c_{E1} \simeq -0.74,\ ~~~~~
&&c_{E2} \simeq - 0.65 ,\ ~~~~~
c_{E3} \simeq -0.55.
\end{eqnarray}
On the other hand, for $c_{E3} \simeq 0$, one finds
\begin{eqnarray}
c_{L1} \simeq 0.68,\ ~~~~~
&&c_{L2} \simeq 0.61 ,\ ~~~~~
c_{L3} \simeq 0.61 ,\nonumber\\
c_{E1} \simeq -0.65,\ ~~~~~
&&c_{E2} \simeq - 0.55 ,\ ~~~~~
c_{E3} \simeq 0 .
\end{eqnarray}
There is no strict upper bound on the bulk masses, but if $c_{E3}$
is much larger than 0.5, the first KK neutrino in $SU(2)_R$
doublet $E$, which has $(+-)$ BC, becomes too light. For instance,
$c_{E3}\simeq 0.7$ leads $m_N^{(1)}\sim 1$ GeV and if $c_{E3}$
approaches to the value $1$, the mass become lower than MeV and
can be considered as a sterile neutrino. This type of neutrino KK
mode may conflict with experimental or cosmological data
\cite{Chang:2005vj,Agashe:2004bm}.
Even though we fix $\nu_2$ and $\nu_3$ masses in the NH case,
there is no data which determines the lightest neutrino mass.
In other words, two right-handed neutrinos are just enough to explain all
the existing experimental data. Using the similar method, we can determine
the two bulk neutrino masses with the relations,
\begin{eqnarray}
F_L(c_{L2}) F_R(c_{N2}) \simeq \lambda^{17.5} ,\ ~~~~
F_L(c_{L3}) F_R(c_{N3} ) \simeq \lambda^{16}.
\end{eqnarray}
In the valid range where $c_{L3} >0.5$, the lower bound becomes,
\begin{eqnarray}
c_{N2} \simeq -1.2 ,\ ~~~~
c_{N3} \simeq -1.1 .
\end{eqnarray}
This value does not vary much in the range $0.5 <c_{L3}<0.6$. Note that
$c_{E3}$ is the most sensitive parameter and might be the easiest one
to test at the near future high energy experiments.
Finally, we examine the case where
the Majorana mass $m_M=\lambda_L \delta(z-1/k)$ is present at the UV brane.
It is known that the neutrinos can acquire a small Majorana mass via
bulk seesaw mechanism even
for a small $\lambda_L >10^{-11}$ \cite{Huber:2003sf},
\begin{eqnarray}
(M_\nu)_{ij} \simeq v_{W}^2 \sum_{kl} h^\nu_{ik} h_{jl}^\nu F_L(c_{Li})
F_R(c_{Nk})
M_{Rkl}^{-1} F_L(c_{Lj})
F_R(c_{Nl}).
\end{eqnarray}
The Majorana mass matrix can be written as
\begin{eqnarray}
M_{Rij} \simeq \frac{\lambda_{Lij}}{2} k F_R(c_{Ni})
F_R(c_{Nj})\epsilon^{-c_{Ni}-c_{Nj}+1} .
\end{eqnarray}
The assumption of the coupling universality for both boundaries,
$\lambda_{Lij}\sim \lambda_L$ leads,
\begin{eqnarray}
(M_\nu)_{ij} \simeq \frac{F_L(c_{Li}) F_L(c_{Lj}) v_{W}^2
}{\lambda_L T}
\epsilon^{ 2 c_{N1} },
\end{eqnarray}
where $c_{N1} = min\{c_{Ni}\}$.
The light neutrino mass is proportional to the charged
lepton mass square,
\begin{equation}
M_\nu=\eta^2 \epsilon^{2c_{N1}} C_L^{-2} M_e^2 ,
\end{equation}
where $ C_L\simeq F_R(c_{E3})$ and $\eta^2 \equiv v_{W}/ (\lambda_L T)$.
The lightest bulk neutrino mass becomes
\begin{equation}
c_{N1} \simeq \frac{ 10 +\ln(\eta C_L^{-1})}{\ln(T/k)}.
\end{equation}
If $\eta C_L^{-1}\sim 1$,
the bulk neutrino mass is $c_{N1}\simeq
-0.28$, which is quite different from the Dirac neutrino case. While the
charged lepton bulk mass is the same, the Majorana neutrino case contains much
larger bulk masses.
However,
to achieve the MNS matrix (\ref{Un}), $2n \mathrel{\raise.3ex\hbox{$<$\kern-.75em\lower1ex\hbox{$\sim$}}} 1.5$ is required
in Majorana neutrino case even for the maximally hierarchical
case ($m_1^\nu=0$). The condition yields $U_{e3} \sim 0.3 $ which is over the experimental bound
$0.16$. Even with the maximal ambiguity in the approximation, the value is
marginally allowed. It is difficult to match the current experimental data with
the Majorana neutrino in the almost universal Yukawa coupling model.
\section{Conclusions}
In the warped bulk SM, the fermion mixing and mass hierarchy can be induced from
the suppressed zero mode of KK field at the physical boundary.
In the case where the Yukawa couplings are almost universal to all bulk
fermions,
we can
determine the allowed regions of the bulk fermion masses through
the data of mixings and masses of the SM particles
with a simple analytic method.
If the Yukawa couplings of all SM fermions
are universal
and if there is no large cancellation in the multiplications
between the different fermion mixing matrices, the current experimental data
almost determine the bulk quark masses.
For the bulk lepton masses, it yield a wide range of solutions.
The existing data cannot narrow down the solution range much.
Still, a few interesting predictions have been found in the lepton sector.
One of them is that only the normal hierarchy is valid neutrino mass hierarchy in this
model. Another is the fact that it is favorable to consider the
light neutrinos are Dirac fermions. It is because that the seesaw mechanism in
this model generates too large $U_{e3}$.
One of the most notable predictions is on the MNS matrix component
$U_{e3}$ which is predicted to be $\sim 0.1$. This value
is not so far from the current experimental upper bound and can be tested by
neutrino oscillation experiments in
near future.
The bulk quarks and lepton masses may be explored at future high energy
colliders. The third generation of charged fermions
has significantly different features from others and thus can be a probe for
the bulk SM.
\acknowledgements
\noindent S.C. was supported
by the Korea Research Foundation Grant funded
by the Korean Government (MOEHRD) No. KRF-2005-070-C00030.
C.S.K. was supported
by the Korea Research Foundation Grant funded
by the Korean Government (MOEHRD) No. R02-2003-000-10050-0.
M.Y. was supported by the Scientific Grants from the Ministry
of Education, Science, Sports, and Culture of Japan, No.~16081202 and 17340062.
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
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//
// NSDate+Core.h
// test
//
// Created by Dao Duy Thuy on 4/14/14.
// Copyright BunLV 2014. All rights reserved.
// Provider : Dao Duy Thuy
//
#import <Foundation/Foundation.h>
@interface NSDate (TDCore)
// Relative dates from the current date
+ (NSDate *)td_dateTomorrow;
+ (NSDate *)td_dateYesterday;
+ (NSDate *)td_dateWithDaysFromNow:(NSInteger)days;
+ (NSDate *)td_dateWithDaysBeforeNow:(NSInteger)days;
+ (NSDate *)td_dateWithHoursFromNow:(NSInteger)dHours;
+ (NSDate *)td_dateWithHoursBeforeNow:(NSInteger)dHours;
+ (NSDate *)td_dateWithMinutesFromNow:(NSInteger)dMinutes;
+ (NSDate *)td_dateWithMinutesBeforeNow:(NSInteger)dMinutes;
// Comparing dates
- (BOOL)td_isEqualToDateIgnoringTime:(NSDate *)aDate;
- (BOOL)td_isToday;
- (BOOL)td_isTomorrow;
- (BOOL)td_isYesterday;
- (BOOL)td_isSameWeekAsDate:(NSDate *)aDate;
- (BOOL)td_isThisWeek;
- (BOOL)td_isNextWeek;
- (BOOL)td_isLastWeek;
- (BOOL)td_isSameMonthAsDate:(NSDate *)aDate;
- (BOOL)td_isThisMonth;
- (BOOL)td_isSameYearAsDate:(NSDate *)aDate;
- (BOOL)td_isThisYear;
- (BOOL)td_isNextYear;
- (BOOL)td_isLastYear;
- (BOOL)td_isEarlierThanDate:(NSDate *)aDate;
- (BOOL)td_isLaterThanDate:(NSDate *)aDate;
- (BOOL)td_isInFuture;
- (BOOL)td_isInPast;
// Date roles
- (BOOL)td_isTypicallyWorkday;
- (BOOL)td_isTypicallyWeekend;
// Adjusting dates
- (NSDate *)td_dateByAddingDays:(NSInteger)dDays;
- (NSDate *)td_dateBySubtractingDays:(NSInteger)dDays;
- (NSDate *)td_dateByAddingHours:(NSInteger)dHours;
- (NSDate *)td_dateBySubtractingHours:(NSInteger)dHours;
- (NSDate *)td_dateByAddingMinutes:(NSInteger)dMinutes;
- (NSDate *)td_dateBySubtractingMinutes:(NSInteger)dMinutes;
- (NSDate *)td_dateAtStartOfDay;
// Retrieving intervals
- (NSTimeInterval)td_minutesAfterDate:(NSDate *)aDate;
- (NSTimeInterval)td_minutesBeforeDate:(NSDate *)aDate;
- (NSTimeInterval)td_hoursAfterDate:(NSDate *)aDate;
- (NSTimeInterval)td_hoursBeforeDate:(NSDate *)aDate;
- (NSTimeInterval)td_daysAfterDate:(NSDate *)aDate;
- (NSTimeInterval)td_daysBeforeDate:(NSDate *)aDate;
- (NSInteger)td_distanceInDaysToDate:(NSDate *)anotherDate;
#pragma mark - Converter
/** Convert date to string with format, time zone = system timezone. */
- (NSString *)td_stringFromFormat:(NSString *)format;
/** Convert date to string with format, time zone = GMT+0 */
- (NSString *)td_utcStringFromFormat:(NSString *)format;
/** Convert date to string with format, custom time zone */
- (NSString *)td_stringFromFormat:(NSString *)format timeZone:(NSTimeZone *)timeZone;
/** Convert string to date with format, system time zone */
+ (NSDate *)td_dateFromString:(NSString *)str format:(NSString *)format;
/** Convert string to date with format, time zone = GMT+0 */
+ (NSDate *)td_utcDateFromString:(NSString *)str format:(NSString *)format;
/** Convert string to date with format, custom time zone */
+ (NSDate *)td_dateFromString:(NSString *)str format:(NSString *)format timeZone:(NSTimeZone *)timeZone;
// Decomposing dates
@property (readonly) NSInteger td_nearestHour;
@property (readonly) NSInteger td_hour;
@property (readonly) NSInteger td_minute;
@property (readonly) NSInteger td_seconds;
@property (readonly) NSInteger td_day;
@property (readonly) NSInteger td_month;
@property (readonly) NSInteger td_week;
@property (readonly) NSInteger td_weekday;
@property (readonly) NSInteger td_nthWeekday; // e.g. 2nd Tuesday of the month == 2
@property (readonly) NSInteger td_year;
@end
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 9,140
|
\section{Introduction}
\label{sec:intro}
Our main ingredient is a connected graph $G$ with vertex set $\vertices(G)$ typically identified with $[n]\coloneqq \{1,\dots,n\}$.
Attached to $G$ are two mathematical notions: its automorphism group $\aut{G}$, and the graphical matroid $M_G$ constructed from the (oriented) incidence matrix $\hat{X}_G$ with column vectors $e_i-e_j$ where $\{i<j\}$ is an edge of $G$.
It is classical that the bases of $M_G$ are in bijection with edge sets of spanning trees of $G$.
At the heart of this article are several spaces built using $\hat{X}_G$ that carry $\aut{G}$-representations which are non-obviously isomorphic. We link notions and ideas with genesis in approximation theory (work of Dahmen--Micchelli on splines \cite{DM85}), graph theory and tropical geometry (sandpile model and divisors on graphs, after \cite{ABKS14,BW18,PS03}), orbit-harmonics (as outlined by Kostant \cite{Kostant} and subsequently employed to great effect by the Macdonald polynomials community taking the cue from Garsia--Procesi \cite{GP92}), and Cohomological Hall algebras (work of Efimov \cite{Efi}, Kontsevich--Soibelman \cite{KS11}, Mozgovoy \cite{Mo13}, and Reineke \cite{Rei12} among others).
Figure~\ref{fig:big_picture} describes the main protagonists in this article and how they link. We proceed to discuss our results.
\begin{figure}
\includegraphics[scale=0.65]{big_picture_DT}
\caption{Summary of article}
\label{fig:big_picture}
\end{figure}
\subsection{Discussion of main results}
\label{subsec:discussion}
The first space is the \emph{central $P$-space} $\mc{P}(G)\coloneqq \mc{P}(\hat{X}_G)$. In general, the central $P$-space is attached to a collection $X$ of nonzero vectors and forms one half of a pair of spaces $(\mc{P}(X),\mc{D}(X))$.
These spaces were introduced and studied intensively by the approximation theory community in the 1980s in the context of splines; see \cite{dBHR93} for a book-length treatment, and to \cite[Section 1.2]{HR11} for brief yet insightful historical context. Our primary reference is the fantastic text of De Concini--Procesi \cite{DCP} that gives an in-depth survey of the variety of ways that the study of splines touches seemingly disparate areas in mathematics.
The space $\mc{D}(X)$ is called the \emph{Dahmen--Michelli space} and is the vector space dual to $\mc{P}(X)$.
The space $\mc{P}(X)$ was introduced later \cite{AA88, DR90} and turns out to be easier to work with. As we demonstrate in this article, the space
$\mc{P}(G)$ is hiding in Efimov's work \cite{Efi} resolving a conjecture of Kontsevich--Soibelman \cite{KS11}.
We denote the polynomial ring $\mathbb{Q}[x_1,\dots,x_n]$ in $n$ variables $x_1$ through $x_n$ by $\mathbb{Q}[\bfx{n}]$.
Our second space is a quotient $\mathbb{Q}[\bfx{n}]/\mc{I}(G)$.
Here $\mc{I}(G)$ is a homogeneous ideal generated by powers of certain linear forms determined from $G$.
These ideals are instances of \emph{power ideals}, whose general theory was developed in work of Ardila--Postnikov \cite{AP10} beautifully bringing results obtained and phenomena observed by various authors (for instance \cite{Be10,DM85,HR11,OT94,PS06, SX10, Te02}) under the same umbrella.
Like $\mc{P}(X)$, there is a power ideal $\mc{I}(X)$ defined for collections of nonzero vectors $X$.
In fact, $\mc{P}(X)$ is the Macaulay-inverse to the ideal $\mc{I}(X)$, and this will be pertinent for our purposes.
The quotient $\mathbb{Q}[\bfx{n}]/\mc{I}(G)$ has been called the \emph{central zonotopal algebra} by Holtz--Ron \cite[Section 3]{HR11}.
It is known \cite{PS03} that the central zonotopal algebra has a monomial basis indexed by \emph{$G$-parking functions}, which are essentially the same as \emph{$q$-reduced divisors} \cite{BN07,BS13}.
These combinatorial objects are in bijection with the set of spanning trees of $G$.
Closely related to these divisors are the \emph{\textup{(}integral\textup{)} break divisors}, and these are the ones relevant to our purposes.
Our point of departure is the fact that spanning trees on $G$ are also in bijection with break divisors on $G$ \cite{ABKS14,MZ08}; see \cite{BBY19,Yu17} for an in-depth study of \emph{geometric} bijections that arise in this framework.
A first hint that the set of break divisors $\brkd(G)$ holds interesting representation-theoretic phenomena comes from considering the case where $G$ is the complete graph $K_n$.
Then $|\brkd(K_n)|=n^{n-2}$, and the fact that $\aut{K_n}$ is the symmetric group $S_n$ translates to $\brkd(K_n)$ carrying an ungraded $S_n$-representation. Given the numerology, one naturally suspects a link to the classical parking function representation $\mathrm{PF}_{n-1}$ \cite{Hai94} of $S_{n-1}$.
Indeed, as shown in \cite{KST21}, and more generally in \cite{KRT21}, the $S_n$ action on $\brkd(K_n)$ when restricted to $S_{n-1}$ is isomorphic to $\mathrm{PF}_{n-1}$; in other words, the $S_n$-representation $\brkd(K_n)$ `extends the parking space'. This allows us establish a link with one of main motivations for this article\textemdash{}
Berget--Rhoades had already proposed a (graded) extension to $\mathrm{PF}_{n-1}$ using the \emph{slim subgraph space} of Postnikov--Shapiro \cite{PS03}.
Konvalinka--Tewari \cite[Conjecture 3.3]{KT21} conjectured that $\brkd(K_n)$ as an ungraded representation is isomorphic to the Berget--Rhoades extension.
In particular, this would imply that the ungraded Frobenius characteristic of the Berget--Rhoades extension is $h$-positive, which is not at all immediate.
In view of these results, it is natural to inquire about the case of more general graphs.
Surprisingly, the method of \emph{orbit harmonics} allows us to tie these various strands together. Briefly put, one first interprets divisors in $\brkd(G)$ as lattice points in $\mathbb{Q}^n$. One can attach a quotient $\mathbb{Q}[\bfx{n}]/\mathsf{T}(G)$, where the ideal $\mathsf{T}(G)$ is homogenous, carrying a graded
$\aut{G}$-representation.
We have the isomorphism $\mathbb{Q}[\brkd(G)] \cong \mathbb{Q}[\bfx{n}]/\mathsf{T}(G)$ of ungraded $\aut{G}$-modules, so that
$\mathbb{Q}[\bfx{n}]/\mathsf{T}(G)$ gives a graded refinement of the permutation module $\mathbb{Q}[\brkd(G)]$.
This ideal $\mathsf{T}(G)$ surprisingly turns out to equal the power ideal $\mc{I}(G)$ defining the central zonotopal algebra earlier.
Here is our first main result.
\begin{theorem}[restatement of Theorem~\ref{thm:piecing_things}]
\label{thm:main_1}
We have the following isomorphisms and equalities of ungraded $\aut{G}$-modules
\[
\mathbb{Q}[\brkd(G)]\cong \mathbb{Q}[\bfx{n}]/\mathsf{T}(G) = \mathbb{Q}[\bfx{n}]/\mc{I}(G) \cong \mc{P}(G),
\]
where the middle equality and right isomorphism are in the category of graded $\aut{G}$-modules.
\end{theorem}
In a completely different direction, the case $G=K_n$ again provides some tantalizing hints by way of the following fact.
The number of orbits under the $S_n$-action on $\brkd(K_n)$ equals the numerical Donaldson--Thomas (DT) invariant $\mathrm{DT}_{Q,(n)}$ where $Q$ is the $2$-loop quiver and the dimension vector is $(n)$; see \cite[Theorem 3.7]{KRT21}.
\emph{What is the underlying reason for why this is the case, or is this coincidence purely numerological?}
As we now describe, this story permits a generalization to numerical DT invariants of symmetric quivers $Q$.
We work under the assumption that $Q$ has at least one loop at each vertex, i.e. \emph{has enough loops}. Given a dimension vector $\gamma$, we associate a connected graph $G_{Q,\gamma}$. All our spaces mentioned before make sense for $G_{Q,\gamma}$, even if it is unclear what they are good for.
Efimov \cite[Section 3]{Efi} describes an algebraic construction for a vector space $V$ that freely generates the cohomological Hall algebra $\mc{H}$ of a symmetric quiver $Q$. The space $V$ is built out of various graded spaces $V_{\gamma}^{\prim}$ as $\gamma$ varies over all dimension vectors for $Q$. For a fixed $\gamma$, the dimensions of the graded pieces $V_{\gamma,k}^{\prim}$ give the coefficients of the \emph{quantum} DT invariant $\tilde{\Omega}_{\gamma}(q)$, and the sum of these coefficients, i.e. the evaluation of $\tilde{\Omega}_{\gamma}$ at $q=1$, is the numerical DT invariant $\mathrm{DT}_{Q,\gamma}$.
Each space $V_{\gamma}^{\prim}$ is itself the space of $S_{\gamma}\coloneqq S_{\gamma_1}\times \cdots \times S_{\gamma_k}$ invariants of a larger space that we call $W_{\gamma}$.
We emphasize here that this larger space plays no role in \cite{Efi}.
It turns out that `combinatorializing' Efimov's construction using the graph $G_{Q,\gamma}$ results in exactly studying the space of $S_{\gamma}$-invariants of slim subgraph space $\mc{P}(G_{Q,\gamma})$. In fact, $G_{Q,\gamma}$ is such that $S_{\gamma}$ is a subgroup of $\aut{G_{Q,\gamma}}$. This allows us to put the chain of isomorphisms in Theorem~\ref{thm:main_1} to good effect and obtain:
\begin{theorem}[restatement of Theorems~\ref{thm:graded_multiplicity_quantum_DT} and~\ref{thm:numerical_dt_break}]
\label{thm:main_2}
The dimensions of the graded pieces of $\mathcal{P}(G_{Q,\gamma})^{S_{\gamma}}$ are the coefficients of the quantum DT invariant $\tilde{\Omega}_{\gamma}(q)$. In particular, the numerical DT invariant $\mathrm{DT}_{Q,\gamma}\coloneqq \tilde{\Omega}_{\gamma}(1)$ equals the number of $S_{\gamma}$-orbits on $\brkd(G)$.
\end{theorem}
Theorem~\ref{thm:main_2} gives, to the best of our knowledge, the first manifestly nonnegative combinatorial interpretation for $\mathrm{DT}_{Q,\gamma}$.
It bears emphasizing that this combinatorial interpretation relies crucially on employing orbit harmonics to the point set determined by break divisors, and this is the novelty of our approach.
An algebraic interpretation for $\tilde{\Omega}_{\gamma}(q)$ distinct from that in Theorem~\ref{thm:main_2} was given in the groundbreaking work of Hausel--Letellier--Rodriguez-Villegas \cite{HLRV13} settling a conjecture of Kac \cite{Ka83}.
Recently two other interesting interpretations for $\tilde{\Omega}_{\gamma}(q)$ have been given \cite{DFR21,DM21}, both of which identify the coefficients as the dimensions of some graded piece in an algebra. The objects involved are vertex algebras, and deriving our combinatorial interpretation from these interpretations does not appear to be straightforward.
It would be an interesting endeavor relating these approaches to ours.
\smallskip
\noindent \textbf{Outline of the article.}
Section~\ref{sec:central_zonotopal} introduces the central $P$-space as well as the central zonotopal algebra. Sections~\ref{subsec:graphic_matroid} and \ref{subsec:variations} discuss the only vector configurations that concern us. In this setting, the central $P$-space is the slim subgraph space of Postnikov--Shapiro.
In Section~\ref{sec:orbit_harmonics}, we recall the notion of break divisors, recount the method of orbit harmonics, and assemble the pieces to prove our first main result (Theorem~\ref{thm:main_1} above).
We digress briefly in Section~\ref{subsec:more_orbit_harmonics} and realize internal and external zonotopal algebras by applying orbit harmonics to orientable divisors.
We describe Efimov's construction in Section~\ref{subsec:quantum_dt}, and in Section~\ref{subsec:symmetric_matrix_to_graph} introduce the covering graph $G_{Q,\gamma}$ whose slim subgraph space encodes quantum DT-invariants, thereby establishing the first half of Theorem~\ref{thm:main_2}. The second half is established in Section~\ref{subsec:numerical_DT}.
Section~\ref{sec:applications} discusses applications of a representation-theoretic flavor.
\section{Central zonotopal algebras}
\label{sec:central_zonotopal}
Let $X\subset \mathbb{R}^n$ be a finite set of nonzero vectors such that $\mathrm{span}(X)=\mathbb{R}^n$.
With $v=(v_1,\dots,v_n)\in \mathbb{R}^n$ we attach the linear form $p_v\coloneqq v_1x_1+\cdots+v_nx_n$, and subsequently define for $Y\subseteq X$ the polynomial
\begin{align}
p_Y=\prod_{y\in Y}p_y.
\end{align}
A \emph{cocircuit} in $X$ is a minimal-under-inclusion subset $Y$ such that $X\setminus Y$ does not contain a basis for $\mathbb{R}^n$.
The \emph{cocircuit ideal} $I(X)$ is defined as
\begin{align}
\label{eq:def_cocircuit_ideal}
I(X)\coloneqq \langle p_Y\;|\; Y\subseteq X \text{ a cocircuit}\rangle.
\end{align}
Observe that we could also have defined $I(X)$ to be generated by \emph{all} $p_Y$ where $Y\subseteq X$ are such that $X\setminus Y$ does not contain a basis for $\mathbb{R}^n$. All such elements are multiples of $p_Y$ for $Y$ a cocircuit.
Define the \emph{central $P$-space} associated to $X$ as
\begin{align}
\mc{P}(X)\coloneqq \mathbb{Q}\left\lbrace p_Y\;|\; \mathrm{rank}(X\setminus Y)=n\right\rbrace.
\end{align}
In other words, $\mc{P}(X)$ is the span of all $p_Y$ over subsets $Y\subset X$ such that $X\setminus Y$ contains a basis.
Let $b(X)$ denote the number of bases in $X$.
We then have the following important results:
\begin{enumerate}
\item $\mathbb{Q}[\bfx{n}]=\mc{P}(X)\oplus I(X)$ \cite{DR90},
\item $\dim \mc{P}(X)=b(X)$ \cite[Corollary 2.17]{dBDR91}.
\end{enumerate}
See also \cite[Theorem 3.8]{HR11} for these statements in one place.
Recall that with a graded vector space $A\coloneqq \bigoplus_{d\geq 0}A_d$ one can attach its \emph{Hilbert series} $\hilb(A)$ as follows:
\begin{align}
\hilb(A)=\sum_{d\geq 0}\dim(A_d)q^d.
\end{align}
Since $\mc{P}(X)$ is graded by degree, one may ask for its Hilbert series (or equivalently for that of the quotient $\mathbb{Q}[\bfx{n}]/I(X)$). This is described in terms of the Tutte polynomial $T_{X}(x,y)$ of the linear matroid determined by $X$.
One definition of $T_{X}(x,y)$ involves the notion of internal and external activity.
We will only need the latter for the Hilbert series we are interested in.
Endow the vectors in $X$ with a total order.
For any basis $B$ in $X$, we say that $v\in X\setminus B$ is \emph{externally active} if $v$ is the smallest element in the minimal dependent subset of $B\cup \{v\}$.
Let the total number of externally active elements with respect to $B$ be $\mathrm{ea}(B)$.
Then we have the following result (see \cite[Proposition 4.14]{AP10} or \cite[Theorem 11.8]{DCP}, both of which apply to the quotient $\mathbb{Q}[\bfx{n}]/\mc{I}(X)$):
\begin{align}
\label{eq:hilb_p(x)}
\hilb(\mc{P}(X))&=\sum_{\text{ bases } B\subset X}q^{|X|-\mathrm{rank}(X)-\mathrm{ea}(B)}\nonumber\\&=
q^{|X|-\mathrm{rank}(X)}T_X(1,q^{-1}).
\end{align}
As mentioned in the introduction, $\mc{P}(X)$ may also be described as a Macaulay-inverse to a \emph{power ideal} determined by $X$. We proceed to describe this next.
Let $H$ be any \emph{hyperplane} in $X$. Recall that a hyperplane is a maximal collection of vectors in $X$ whose span is $(n-1)$-dimensional. This necessarily determines a linear form $\phi_H$ that vanishes on $H$. Let $m_H\coloneqq m_H(X)$ equal the number of vectors in $X$ that do not lie on $H$.
Consider the ideal $\mc{I}(X)$ (see \cite[Section 3.1]{HR11} or \cite[Section 4.1]{AP10}) defined as
\begin{align}
\label{eq:def_power_ideal}
\mc{I}(X)\coloneqq \langle \phi_H^{m_H} \;|\; H\text{ a hyperplane in } X\rangle.
\end{align}
Let $\partial_i=\frac{\partial}{\partial x_i}$.
We then have (\cite[Theorem 3.8 (5)]{HR11}, \cite[Theorem 2.7]{dBDR91}, or \cite[Theorem 11.25]{DCP}):
\begin{align}
\mc{P}(X) = \{f\in \mathbb{Q}[\bfx{n}]\;|\; p(\partial_1,\dots,\partial_n)f=0 \,\forall p\in \mc{I}(X)\},
\end{align}
which says that $\mc{P}(X)$ is the Macaulay-inverse to $\mc{I}(X)$.
\begin{example}
\label{ex:central_p_space}
\emph{
Suppose $X$ is the collection of vectors in $\mathbb{R}^2$ determined by the columns of
\[
X=\left[\begin{array}{ccc}1 & 0 & 1\\ 0 & 1 & -1\end{array}\right].
\]
Let us refer to the vectors read from left to right as $v_1$, $v_2$, and $v_3$, and assume the total order $v_1<v_2<v_3$.
The cocircuits are $\{v_1,v_2\}$, $\{v_1,v_3\}$, and $\{v_2,v_3\}$. Thus
\[
I(X)=\langle x_1x_2, x_1(x_1-x_2),x_2(x_1-x_2) \rangle.
\]
One checks that
\[
\mc{P}(X)=\mathbb{Q}\{1,x_1,x_2\}.
\]
Observe that one can extract exactly 3 bases for $\mathbb{R}^2$ from $X$ and that $\dim(\mc{P}(X))=3$. Additionally, we have
\[
\hilb(\mc{P}(X))=1+2q=q^{3-2}(2+q^{-1}),
\]
and so the right-hand side agrees with $qT_X(1;q^{-1})$. Indeed, there are two bases $B$ with $\mathrm{ea}(B)=0$ (i.e. \emph{unbroken bases}) and one with $\mathrm{ea}(B)=1$.
}
\emph{Note further that every vector is also a hyperplane in $X$ and the line spanned by any vector does not contain the remaining two vectors. Thus
\[
\mc{I}(X)=\langle x_1^2, x_2^2, (x_1+x_2)^2\rangle.
\]
We leave it to the reader to check that $\mc{P}(X)$ above is indeed the Macaulay-inverse to $\mc{I}(X)$.}
\end{example}
\subsection{The graphical matroid}
\label{subsec:graphic_matroid}
Let $G$ be a connected graph where we allow multiple edges between distinct vertices but forbid self-loops. This assumption will be implicit throughout the article.
Denote the set of edges (respectively vertices) of $G$ by $\edges(G)$ (respectively $\vertices(G)$). We begin by recalling some standard graph-theoretic jargon; see \cite{BM76} for one source.
Given a nonempty proper subset $S\subset \vertices \coloneqq \vertices(G)$, we denote by $G[S]$ the graph induced on vertices in $S$.
We define the \emph{edge cut} $\partial(S)$ of $G$ associated to $S$ to be the set of edges with one endpoint in $S$ and the other in $\bar{S}\coloneqq \vertices \setminus S$.
We denote the cardinality of $\partial(S)$ by $d(S)$.
We denote the set of cuts by $\cuts(G)$.
A minimal non-empty edge cut is called a \emph{bond}.
We denote the set of bonds by $\bonds(G)$.
The following property \cite[Exercise 2.2.8]{BM76} of bonds in connected graphs is relevant for us: given a nonempty proper $S\subset \vertices$, the cut $\partial(S)$ is a bond if and only if $G[S]$ and $G[\bar{S}]$ are both connected.
We now isolate the case of our interest.
Consider the set of vectors $X_G$ determined by a connected graph $G$ on the vertex set $[n]$.
Let $e_i$ denote the $i$th standard basis vector in $\mathbb{R}^n$.
For any edge $\{i,j\}\in \edges(G)$ where $i<j$, the vector $e_i-e_j$ belongs to $X_G$ (as many times as there is an edge between $i$ and $j$).
Include the vector $e_1+\cdots+e_n$ as well, thereby
ensuring $\mathrm{span}(X_G)=\mathbb{R}^n$.
Suppose $Y\subset X_G$ is such that the corresponding set of edges in $G$ has the property that its complement in $\edges(G)$ results in a connected subgraph of $G$.
We say that $Y$ (or the subgraph in $G$ determined by the associated set of edges) is \emph{slim}.
It is clear that if $Y$ is slim, then $X_G\setminus Y$ contains a basis for $\mathbb{R}^n$.
Indeed one only needs to take a spanning tree in the complement (which is connected) and throw in the vector $e_1+\cdots+e_n$ to get a basis. In particular, slim subgraphs do not give cocircuits.
Recall that a cocircuit is a minimal subset $Y\subset X_G$ such that $X_G\setminus Y$ does not contain a basis.
Clearly, $e_1+\cdots+e_n$ is a cocircuit.
It is straightforward to see that all other cocircuits correspond to collections of vectors corresponding to edges of bonds in $G$.\footnote{Put differently, a bond is code for \emph{minimally non-slim}.}
In summary we have
\begin{align}
I(G)\coloneqq I(X_G)=\langle x_1+\cdots+x_n, p_Y \text{ for } Y \text{ a bond}\rangle.
\end{align}
We thus have
\begin{align}
\mc{P}(G)\coloneqq \mc{P}(X_G)= \mathbb{Q}\{p_Y\;|\; Y \text{ slim}\}.
\end{align}
We will refer to $\mc{P}(G)$ as the \emph{\textup{(}Postnikov--Shapiro\textup{)} slim-subgraph space} of $G$.
Standard matroid-theoretic techniques allow us to extract a basis for this space after endowing the set of edges with a total order and consider externally active edges for spanning trees.
We now describe the power ideal $\mc{I}(G)\coloneqq \mc{I}(X_G)$ as well. To this end we need to describe all hyperplanes in $X_G$, i.e. all maximal subsets of $X_G$ such that the resulting rank is $n-1$.
These are exactly the complements of cocircuits.
Henceforth set $x_S\coloneqq \sum_{i\in S}x_i$.
Consider first the cocircuit $Y$ determined by $e_1+\cdots+e_n$. The vectors in the complement $X_G\setminus Y$ all lie on the hyperplane $x_{[n]}=0$. Thus we get that $x_{[n]}\in \mc{I}(G)$.
Now consider the cocircuit determined by vectors corresponding to edges of a cut $\partial(S)$.
It is immediate that collection of vectors in $X_G\setminus Y$ all lie on the hyperplane
\begin{align*}
|\bar{S}|\sum_{i\in S}x_i-|S|\sum_{i\in \bar{S}}x_i=0.
\end{align*}
Taking into account that $x_{[n]}\in\mc{I}(G)$, we thus infer that
$x_{S}^{d(S)}\in \mc{I}(G)$,
and, by symmetry, that
$x_{\bar{S}}^{d(S)}\in \mc{I}(G)$.
We have thus obtained the following presentation:
\begin{align}
\mc{I}(G)=\langle x_{[n]}, x_S^{d(S)} \text{ where $\partial(S)\in\bonds(G)$}\rangle.
\end{align}
\begin{example}
\emph{Consider $G$ in Figure~\ref{fig:k4-e} with $\vertices(G)=[4]$. Then $X_G$ is:
\begin{align*}
\left[\begin{array}{cccccc}1 & 1 &0 &0 &0 & 1\\
-1 & 0 &1 &1 &0 & 1\\
0 & 0 &-1 &0 &1 & 1\\
0& -1 &0 &-1 &-1 & 1\\
\end{array}\right].
\end{align*}
In this case, we have
\[
\mc{I}(G)=\langle x_1^2,x_2^3,x_3^2,x_4^3, (x_1+x_2)^3,(x_1+x_4)^3,x_1+x_2+x_3+x_4\rangle.
\]
It may be checked that
\[
\hilb\left(\mathbb{Q}[\bfx{4}]/\mc{I}(G)\right)=1+3q+4q^2,
\]
which evaluates to $8$ at $q=1$. The latter is also the number of spanning trees of $G$.
}
\end{example}
\begin{figure}
\includegraphics[scale=0.7]{k4-e.pdf}
\caption{The graph $K_4-\text{edge}$.}
\label{fig:k4-e}
\end{figure}
The quotient $\mathbb{Q}[\bfx{n}]/\mc{I}(G)$ is essentially what Postnikov--Shapiro \cite[\S 3]{PS03} call $\mc{B}_G$ in their seminal article, even though the presentation here appears different.
Indeed, the Postnikov--Shapiro ideal only involves the variables $x_1$ through $x_{n-1}$, but this may be achieved by eliminating the variable $x_n$ given the linear relation $x_1+\cdots+x_n\in \mc{I}(G)$.
Other than that, observe that Postnikov--Shapiro consider linear forms coming from \emph{all} subsets $S\subseteq[n-1]$ whereas we have only included those $S$ that give rise to bonds $\partial(S)$.
It turns out that the resulting ideals are in fact the same; this follows from applying \cite[Theorem 4.17]{AP10} with $\mc{A}$ equal to the collection of vectors coming from edges of $G$ and $k$ equal to $-1$.\footnote{This is the value of $k$ that corresponds to the central zonotopal algebra. The cases $k=0$ and $k=-2$ give the \emph{external} and \emph{internal} zonotopal algebras respectively.}
Postnikov and Shapiro give a monomial basis for $\mc{B}_G$ indexed by \emph{$G$-parking functions} \cite[Theorem 3.1]{PS03}, and show that the Hilbert series is a specialization of the Tutte polynomial of $G$ \cite[Theorem 3.3]{PS03}.
It is also known that \emph{$G$-parking functions} are \emph{$q$-reduced divisors} on $G$ (once a distinguished vertex $q$ is chosen); it is a different set of divisors on graphs that is relevant for our purposes and we introduce those in Section~\ref{sec:orbit_harmonics}.
\subsection{Two variations on this theme}
\label{subsec:variations}
Our treatment of the graphical matroid is slightly non-standard, and we discuss two other ways in which it is usually presented. As we hope to demonstrate, all perspectives have their benefits.
In the first perspective, for a connected graph $G$ with $\vertices(G)$ identified with $[n]$, one constructs an $n\times |\edges(G)|$ matrix with $e_i-e_j$ for edge $\{i<j\}\in \edges(G)$. This is a rank $n-1$ matrix with columns in $\mathbb{R}^n$. If one strikes out the last row (i.e. the row corresponding to the vertex $n$ in $G$), then one obtains a full rank matrix with columns in $\mathbb{R}^{n-1}$. If we denote this collection of vectors in $\mathbb{R}^{n-1}$ by $\check{X}_G$, then it is not hard to verify that the power ideal $\check{\mc{I}}(G)\coloneqq \mc{I}(\check{X}_G) \subset \mathbb{Q}[x_1,\dots,x_{n-1}]$ has the following presentation:
\begin{align}
\check{\mc{I}}(G)=\langle x_S^{d(S)} \text{ where $\partial(S)$ is a bond with $S\subseteq [n-1]$}\rangle.
\end{align}
From this we have the following isomorphism
\begin{align}
\label{eq:strike_out_last_row}
\mathbb{Q}[\bfx{n}]/\mc{I}(G) \cong \mathbb{Q}[\bfx{n-1}]/\check{\mc{I}}(G),
\end{align}
with the latter being more in the spirit of \cite{PS03}. The reader is welcome to check that Example~\ref{ex:central_p_space} applies this construction with $G$ equal to $K_3$. We record an observation here (to be addressed in more detail later): for $G=K_n$, the quotient on the right hand side carries an $S_{n-1}$-action, but `hides' the $S_n$-action, unlike the quotient on the left hand side.
\begin{remark}
\emph{There is nothing special about striking out the last row. Indeed one can strike out \emph{any} row and obtain a rank $n-1$ matrix that determines an isomorphic matroid, and a quotient isomorphic to that in~\eqref{eq:strike_out_last_row}.}
\end{remark}
We now describe our second perspective. The reader may find our insistence on working with a collection of vectors $X$ in $\mathbb{R}^n$ that span $\mathbb{R}^n$ as stringent.
Indeed as discussed in the beautiful book of De Concini--Procesi \cite{DCP}, one can work with a collection $X$ that spans an $s$-dimensional real space $V$. All results in this section still hold with the simple adjustment that one work with polynomial functions on $V$ (in the case $V=\mathbb{R}^n$, this translates to working in $\mathbb{Q}[\bfx{n}]$.)
With this guidance, we now return to our collection $\hat{X}_G\coloneqq X_G\setminus \{e_1+\cdots+e_n\}$. In other words we omit the vector that was added to ensure $\mathrm{span}(X_G)=\mathbb{R}^n$. Since $G$ is connected, we have that $\mathrm{span}(\hat{X}_G)$ is the hyperplane $V$ in $\mathbb{R}^n$ cut out by $x_1+\cdots+x_n=0$.
The ring of regular functions on $V$ can be identified by the polynomial ring $\mathbb{Q}[x_i-x_j\;|\; i<j]$.
We now have
\begin{align}
\hat{I}(G)\coloneqq I(\hat{X}_G)&=\langle p_Y \text{ for } Y \in \bonds(G)\rangle\\
\mc{P}(G)=\mc{P}(\hat{X}_G)&=\mathbb{Q}\{p_Y\;|\; Y \text{ slim}\}.
\end{align}
Note here that the ideal $\hat{I}(G)$ is taken in $\mathbb{Q}[x_i-x_j\;|\; i<j]$.
By the general result \cite[Corollary 11.23]{DCP}, we have the direct sum decomposition
\begin{align}
\label{eq:central_p_decomposition}
\mathbb{Q}[x_i-x_j\;|\; i<j]=\mc{P}(G)\oplus \hat{I}(G).
\end{align}
Note that the $\mathbb{Q}$-vector spaces $\mc{P}(X_G)$ and $\mc{P}(\hat{X}_G)$ are in fact the same, which is why we have chosen to refer to both as $\mc{P}(G)$.
In summary, throwing in the vector $e_1+\cdots+e_n$ is harmless to our story, and omitting it will make the link to Efimov's construction in the context of the COHA of symmetric quivers a bit more transparent.
\section{Orbit harmonics and break divisors}
\label{sec:orbit_harmonics}
\subsection{Break divisors}
Let $G$ be a connected graph.
We define the \emph{genus} of $G$ to be $g(G)\coloneqq |\edges(G)|-|\vertices(G)|+1$.
A \emph{divisor} $D$ on $G$ is an assignment $D:\vertices(G)\to \mathbb{Z}$.
The sum $\sum_{v\in \vertices(G)}D(v)$ is called the \emph{degree} of $D$ and denoted by $\deg(D)$.
If $D(v)\geq 0$ for all $v\in \vertices(G)$, then we say that $D$ is \emph{effective}.
If $H$ is a connected subgraph of $G$, then a divisor $D$ on $G$ naturally restricts to a divisor $D|_H$ on $H$.
An effective divisor $D$ of degree $g(G)$ is said to be a \emph{break} divisor if for every connected subgraph $H$ of $G$ we have
\begin{align}
\deg(D|_H)\geq g(H).
\label{eq:def_break_divisor}
\end{align}
We denote by $\brkd(G)$ the set of break divisors on $G$.
It is known that $|\brkd(G)|$ equals the number of spanning trees on $G$ \cite[Theorem 4.25]{ABKS14}.
By identifying $\vertices(G)$ with $[n]$, we can, and will, interpret elements of $\brkd(G)$ as lattice points in $\mathbb{R}^{n}$.
Consider the \emph{graphical zonotope} $\mc{Z}_G\in\mathbb{R}^n$ determined by $G$ by consider the Minkowski sum of line segments $[e_i,e_j]$ for every edge $\{i,j\}\in E(G)$.
Let $\Delta_{n-1,n}$ denotes the $(n-1)$-th hypersimplex determined by taking the convex hull of the $S_n$-orbit of the point $(1^{n-1},0)\in \mathbb{R}^n$.
This given, break divisors are lattice points in the \emph{trimmed graphical zonotope} $\mc{Z}_G-\Delta_{n-1,n}$ \cite[Proposition 2.1]{KRT21}.
\begin{example}
\label{ex:break_divisors_orbits}
\emph{
Consider the graph $G$ in Figure~\ref{fig:k23}.
Elements of $\brkd(G)$ are tuples $(a,b,c,d,e)\in \mathbb{Z}_{\geq 0}^5$ that satisfy \eqref{eq:def_break_divisor}.
Any subgraph that is a tree gives a trivial constraint. Furthermore, note the $S_2\times S_3$ symmetry in $G$. So given any break divisor we can permute $a$ and $b$ (respectively $c$, $d$, and $e$) to get another break divisor. Thus (up to $S_2\times S_3$ symmetry) the only relevant inequality is
\begin{align*}
a+b+c+d\geq 1
\end{align*}
on top of the equality $a+b+c+d+e=2$. In summary we obtain four orbit representatives for $S_2\times S_3$-action on $\brkd(G)$:
\begin{align*}
(2,0,0,0,0), (1,1,0,0,0), (1,0,1,0,0), (0,0,1,1,0).
\end{align*}
We thus obtain $|\brkd(G)|=12$, which agrees with the number of spanning trees of $G$.\footnote{Recall that the number of spanning trees of the complete bipartite graph $K_{m,n}$ equals $m^{n-1}n^{m-1}$.}}
\end{example}
\begin{figure}
\includegraphics[scale=0.8]{k23.pdf}
\label{fig:k23}
\caption{The complete bipartite graph $K_{2,3}$.}
\end{figure}
In the example earlier, we incorporated the $S_2\times S_3$ symmetry into our computation to make things concise. In general, from the inequalities defining break divisors, it is clear that $\aut{G}$ acts on $\brkd(G)$ by permutations.\footnote{It is entirely possible that a larger group acts on $\brkd(G)$. For instance if one takes an $n$-cycle, then $\aut{G}$ is the cyclic group $\mathbb{Z}/n\mathbb{Z}$. On the other hand, the set of break divisors is given by the vertices of the standard simplex, and thus enjoys $S_n$-symmetry.}
The situation is ideal for invoking the method of orbit harmonics.
\subsection{Orbit harmonics}
The method of {\em orbit harmonics} gives a technique for turning an ungraded permutation representation of some linear group $\mathscr{G}$
acting on a finite point
locus $Y$ into a graded $\mathscr{G}$-module.
Orbit harmonics was introduced by Kostant \cite{Kostant} and has seen subsequent application (for example)
by Garsia--Procesi \cite{GP92} in the context of Springer fibers and by
Haglund--Rhoades--Shimozono \cite{HRS18} in the context of Macdonald-theoretic delta
operators. See \cite{Rh22} for a survey of recent developments.
Consider a finite point set $Y \subset \mathbb{Q}^n$ and let $\mathsf{I}(Y) \subseteq \mathbb{Q}[x_1, \dots, x_n]$
be the ideal of polynomials which vanish on $Y$. The quotient of $\mathbb{Q}[x_1, \dots, x_n]$ by the ideal
$\mathsf{I}(Y)$ has vector space dimension $\dim_{\mathbb{Q}}\left(\mathbb{Q}[\bfx{n}]/\mathsf{I}(Y)\right)=|Y|$.
If the set $Y$ is $\mathscr{G}$-stable for some group $\mathscr{G}\subset \mathrm{GL}_n(\mathbb{Q})$, then we have an isomorphism of ungraded
$\mathscr{G}$-modules
\[
\mathbb{Q}[\bfx{n}]/\mathsf{I}(Y)\cong_{\mathscr{G}} \mathbb{Q}[Y].
\]
Orbit harmonics produces a quotient that will afford the structure of a {\em graded} $\mathscr{G}$-module.
Given a nonzero polynomial $f \in \mathbb{Q}[x_1, \dots, x_n]$, let $\tau(f)$ be the top degree homogeneous component of $f$.
That is, if $f = f_d + \cdots + f_1 + f_0$ with $f_i$ homogeneous of degree $i$ and $f_d \neq 0$, then we have $\tau(f) = f_d$.
Define an ideal $\mathsf{T}(Y) \subseteq \mathbb{Q}[\bfx{n}]$ by
\[
\mathsf{T}(Y) = \langle \tau(f) \,:\, f \in \mathsf{I}(Y), \, \, f \neq 0 \rangle.
\]
The $\mathscr{G}$-module isomorphism given above extends to a chain
\[
\mathbb{Q}[\bfx{n}]/\mathsf{T}(Y) \cong_{\mathscr{G}}
\mathbb{Q}[\bfx{n}]/\mathsf{I}(Y)\cong_{\mathscr{G}} \mathbb{Q}[Y],
\]
with the added feature that the left hand side is a graded $\mathscr{G}$-module.
\subsection{Applying orbit harmonics to $\brkd(G)$}
\label{subsec:gp_to_brkd}
Throughout this subsection, our group $\mathscr{G}$ will be the automorphism group $\aut{G}$ of our graph $G$ and our point set $Y$
carrying the $\aut{G}$ action will be the set $\brkd(G)$ of break divisors of $G$.
For brevity we will refer to the ideals $\mathsf{I}(\brkd(G))$ and $\mathsf{T}(\brkd(G))$ by $\mathsf{I}(G)$ and $\mathsf{T}(G)$ respectively.
Our strategy is as follows.
\begin{enumerate}
\item Produce a family of polynomials indexed by $\bonds(G)$ that vanish on $\brkd(G)$.
\item Consider $\tilde{\mathsf{T}}(G)$ the ideal generated by top degree homogeneous summands from the polynomials in the aforementioned family.
\item Use the inclusion $\tilde{\mathsf{T}}(G) \subset \mathsf{T}(G)$ to infer on the one hand that
\[
\dim\left(\mathbb{Q}[\bfx{n}]/\tilde{\mathsf{T}}(G)\right) \geq \dim\left(\mathbb{Q}[\bfx{n}]/\mathsf{T}(G)\right).
\]
On the other hand, it will transpire that the $\tilde{\mathsf{T}}(G)$ equals the power ideal $\mc{I}(G)$ and thus its dimension equals the number of spanning trees in $G$. Additionally, the right hand side equals $|\brkd(G)|$. This will allow us to conclude that $\tilde{\mathsf{T}}(G)=\mathsf{T}(G)$.
\end{enumerate}
\begin{proposition}
\label{prop:GP_break_divisors}
We have the equality of ideals
\[
\mathsf{T}(G)=\mc{I}(G).
\]
\end{proposition}
\begin{proof}
As before, set $x_S\coloneqq \sum_{i\in S}x_i$ for $S\subset \vertices(G)=[n]$.
Since the degree of any break divisor is $g(G)$, we know that $x_{[n]}-g(G)\in \mathsf{I}(G)$.
Now consider a nonempty proper $S\subset \vertices(G)$ such that $\partial(S)\in \bonds(G)$. We will be interested in the values $x_S(p)$ as $p$ ranges over $\brkd(G)$.
Since $G[S]$ is connected, we get the lower bound
\begin{align}
x_S(p)\geq g(G[S]).
\end{align}
Since $G[\bar{S}]$ is also connected, and because $x_S(p)+x_{\bar{S}}(p)=g(G)$, we get the upper bound
\begin{align}
x_S(p)\leq g(G)-g(G[\bar{S}]).
\end{align}
Thus we see that $x_S(p)\in [g(G[S]), g(G)-g(G[\bar{S}])]$.
Observe also that there are $g(G)-g(G[S])-g(G[\bar{S}])+1$ integers in this interval.
This quantity is exactly the size $d(S)$ of the bond $\partial(S)$. Indeed, using the definition of genus, one may check that
\begin{align}
g(G)-g(G[S])-g(G[\bar{S}])+1&=|\edges(G)|-|\vertices(G)|-|\edges(G[\bar{S}])|+|\vertices(G[\bar{S}])|-|\edges(G[S])|+|\vertices(G[S])|\nonumber\\
&=|\edges(G)|-|\edges(G[\bar{S}])|-|\edges(G[S])|=d(S).
\end{align}
We now proceed to show that $x_S(p)$ achieves all values in $[g(G[S]),g(G[S])+d(S)]$.
\emph{While we do not need the full strength of this preceding statement to establish the proposition, we have retained it in the hope that it might be of independent combinatorial interest.}
We first show that $x_S$ achieves the values $g(G)$ and $g(G)+d(S)$.
To this end, we need the following alternative description \cite[Section 3]{ABKS14} (see also \cite[Section 2.2]{BW18}) for break divisors on $G$ given a spanning tree $T$.
For every edge in $\edges(G)\setminus \edges(T)$, assign a chip to one of its two endpoints. The sequence tracking the number of chips at each vertex is always a break divisor.
Note also that flipping a given assignment across an edge produces another break divisor, which differs from the initial break divisor by an appropriate type $A$ root $e_i-e_j$.
We thus get $2^{|\edges(G)\setminus \edges(T)|}$ break divisors for any choice of spanning tree $T$.
For the bond $\partial(S)$, pick spanning trees $T_{S}$ and $T_{\bar{S}}$ for $G[S]$ and $G[\bar{S}]$ respectively.
Let $e\in \partial(S)$ be any edge such that $T_S\cup \{e\}\cup T_{\bar{S}}$ is a spanning tree in $G$.
We now apply the procedure above to produce a break divisor $p$ with $x_S(p)=g(G[S])$.
Note that
\begin{align}
\edges(G)\setminus \edges(T)=(\edges(G[S])\setminus \edges(T_S)) \cup (\partial(S)\setminus \{e\})\cup (\edges(G[\bar{S}])\setminus \edges(T_{\bar{S}})).
\end{align}
Consider edges in $\edges(G)\setminus \edges(T)$ depending on which of the three sets on the right-hand side they belong to.
If an edge is in $(\partial(S)\setminus \{e\})$, then assign a chip to the endpoint in $\bar{S}$. Otherwise, assign randomly.
Since vertices in $S$ get assigned chips only from edges in $\edges(G[S])\setminus \edges(T_S)$, our procedure is guaranteed to have a produced a break divisor $p$ on $G$ that restricts to a break divisor on $G[S]$. Thus we must have $x_S(p)=g(G[S])$.
A symmetric argument with the change that for edges in $(\partial(S)\setminus \{e\})$, assign a chip to the endpoint in $S$ produces a break divisor $p$ on $G$ that restricts to a break divisor on $G[\bar{S}]$. This in turn means $x_S(p)=g(G)-g(G[\bar{S}])$. Thus at this stage we have produced break divisors that attain the bounds $g(G[S])$ and $g(G)-g(G[\bar{S}])$ respectively.
It is now easy to see how one may interpolate between these extremes one step at a time whilst incrementing $x_S$ by $1$ at each step.
To attain the value $g(G[S])+k$ where $0< k< d(S)-1$, for $k$ edges in $\partial(S)\setminus \{e\}$, assign a chip to the endpoint in $S$. Otherwise assign to the endpoint in $\bar{S}$.
It follows from the preceding discussion that
\[
\prod_{i=g(G[S])}^{g(G)-g(G[\bar{S}])} (x_S-i)\in \mathsf{I}(G).
\]
for any nonempty proper $S\subset \vertices(G)$ for which $\partial(S)\in \bonds(G)$.
Next note that the top degree homogeneous summands from such polynomials above generate exactly the power ideal $\mc{I}(G)$. Thus we must have the inclusion
\begin{align}
\mc{I}(G)\subset \mathsf{T}(G),
\end{align}
which in turn implies the inequality
\begin{multline}
\text{ \# of spanning trees}= \dim\left( \mathbb{Q}[\bfx{n}]/\mc{I}(G) \right)\geq \dim\left( \mathbb{Q}[\bfx{n}]/\mathsf{T}(G) \right)=|\brkd(G)|.
\end{multline}
Given that the quantities on either extreme are in fact equal \cite[Theorem 4.25]{ABKS14}, the claim follows.
\end{proof}
\begin{theorem}
\label{thm:piecing_things}
We have the following isomorphisms and equalities of ungraded $\aut{G}$-modules:
\[
\mathbb{Q}[\brkd(G)]\cong \mathbb{Q}[\bfx{n}]/\mathsf{T}(G) = \mathbb{Q}[\bfx{n}]/\mc{I}(G) \cong \mc{P}(G).
\]
where the middle equality and right isomorphism are in the category of \emph{graded} $\aut{G}$-modules.
\end{theorem}
\begin{proof}
The first isomorphism comes from orbit harmonics. The second equality is exactly Proposition~\ref{prop:GP_break_divisors}. The last isomorphism follows since $\mc{P}(G)$ is the Macaulay-inverse system of $\mc{I}(G)$.
\end{proof}
\begin{remark}
\emph{
Theorem~\ref{thm:piecing_things} provides an algebraic perspective on the fact that the set of $q$-reduced divisors on $G$ (essentially $G$-parking functions) has the same cardinality as $\brkd(G)$. Indeed, as was mentioned earlier, by work of Postnikov--Shapiro, the quotient $\mathbb{Q}[\bfx{n}]/\mc{I}(G)$ has a monomial basis indexed by $G$-parking functions. On the other hand we just showed that this same quotient arises when applying the point orbit method to the set of break divisors on $G$.
}
\end{remark}
\subsection{External and internal zonotopal algebras via orbit harmonics}
\label{subsec:more_orbit_harmonics}
It is natural to ask whether two other well-known zonotopal algebras \textemdash{} \emph{external} and \emph{internal} \textemdash{} arise in this story.
We demonstrate how these algebras arise by applying orbit harmonics to graphical zonotopes. \emph{It bears repeating that the central case is central to this article, and we will have no further use for the results of this subsection.}
We begin by establishing some notation reminiscent of that employed in the central case.
As usual, fix $G=([n],E)$.
Consider the ideals:
\begin{align}
\label{eq:external_internal}
\mc{I}_+(G)&=\langle x_{[n]}, x_S^{d(S)+1} \text{ where $\partial(S)\in\bonds(G)$}\rangle\\
\mc{I}_-(G)&=\langle x_{[n]}, x_S^{d(S)-1} \text{ where $\partial(S)\in\bonds(G)$}\rangle.
\end{align}
The external and internal zonotopal algebras are defined as respective quotients of $\mathbb{Q}[\bfx{n}]$ by these ideals.
The dimensions of these algebras are conveniently described in terms of lattice points in the graphical zonotope $\mc{Z}_G$.
Let $\mc{Z}_G^{\circ}$ denote the interior of $\mc{Z}_G$.
It is known \cite[Proposition 1.1]{HR11} that
\begin{align}
\label{eq:external_dimension}
\dim(\mathbb{Q}[\bfx{n}]/\mc{I}_+(G))&=|\mc{Z}_G\cap \mathbb{Z}^n|\\
\label{eq:internal_dimension}
\dim(\mathbb{Q}[\bfx{n}]/\mc{I}_+(G))&=|\mc{Z}_G^{\circ}\cap \mathbb{Z}^n|.
\end{align}
We will now realize these quotients by applying orbit harmonics.
Like before, our point sets on which $\aut{G}$ acts are given to us. Let us recast them in the language of divisors to fit with the theme in this article.
Fix an orientation $\mc{O}$ of the edges of $G$.
This determines the \emph{orientable divisor} \[
(\mathrm{indeg}_{\mc{O}}(1)-1,\dots,\mathrm{indeg}_{\mc{O}}(n)-1)\] where $\mathrm{indeg}_{\mc{O}}(i)-1$ is one less than the number of directed edges pointing to $i$.
Note that the degree of this divisor is $|E|-|V|=g(G)-1$.
Denote the set of orientable divisors on $G$ by $\orid(G)$.
By interpreting orientable divisors as lattice points in $\mathbb{Z}^{n}$, we obtain a polytope in $\mathbb{R}^{n}$ which is the translation of $\mc{Z}_G$ by the vector $(1,\dots,1)\in \mathbb{R}^n$. Note that it is contained in the hyperplane $x_1+\cdots+x_n=g(G)-1$.
We refer to the set of \emph{interior} lattice points in this polytope by $\orid^{\circ}(G)$.
Clearly, both $\orid(G)$ and $\orid^{\circ}(G)$ carry $\aut{G}$-actions.
Now define the ideal $\mathsf{T}_+(G)$ (respectively $\mathsf{T}_-(G)$) as resulting from applying orbit harmonics to $\orid(G)$ (respectively $\orid^{\circ}(G)$), in analogy to $\mathsf{T}(G)$ resulting from $\brkd(G)$.
\begin{proposition}
We have the equality of ideals
\begin{align*}
\mathsf{T}_+(G)&=\mc{I}_+(G),\nonumber\\
\mathsf{T}_-(G)&=\mc{I}_-(G).
\end{align*}
\end{proposition}
\begin{proof}
We consider the first equality. The proof is similar to that for Proposition~\ref{prop:GP_break_divisors}.
Since the degree of any orientable divisor is $g(G)-1$, we know that $x_1+\cdots+x_n\in \mathsf{T}_+(G)$. Now fix a proper nonempty $S\subset \vertices(G)$. Consider the linear form $x_S$ as we range over $\orid(G)$. By picking any orientation with the property that all edges in the cut $\partial(S)$ go from $\vertices(G[S])$ to $\vertices(G[\bar{S}])$, we are guaranteed that $x_S$ attains the value $g(G[S])-1$. This is also clearly the minimum. By reversing the orientation on all edges in the cut, we see that $x_S$ attains the value $g(G[S])-1+d(S)$, and that is the maximum such.
Thus we can see that $x_S$ takes (all) values in the interval $[g(G[S])-1,g(G[S])-1+d(S)]$, which has size $d(S)+1.$
It follows that $x_S^{d(S)+1}\in \mathsf{T}_+(G)$.
The equality $\mathsf{T}_+(G)=\mc{I}_+(G)$ now follows from the fact that $|\orid(G)|=|\mc{Z}_G\cap \mathbb{Z}^n|$ and equation~\eqref{eq:external_dimension}.
The internal case is essentially the same. One only needs to note that for an orientable divisor corresponding to an interior point in $\orid^{\circ}(G)$, the minimum and maximum values attained by the linear form $x_S$ are $(g(G[S])-1)+1$ and $(g(G[S])-1)+(d(S)-1)$ respectively. This in turn implies that $x_S^{d(S)-1}\in \mathsf{T}_-(G)$.
\end{proof}
We conclude this subsection with one important instance.
Consider $G=K_n^m$ for $m\geq 1$.
Then $\mc{Z}_G$ is the $m$-fold dilation of the standard permutahedron in $\mathbb{R}^n$ whose vertices are given by permutations of $(n-1,\dots,1,0)$.
The number of lattice points in $\mc{Z}_{G}$ is given by the number of forests on $G$. Orbit harmonics tells us that the permutation action on these lattice points (or equivalently, $\orid(G)$) can be used to construct a graded $S_n$-module given by the quotient \[
\mathbb{Q}[\bfx{n}]/\langle (x_{i_1}+\cdots x_{i_k})^{mk(n-k)+1} \text{ for } 1\leq i_1<\cdots<i_k\leq n \text{ where } k\in [n] \rangle.
\]
At $m=1$, this quotient was introduced by Shapiro--Shapiro in a geometric context \cite{ShSh98} (see also \cite{PSS99}), and the problem of determining its graded $S_n$-module structure is posed \cite[Problem 3]{ShSh98}.
\section{Efimov's construction}
\label{sec:Efimov}
Let $A=(a_{ij})_{i,j\in [k]}$ be a symmetric matrix with nonnegative entries. We assume $a_{ii}\geq 1$ throughout.
The matrix $A$ determines a quiver $Q$ on $k$ vertices labeled $1$ through $k$, with $a_{ij}$ arrows from $i$ to $j$ for $i,j\in [k]$.
We assume that $A$ is such that $Q$ is connected.
Let $\gamma=(\gamma_1,\dots,\gamma_k)\in \mathbb{Z}_{\geq 0}^k$ be a dimension vector.
We begin by describing the essential construction in \cite{Efi}.
\subsection{Quantum Donaldson--Thomas (DT) invariants}
\label{subsec:quantum_dt}
We consider variables $x_{i,\alpha}$ for $1\leq i\leq k$ and $1\leq \alpha\leq \gamma_i$, and let $\sigma_{\gamma}$ be their sum.
Define the polynomial ring
\begin{align}
A_{\gamma}=\mathbb{Q}[x_{i,\alpha}\;|\; 1\leq i\leq k,1\leq \alpha\leq \gamma_i].
\end{align}
Furthemore, let
\begin{align}
A_{\gamma}^{\prim}=\mathbb{Q}[x_{j,\alpha_2}-x_{i,\alpha_1}\;|\; 1\leq i,j\leq k,1\leq \alpha_1\leq \gamma_i, 1\leq \alpha_2\leq \gamma_j].
\end{align}
Then we have $A_{\gamma}=A_{\gamma}^{\prim}\otimes \mathbb{Q}[\sigma_{\gamma}]$.
Define $S_{\gamma}\coloneqq S_{\gamma_1}\times \cdots \times S_{\gamma_k}$.
Define $J_{\gamma}$ to be the smallest $S_{\gamma}$-stable $A_{\gamma}^{\prim}$-submodule of $A_{\gamma}^{\prim}$ such that the following holds: for any decomposition of $\gamma=\delta+\bar{\delta}$ where both $\delta$ and $\bar{\delta}$ are nonzero we have that
\begin{align}
\label{eq:important_poly}
f_{\delta,\bar{\delta}}=\displaystyle\prod_{i\neq j\in[k]}\prod_{\alpha_1=1}^{\delta_i}\prod_{\alpha_2=\delta_j+1}^{\gamma_j}(x_{j,\alpha_2}-x_{i,\alpha_1})^{a_{ij}}\displaystyle\prod_{i\in[k]}\prod_{\alpha_1=1}^{\delta_i}\prod_{\alpha_2=\delta_i+1}^{\gamma_i}(x_{i,\alpha_2}-x_{i,\alpha_1})^{a_{ii}-1} \in J_{\gamma}.
\end{align}
We shall reinterpret $f_{\delta,\bar{\delta}}$ in terms of cuts (as the indexing hints) in a graph constructed from $(A,\gamma)$.
Letting $\mc{H}_{\gamma}^{\prim}\coloneqq (A_{\gamma}^{\prim})^{S_{\gamma}}$, consider the decomposition \cite[p. 1139]{Efi}
\begin{align}
\label{eq:Efimov_decomposition}
\mc{H}_{\gamma}^\prim=V_{\gamma}^{\prim}\oplus J_{\gamma}^{S_{\gamma}}.
\end{align}
The quantum DT invariants of the quiver $Q$ with dimension vector $\gamma$ (assuming trivial potential and stability) arise as dimensions of the graded pieces of the graded vector space $V_{\gamma}^{\prim}$ as explained in \cite[Section 4]{Efi}. We describe the $\mathbb{Z}$-grading employed.
The \emph{Euler form} $\chi_Q(\gamma,\delta)$ given dimension vectors $\gamma$ and $\delta$ is defined as
\begin{align}
\chi_Q(\gamma,\delta)\coloneqq \sum_{1\leq i\leq k}\gamma_i\delta_i-\sum_{1\leq i,j\leq k}a_{ij}\gamma_i\delta_j.
\end{align}
Polynomials $f\in \mc{H}_{\gamma}$ of degree $k$ get assigned the grading $2k+\chi_Q(\gamma,\gamma)$.
We let $V_{\gamma,k}^{\prim}$ be the space of elements in $V_{\gamma}^{\prim}$ with this grading.
Following \cite[Section 4]{Efi}, set
\begin{align}
c_{\gamma,k}\coloneqq \dim(V_{\gamma,k}^{\mathrm{prim}}),
\end{align}
and consider the polynomial in $\mathbb{Z}_{\geq 0}[q^{\pm \frac{1}{2}}]$:
\begin{align}
\Omega_{\gamma}(q)=\sum_{k\in \mathbb{Z}}c_{\gamma,k}q^{k/2}.
\end{align}
These $\Omega_{\gamma}(q)$ are the \emph{quantum DT-invariants} of the quiver $Q$.
We get a necessary condition for when $V_{\gamma,k}^{\prim}$ is nonzero in \cite[Theorem 1.2]{Efi} (also presented as \cite[Theorem 3.10]{Efi}). To state it we need the quantity $N_{\gamma}(Q)$ \cite[Section 1]{Efi} defined\footnote{The original definition looks slightly different as we have simplified the expression using our assumption $a_{ii}\geq 1$.} as
\begin{align}
\label{eq:n_gamma}
N_{\gamma}(Q)\coloneqq \frac{1}{2}\left( \sum_{1\leq i\neq \leq k}a_{ij}\gamma_i\gamma_j+\sum_{1\leq i\leq k}(a_{ii}-1)\gamma_i(\gamma_i-1)\right)-\sum_{1\leq i\leq k}\gamma_i +2.
\end{align}
This given, the following holds.
\begin{theorem}[{\cite[Theorem 3.10]{Efi}}]
\label{thm:k_for_nonzero_spaces}
If $V_{\gamma,k}^{\mathrm{prim}}\neq 0$, then $\gamma\neq 0$, and
\[
k\equiv \chi_Q(\gamma,\gamma) \mod 2\quad \text{and} \quad \chi_Q(\gamma,\gamma)\leq k\leq \chi_Q(\gamma,\gamma)+2N_{\gamma}(Q).
\]
\end{theorem}
In view of Theorem~\ref{thm:k_for_nonzero_spaces} we may rewrite $\Omega_{\gamma}(q)$ as
\begin{align}
\Omega_{\gamma}(q)=q^{\frac{1}{2}\chi_Q(\gamma,\gamma)}\sum_{0\leq k\leq N_{\gamma}(Q)-1}c_{\gamma,2k+\chi_Q(\gamma,\gamma)}q^{k}.
\end{align}
Let us denote the sum on the right by $\tilde{\Omega}_{\gamma}(q)$. This lies in $\mathbb{Z}_{\geq 0}[q]$ and its degree is bounded above by $N_{\gamma}(Q)-1$. We will abuse notation and refer to $\tilde{\Omega}_{\gamma}(q)$ as the quantum DT invariant as well.\footnote{As the careful reader may have realized, we already do so in the introduction.}
The reader might find the preceding construction both ingenious and mysterious.
It transpires that the space $V_{\gamma,k}^{\prim}$ is the space of $S_\gamma$-invariants for a central $P$-space determined rather naturally from the quiver and the dimension vector.
We proceed to describe this construction.
\subsection{The covering graph construction}
\label{subsec:symmetric_matrix_to_graph}
Our point of departure from Efimov is to consider an analogue of \eqref{eq:Efimov_decomposition} where we do not take $S_{\gamma}$-invariants.
We will construct an $S_\gamma$-stable space $W_{\gamma}^{\prim}$ so that the following holds:
\begin{align}
\label{eq:general_efimov}
A_{\gamma}^{\prim}=W_{\gamma}^{\prim}\oplus J_{\gamma}.
\end{align}
Our next construction is crucial to this end.
Given the symmetric quiver $Q$ as before, we construct an undirected graph $G_{Q,\gamma}$ as follows.
Consider a set of vertices $v_{i,\alpha}$ for $1\leq i\leq k$ and $1\leq \alpha\leq \gamma_i$. For $i\in [k]$, the restriction of $G_{Q,\gamma}$ to the vertices $v_{i,1},\dots, v_{i,\gamma_i}$ is the clique on $\gamma_i$ vertices with $a_{ii}-1$ edges between any two distinct vertices. In particular, if $a_{ii}=1$, then we have a collection of $\gamma_i$ totally disconnected vertices.
For $i\neq j\in [k]$ we draw $a_{ij}$ edges between any vertex $v_{i,\alpha_1}$ and $v_{j,\alpha_2}$ for $1\leq \alpha_1\leq \gamma_i$ and $1\leq \alpha_2\leq \gamma_j$.
This determines $G_{Q,\gamma}$. See Figure~\ref{fig:Gqgamma} for example of this construction.
\begin{figure}
\includegraphics[scale=0.75]{Gqgamma_1_prime.pdf}
\caption{A symmetric matrix, its associated quiver, and an instance of $G_{Q,\gamma}$}
\label{fig:Gqgamma}
\end{figure}
\emph{We will assume throughout that $G_{Q,\gamma}$ is connected. Furthermore, for the remainder of this section, we fix our symmetric quiver $Q$ and dimension vector $\gamma$ henceforth, and we will drop them from notation. In particular, unless otherwise noted, we let $G\coloneqq G_{Q,\gamma}$.
}
We reinterpret the important element $f_{\delta,\bar{\delta}}\in J_{\gamma}$ as a polynomial $p_Y$ for a cut in $G$.
\begin{lemma}
\label{lem:efimov_translated}
Consider a decomposition $\gamma=\delta+\bar{\delta}$ where $\delta,\bar{\delta}\neq \gamma$.
The following hold.
\begin{enumerate}
\item $f_{\delta,\bar{\delta}}=p_Y$ for $Y\in \cuts(G)$.
\item For $S\subseteq \vertices(G)$ such that $\partial(S)\in \bonds(G)$, we have that $p_{\partial(S)}\in J_{\gamma}$.
More specifically, there exists a decomposition $\gamma=\delta+\bar{\delta}$ such that $\sigma(f_{\delta,\bar{\delta}})=p_{\partial(S)}$ for some $\sigma\in S_{\gamma}$.
\end{enumerate}
\end{lemma}
\begin{proof}
Recall that
\begin{align}
\label{eq:f_delta_again}
f_{\delta,\bar{\delta}}=\textcolor{blue}{\displaystyle\prod_{i\neq j\in[k]}\prod_{\alpha_1=1}^{\delta_i}\prod_{\alpha_2=\delta_j+1}^{\gamma_j}(x_{j,\alpha_2}-x_{i,\alpha_1})^{a_{ij}}} \textcolor{magenta}{\displaystyle\prod_{i\in[k]}\prod_{\alpha_1=1}^{\delta_i}\prod_{\alpha_2=\delta_i+1}^{\gamma_i}(x_{i,\alpha_2}-x_{i,\alpha_1})^{a_{ii}-1}}.
\end{align}
We understand each triple product separately.
Decompose $\vertices(G)$ as $\vertices_1\sqcup \cdots \sqcup \vertices_k$ where
\[
\vertices_i\coloneqq \{v_{i,\alpha}\;|\; 1\leq \alpha\leq \gamma_i\}.
\]
The decomposition $\gamma=\delta+\bar{\delta}$ induces a decomposition of each $\vertices_i=S_i\sqcup \bar{S}_i$ where
\begin{align*}
S_i=\{v_{i,\alpha}\;|\; 1\leq\alpha\leq \delta_i\}, \hspace{10mm}\bar{S}_i=\{v_{i,\alpha}\;|\; \delta_i+1\leq\alpha\leq \gamma_i\}.
\end{align*}
Set $S\coloneqq \sqcup_{1\leq i\leq k}S_i$ and consider the polynomial $p_{\partial(S)}$ attached to the cut $\partial(S)$.
Given the construction of $G$, edges in $\partial(S)$ come in the following two flavors.
\begin{itemize}
\item For $i\neq j\in [k]$, every vertex in $S_i$ is connected to every vertex in $\bar{S}_j$ via $a_{ij}$ edges.
\item For $i\in [k]$, every vertex in $S_i$ is connected to every vertex in $\bar{S}_i$ via $a_{ii}-1$ edges.
\end{itemize}
It follows that $f_{\delta,\bar{\delta}}=p_{\partial(S)}$, which implies the first part of the claim.
Figure~\ref{fig:f_delta_example} decomposes the graph in Figure~\ref{fig:Gqgamma} with $\gamma=(2,2,3)=(1,0,2)+(1,2,1)$. The shaded cells contain the vertices in $S$. Observe that all edges have one end point in the gray shaded region and the other end point in the unshaded region. Edges colored blue (respectively magenta) contribute to the blue (respectively magenta) term in the expression for $f_{\delta,\bar{\delta}}$ in~\eqref{eq:f_delta_again}.
\begin{figure}[!h]
\includegraphics[scale=0.75]{Gqgamma_1_prime_dec.pdf}
\caption{$f_{\delta,\bar{\delta}}$ corresponding to a cut}
\label{fig:f_delta_example}
\end{figure}
We proceed to prove the second statement. Consider a nonempty proper subset $S\subset \vertices(G)$ such that $\partial(S)\in \bonds(G)$.
This induces a decomposition
\begin{align}
S=S_1\sqcup\cdots \sqcup S_k
\end{align}
by letting $S_i\coloneqq S\cap \vertices_i$ for $i\in [k]$.
Define $\delta$ to equal $(|S_1|,\dots,|S_k|)$. This then allows us to decompose $\gamma=\delta+\bar{\delta}$.
Since $S$ is a nonempty proper subset of $\vertices(G)$, we are guaranteed that neither $\delta,\bar{\delta}\neq\gamma$.
We can find a permutation $\sigma\in S_{\gamma}$ that sends $S_i$ to the `initial' set of vertices $\{v_{i,\alpha}\;|\; 1\leq \alpha\leq \delta_i\}$. Since $S_{\gamma}$ is a subgroup of $\aut{G}$, hitting $\vertices(G)$ with $\sigma$ permutes bonds.
Thus we have that $p_{\partial(S)}$, up to reindexing variables, is $f_{\delta,\bar{\delta}}$. Since $J_{\gamma}$ is closed under the $S_{\gamma}$-action, the proof is complete.
\end{proof}
Having inferred that $J_{\gamma}$ is the ideal generated by $p_Y$ for $Y\in \bonds(G)$, by appealing to our discussion at the end of Subsection~\ref{subsec:variations}, we obtain the following corollary that `combinatorializes' Efimov's construction .
\begin{corollary}
\label{cor:J_gamma_revisited}
The following decomposition holds:
\[
A_{\gamma}^{\prim}=\mc{P}(G)\oplus J_{\gamma}.
\]
\end{corollary}
\begin{proof}
Recall that
$A_{\gamma}^{\prim}=\mathbb{Q}[x_{j,\alpha_2}-x_{i,\alpha_1}\;|\; 1\leq i,j\leq k,1\leq \alpha_1\leq \gamma_i, 1\leq \alpha_2\leq \gamma_j].$
Since $p_Y$ for $Y\in \cuts(G)$ is in the ideal generated by $p_{Y'}$ for $Y'\in \bonds(G)$, we get from Lemma~\ref{lem:efimov_translated} that
\begin{align}
J_{\gamma}= \hat{I}(G).
\end{align}
The claim follows by comparison with Equation~\eqref{eq:central_p_decomposition}.
\end{proof}
Now we can realize $\tilde{\Omega}_{\gamma}(q)$ in terms of the space $\mc{P}(G)$ with this new perspective.
Given that usual degree $k$ polynomials end up in the (unusual) grading $2k+\chi_Q(\gamma,\gamma)$ in Efimov's context, by appealing to Corollary~\ref{cor:J_gamma_revisited}, we immediately get our second main result showing that the dimensions of the graded pieces of $\mc{P}(G)^{S_{\gamma}}$ encode coefficients of $\tilde{\Omega}_{\gamma}(q)$.
\begin{theorem}
\label{thm:graded_multiplicity_quantum_DT}
We have the equality
\begin{align*}
\hilb(\mc{P}(G)^{S_{\gamma}})=\tilde{\Omega}_{\gamma}(q).
\end{align*}
\end{theorem}
A couple of remarks are in order.
Note that we have bypassed the intricate argument in the proof of \cite[Theorem 3.10]{Efi} wherein Efimov establishes that only finitely many $V_{\gamma,k}^{\prim}$ are nonzero. This is also where the quantity $N_{\gamma}(Q)$ enters the picture in \emph{loc. cit.}. In fact, by~\eqref{eq:hilb_p(x)} we know that $\hilb(\mc{P}(G))=q^{|\edges(G)|-|\vertices(G)|+1}T_G(1,q^{-1})=q^{g(G)}T_G(1,q^{-1})$.
Thus, we infer the pleasant fact that the degree of $\hilb(\mc{P}(G)^{S_{\gamma}})$, and thereby $\tilde{\Omega}_{\gamma}(q)$, is bounded above by the genus of $G$.
In summary, we have in fact succinctly established \cite[Theorem 3.10]{Efi} once we show that the quantity $N_{\gamma}(Q)$ is essentially the genus.
The straightforward proof of the next lemma is omitted.
\begin{lemma}
\label{lem:N_gamma_reinterpreted}
We have the equality: $g(G)=N_{\gamma}(Q)-1$.
\end{lemma}
\subsection{Numerical DT invariants}
\label{subsec:numerical_DT}
Define the \emph{numerical} DT-invariant \begin{align}
\mathrm{DT}_{Q,\gamma}\coloneqq \tilde{\Omega}_{\gamma}(1).
\end{align}
We will drop $Q$ from the subscript and write $\mathrm{DT}_{\gamma}$ when it is clear from context.
We are ready to give a manifestly nonnegative combinatorial interpretation to these numbers.
To the best of the authors knowledge, while several explicit formulae \textemdash{} invariably signed because of the presence of the number-theoretic M\"{o}bius function (see next section for such expressions, and also \cite{PSS18})\textemdash{} and other algebraic interpretations are available, ours is the first \emph{combinatorial} interpretation.
We let $n=\sum_{i}\gamma_i$ and then identify $\vertices(G)$ with $[n]$ by relabeling $v_{1,1},\dots,v_{1,\gamma_1},\dots,v_{k,1},\dots, v_{k,\gamma_k}$ with integers from $1$ through $n$ in that order. This allows us to identify the bi-indexed variables $x_{1,1},\dots, x_{k,\gamma_k}$ with
$x_1,\dots,x_{n}$.
\begin{theorem}
\label{thm:numerical_dt_break}
The number of $S_{\gamma}$ orbits on $\brkd(G)$ equals $\mathrm{DT}_{\gamma}$.
\end{theorem}
\begin{proof}
Theorem~\ref{thm:piecing_things} gives the isomorphism of graded $\aut{G}$-representations:
\begin{align}
\mc{P}(G)\cong \mathbb{Q}[\bfx{n}]/\mc{I}(G),
\end{align}
and then says that the right-hand side is isomorphic to $\mathbb{Q}[\brkd(G)]$ as an ungraded $\aut{G}$-representation.
Now, $S_{\gamma}$ is a subgroup of $\aut{G}$. By taking $S_{\gamma}$-invariants we get
\begin{align}
\dim(\mc{P}(G)^{S_{\gamma}})=\dim(\mathbb{Q}[\brkd(G)]^{S_{\gamma}}).
\end{align}
The left-hand side equals $\mathrm{DT}_{\gamma}=\tilde{\Omega}_{\gamma}(1)$, whereas the right-hand side equals the number of $S_{\gamma}$-orbits on $\brkd(G)$. The claim follows.
\end{proof}
\begin{remark}
\emph{
The preceding proof employs the consequences of the point-orbit method in a crucial way.
Given the succinctness and simplicity of the statement, one naturally wonders if there is an alternative proof.}
\end{remark}
\begin{example}
\emph{
Consider the quiver $Q$ in Figure~\ref{fig:Gqgamma_2}. Pick $\gamma=(2,3)$.
The resulting graph $G$ is the bipartite graph $K_{2,3}$.
We reindex our variables $X_1= x_{11}$, $x_2=x_{12}$, $x_3=x_{21}$, $x_4=x_{22}$, and $x_5=x_{32}$.
We let $S_2\times S_3$ act on $\mathbb{Q}[x_1,\dots,x_5]$ by letting $S_2$ (respectively $S_3$) act on $x_1,x_2$ (respectively $x_3,x_4,x_5$).
}
\emph{
$\mc{P}(G)$ is spanned by $p_Y$ for slim subgraphs $Y$ which may be obtained as the $S_{\gamma}$-orbit of elements in $\{1,x_1-x_3, (x_1-x_3)(x_1-x_4), (x_1-x_3)(x_2-x_3) \}$.
The space $\mc{P}(G)^{S_\gamma}$ has basis elements
\[
\{1,\sum_{\sigma\in S_{\gamma}}\sigma\cdot(x_1-x_3), \sum_{\sigma\in S_{\gamma}} \sigma\cdot (x_1-x_3)(x_1-x_4), \sum_{\sigma\in S_{\gamma}}\sigma\cdot (x_1-x_3)(x_2-x_3)).\}.
\]
Explicitly, other than the constant polynomial $1$, these equal
\begin{align*}
&3(x_1+x_2)-2(x_3+x_4+x_5)\\
&3(x_1^2+x_2^2)-2(x_1+x_2)(x_3+x_4+x_5)+2(x_3x_4+x_3x_5+x_4x_5)\\
& 6x_1x_2-2(x_1+x_2)(x_3+x_4+x_5)+2(x_3^2+x_4^2+x_5^2).
\end{align*}
We thus infer that
\[
\tilde{\Omega}_{\gamma}(q)=1+q+2q^2,
\]
and therefore that $\tilde{\Omega}_{\gamma}(1)=4$. Going back to Example~\ref{ex:break_divisors_orbits}, this agrees with the number of $(S_2\times S_3)$-orbits on $\brkd(K_{2,3})$.
}
\begin{figure}
\includegraphics[scale=0.75]{Gqgamma_2.pdf}
\caption{A symmetric matrix, its associated quiver, an instance of $G_{Q,\gamma}$.}
\label{fig:Gqgamma_2}
\end{figure}
\end{example}
\begin{remark}
\emph{This example (and others) can be independently verified using a special property of Donaldson-Thomas invariants for quivers with stability; see \cite{ReinekeSmall} and the references therein.}
\emph{These more refined invariants are defined whenever the restriction of the Euler form of a quiver $Q$ to a level set of a stability function $\Theta$ on $Q$ is symmetric \cite[Section 2.5.]{ReinekeSmall}. If the dimension vector $\gamma$ is indivisible, and $\Theta$ is sufficiently generic, the refined DT invariants equals the Poincar\'e polynomial in cohomology of a smooth moduli space of $\Theta$-stable representations of the quiver, which can be computed using a resolved Harder-Narasimhan recursion \cite[Theorem 2.2.]{ReinekeSmall}. If $Q$ is already symmetric, the refined DT invariant equals the ordinary one (a special case of \cite[Corollary 4.4]{ReinekeSmall}), and this allows for its computation without reference to Euler product factorization of a motivic generating series.}
\end{remark}
\subsection{Linking Efimov and Hausel--Sturmfels}
Note that one consequence of Corollary~\ref{cor:J_gamma_revisited}, by invoking~\eqref{eq:hilb_p(x)}, is that
\begin{align}
\hilb(A_{\gamma}^{\prim})=q^{g(G)}T_G(1,q^{-1}).
\end{align}
That the Tutte polynomial appears naturally after we have recast Efimov's construction suggests a concrete connection with work of Hausel--Sturmfels \cite{HS02}; see also recent work of Abdelgadir--Mellit--Rodriguez-Villegas \cite{AMV21} where the hint is explicit in the title itself.
With the benefit of hindsight, we arrive at the curious fact that Efimov's construction \cite[Section 3]{Efi} is precisely one of three constructions for the cohomology rings of toric Nakajima quiver varieties given in \cite{HS02}.
We simply recall the pieces that we need and refer the reader to \emph{loc. cit.} for more.
Like in the previous subsection, we work with the identification $\vertices(G)=[n]$.
Orient edges $\{i<j\}\in E(G)$ so that they point from from $j$ to $i$.
The resulting directed graph may itself be treated as a quiver, which we call $\tilde{Q}$.
Attached to this quiver, and by taking the dimension vector $(1^n)$, one obtains a toric Nakajima quiver variety $Y(\tilde{Q})$.
We note that the definition for this variety in \cite{HS02} has an additional parameter $\theta$. While this parameter plays a role in determining the variety, the description of its cohomology ring does not depend on $\theta$.
By unwinding the definitions in \cite[Section 7]{HS02}, it can be checked that the `economical' presentation for the cohomology ring $H^*(Y(\tilde{Q});\mathbb{Q})$ is what is discussed in Section~\ref{subsec:variations}. Indeed, the matrix $A$ employed by Hausel--Sturmfels to determine $Y(\tilde{Q})$ is the oriented incidence matrix for $G$, i.e. its columns are obtained by first taking the vectors $e_i-e_j$ for edges $\{i<j\}\in E(G)$ and subsequently striking out the first row.
The quotienting ideal on the right-hand side of \cite[Equation 37]{HS02} that describes $H^*(Y(\tilde{Q});\mathbb{Q})$ is, in the language of Section~\ref{sec:central_zonotopal}, equal to the cocircuit ideal $I(A)$ as defined in equation~\ref{eq:def_cocircuit_ideal}.
In summary, the quantum DT invariants are determined by the $S_\gamma$-invariant space of the cohomology ring of the toric Nakajima quiver variety $Y(\tilde{Q})$.
While the similarity of this last statement to a result of Hausel--Letellier--Rodriguez-Villegas \cite[Corollary 1.5, Equation 1.10]{HLRV13} is striking, the quiver variety in \emph{loc. cit.} is not a toric Nakajima quiver variety. In particular, our result is not subsumed by results in \cite{HLRV13}.
Taking a cue from \cite{HLRV13} we now discuss some more representation-theoretic aspects of the $S_{\gamma}$-module $\mc{P}(G)$.
\section{Actions have consequences}
\label{sec:applications}
We now focus on representation-theoretic applications of the theory developed in this article, with motivation stemming from work of Berget--Rhoades \cite{BR14} (see also work of Berget \cite{Ber18} in the context of internal zonotopal algebras).
In the interest of brevity, we assume that the reader is conversant with the vocabulary of symmetric functions and associated combinatorics in the context of symmetric group representations, and refer them to \cite{Mac95, St99} for more on this front.
We let $\Lambda$ denote the ring of symmetric functions. We define the \emph{Frobenius characteristic map} $\frob:\oplus_{n\geq 0}\mathrm{Rep}(S_n) \to \Lambda$ by decreeing that the irreducible representation indexed by the partition $\lambda\vdash n$ is sent to Schur function $s_{\lambda}$, and then extending linearly.
Here $\mathrm{Rep}(S_n)$ denotes the representation ring of $S_n$.
If $V=\oplus_{d\geq 0} V_d$ is a graded $S_n$-module, then we define the \emph{graded Frobenius characteristic} $\grfrob(V;q)$
as $\sum_{d\geq 0}q^d \frob(V).$
Following earlier convention, unless otherwise stated, we take $G$ to be the graph $G_{Q,\gamma}$.
\subsection{The sign-isotypic component also computes DT invariants}
\label{subsec:sign_isotypic}
We do not currently have a decomposition for $\mc{P}(G)$ into $S_\gamma$-irreducibles. Having assigned meaning to the $S_\gamma$-invariant space, we shed some light on a close relative thereof.
Recall that $n=|\vertices(G)|$.
Using the \emph{sign} representation $\varepsilon_n$ of $S_{n}$, we can obtain the sign representation $\varepsilon_{\gamma}$ for $S_{\gamma}$ by restriction.
Given an $S_{\gamma}$-module $V$, let us denote the sign-isotypic component by $V^{\varepsilon_{\gamma}}$.
Assume like before that $A=(a_{ij})_{i,j\in [k]}$ is a symmetric matrix with nonnegative entries which in turn determines a symmetric quiver $Q$. Let $\gamma=(\gamma_1,\dots,\gamma_k)$ be a dimension vector. Define $Q^+$ to be the symmetric quiver corresponding to the matrix $A+I_k$ where $I_k$ denotes the $k\times k$ identity matrix. Equivalently, $Q^+$ is obtained by adding one new loop at each vertex of $Q$. We let
\[
G^+\coloneqq G_{Q^+,\gamma}.
\]
We have the following result saying that $\varepsilon_{\gamma}$-isotypic components also compute DT invariants.
Indeed, our slim subgraph perspective renders this fact quite transparent.
\begin{proposition}
We have that
\[
\dim(\mc{P}(G^+)^{\varepsilon_{\gamma}})=\mathrm{DT}_{Q,\gamma}.
\]
\end{proposition}
\begin{proof}
Note that the right-hand side above is simply $\dim(\mc{P}(G)^{S_{\gamma}})$.
Thus it suffices to establish an isomorphism between $\mc{P}(G^+)^{\varepsilon_{\gamma}}$ and $\mc{P}(G)^{S_{\gamma}}$. Consider the map sending
\begin{align}
\label{eq:vandermonde_multiplication}
f\in \mc{P}(G) \mapsto f^+\coloneqq f \cdot \prod_{1\leq i\leq k}\prod_{1\leq \alpha_1<\alpha_2\leq \gamma_i}(x_{i,\alpha_1}-x_{i,\alpha_2})
\end{align}
Observe that the innermost product is the Vandermonde determinant on the variables $x_{i,1}$ through $x_{i,\gamma_i}$. Each linear form $(x_{i,\alpha_1}-x_{i,\alpha_2})$ corresponds to an edge in $E(G^+)\setminus E(G)$.
First we claim that $f^+\in \mc{P}(G^+)$. It suffices to verify this for a slim $Y\subset E(G)$. The polynomial $p_Y^+$ is attached to the set of edges $Y^+\coloneqq \left(E(G^+)\setminus E(G)\right) \sqcup Y$. This and the fact that $Y$ is slim together imply that $Y^+$ is slim in $G^+$. Thus $f\in \mc{P}(G^+)$ indeed.
Now the fact that the association in \ref{eq:vandermonde_multiplication} is an isomorphism between $\mc{P}(G)^{S_{\gamma}}$ and $\mc{P}(G^+)^{\varepsilon_{\gamma}}$ is straightforward.
Indeed any polynomial $f$ in the variables $(x_{i,\alpha})_{1\leq i\leq k,1\leq \alpha\leq \gamma_i}$ with the property that $\sigma \cdot f=\varepsilon(\sigma)$ for $\sigma \in S_{\gamma}$ must be divisible by $\prod_{1\leq i\leq k}\prod_{1\leq \alpha_1<\alpha_2\leq \gamma_i}(x_{i,\alpha_1}-x_{i,\alpha_2})$ with the ratio being $S_{\gamma}$-invariant.
This concludes the proof.
\end{proof}
\subsection{The top degree of $\mc{P}(G)$ as an $S_\gamma$-module}
\label{subsec:top_degree}
Our second result generalizes a result of Berget--Rhoades \cite[Theorem 5]{BR14} which identifies the top degree graded piece of $\mc{P}(K_n^m)$ with $\mathrm{Lie}_n\otimes \varepsilon_n$.
Here $\mathrm{Lie}_n$ is the well-known \emph{Lie representation} of $S_n$ with the property that upon restriction to $S_{n-1}$, one recovers the regular representation. In particular, the dimension of $\mathrm{Lie}_n$ is $(n-1)!$.
One description of $\mathrm{Lie}_n$ is as the action on $S_n$ on the multilinear part of the free Lie algebra on $n$ symbols.
The graph $G$ (with $\vertices(G)$ identified with $[n]$ like before) determines a hyperplane arrangement $\mc{A}_G$ in $\mathbb{C}^n$ by considering the union of hyperplanes $x_i-x_j=0$ for edges $\{i,j\}\in E(G)$.
We consider the \emph{de Rham cohomology ring} $H^*(\mathbb{C}^n\setminus \mc{A}_G)$ over $\mathbb{C}$ of the complement $\mathbb{C}^n\setminus \mc{A}_G$.
Thanks to seminal work of Orlik--Solomon \cite{OS80,OT92}, $H^*(\mathbb{C}^n\setminus \mc{A}_G)$ is very well understood and it is the exterior algebra over the generators $\mathrm{d}\log(\beta)=\frac{d\beta}{\beta}$ where $\beta$ ranges over the linear forms that cut out $\mc{A}_G$, which in our case are the $x_i-x_j$ for edges $\{i,j\}\in E(G)$.
Recall our collection of vectors $\hat{X}_G$ introduced in Section~\ref{subsec:variations}, and endow this collection with a total order.
The top degree graded piece of $H^*(\mathbb{C}^n\setminus \mc{A}_G)$, denoted by $H^*(\mathbb{C}^n\setminus \mc{A}_G)_{\mathrm{top}}$, has a basis indexed by bases in $\hat{X}_G$ with external activity $0$, i.e. unbroken bases. Such bases also form a basis for the top degree of $\mc{P}(G)$, denoted by $\mc{P}(G)_{\mathrm{top}}$. This is easily seen from the expression~\eqref{eq:hilb_p(x)} describing $\hilb(\mc{P}(G))$ as a specialization of the Tutte polynomial of $\hat{X}_G$.
Thus we see that
\begin{align}
\label{eq:equality_of_dimensions}
\dim(\mc{P}(G)_{\mathrm{top}})=\dim(H^*(\mathbb{C}^n\setminus \mc{A}_G)_{\mathrm{top}}).
\end{align}
\begin{remark}
The quantity in~\eqref{eq:equality_of_dimensions} is known to equal the number of bounded regions in the complement $\mathbb{R}^n\setminus \mc{A}_G$ of the \emph{real} arrangement.
\end{remark}
In fact, following Berget--Rhoades \cite{BR14}, we can say more.
\begin{proposition}
\label{prop:top_degree}
We have the following $S_{\gamma}$-isomorphism:
\[
\mc{P}(G)_{\mathrm{top}}\cong H^*(\mathbb{C}^n\setminus \mc{A}_G)_{\mathrm{top}}\otimes \varepsilon_{\gamma_1}^{a_{11}-1}\otimes \cdots \otimes \varepsilon_{\gamma_k}^{a_{kk}-1}.
\]
Recall that $a_{ii}-1$ is one less than the number of loops at vertex $i$ in $Q$.
\end{proposition}
\begin{proof}
Note that $\mc{P}(G)_{\mathrm{top}}$ is the span of all $p_Y$ for $Y\subset E(G)$, where $E(G)\setminus Y$ is the edge set of a spanning tree in $G$. For a fixed such $Y$, consider the map
\begin{align}
\label{eq:association_top_degree}
p_Y\mapsto p_Y\cdot (\mathrm{d}(x_1-x_2)\wedge \cdots \wedge \mathrm{d}(x_{n-1}-x_n))/\prod_{\{i,j\}\in E(G)}(x_i-x_j).
\end{align}
We claim that the right-hand side is indeed in $H^*(\mathbb{C}^n\setminus \mc{A}_G)$. Note that $\{x_1-x_2,\dots,x_{n-1}-x_n\}$ are a basis for an $(n-1)$-dimensional space;\footnote{The reflection representation of $S_n$} let us call it $V$. Thus $\bigwedge^{n-1}V$ is one dimensional. If $\{i_1,j_1\}, \dots, \{i_{n-1},j_{n-1}\}$ are the edges of any spanning tree of $G$, then $\{x_{i_1}-x_{j_1},\dots,x_{i_{n-1}}-x_{j_{n-1}}\}$ is also a basis for $V$. Thus we must have that
\begin{align}
\mathrm{d}(x_1-x_2)\wedge \cdots \wedge \mathrm{d}(x_{n-1}-x_n)=\pm \mathrm{d}(x_{i_1}-x_{j_1})\wedge \cdots \wedge \mathrm{d}(x_{i_{n-1}}-x_{j_{n-1}}).
\end{align}
Thus the right-hand side in~\eqref{eq:association_top_degree} is, up to a sign, equal to
\[
\mathrm{d}\log(x_{i_1}-x_{j_1}) \wedge \cdots \wedge \mathrm{d}\log(x_{i_{n-1}}-x_{j_{n-1}}),
\]
which is indeed an element of $H^*(\mathbb{C}^n\setminus \mc{A}_G)_{\mathrm{top}}$. It also follows that the map is surjective. The equality of dimensions in~\eqref{eq:equality_of_dimensions} implies that we have a vector space isomorphism.
We proceed to verify that it is in fact an $S_{\gamma}$-module isomorphism.
Now pick $\sigma\coloneqq \sigma^{(1)}\cdots \sigma^{(k)}\in S_{\gamma_1}\times \cdots\times S_{\gamma_k}$.
We know that $\bigwedge^{n-1}(V)$ carries the sign representation of $S_n$, and thus, on the one hand we get
\begin{align}
\sigma\cdot (\mathrm{d}(x_1-x_2)\wedge \cdots \wedge \mathrm{d}(x_{n-1}-x_n))=(\mathrm{d}(x_1-x_2)\wedge \cdots \wedge \mathrm{d}(x_{n-1}-x_n))\prod_{1\leq i\leq k}\varepsilon_{\gamma_i}(\sigma^{(i)}).
\end{align}
On the other hand we get
\begin{align}
\sigma \cdot \prod_{\{i,j\}\in E(G)}(x_i-x_j)=\prod_{\{i,j\}\in E(G)}(x_i-x_j)\prod_{1\leq i\leq k}(\varepsilon_{\gamma_i}(\sigma^{(i)}))^{a_{ii}}.
\end{align}
Thus the action of $\sigma$ on $\mc{P}(G)$ is the action on $H^*(\mathbb{C}^n\setminus \mc{A}_G)_{\mathrm{top}}$ twisted precisely by the appropriate powers of sign representations.
\end{proof}
\begin{remark}
Note that if all $a_{ii}$ are odd positive integers, i.e. we have an odd number of loops are each vertex, then we get the isomorphism $\mc{P}(G)_{\mathrm{top}}\cong H^*(\mathbb{C}^n\setminus \mc{A}_G)_{\mathrm{top}}$ holds.
\end{remark}
\subsection{The $(m+1)$-loop quiver}
\label{subsec:loop quiver}
In the notation of this article, Berget--Rhoades \cite{BR14} consider the $S_n$-modules $\mc{P}(K_n^m)$ and establish several interesting results.
While the graded Frobenius characteristics of these modules remains elusive, we are able to shed light on related matters. In particular, we show that this module encodes a large class of DT invariants.
We begin with the case of the $(m+1)$-loop quiver.
Let $m$ be a positive integer.
We begin by revisiting the case of the $(m+1)$-loop quiver $Q$ with dimension vector $\gamma=(n)$ where $n\geq 1$.
In this case, $G_{Q,\gamma}$ equals the complete multipartite graph $K_n^{m}$, i.e. the graph on $n$ vertices with $m$ edges between any two distinct vertices.
In this case $\aut{G}$ is clearly the symmetric group $S_n$.
Theorem~\ref{thm:piecing_things} then gives us (isomorphic) spaces with dimension $m^{n-1}n^{n-2}$.
In view of Theorem~\ref{thm:piecing_things} we can now connect the space $\mc{P}(K_n^{m})$ to $\mathbb{Q}[\brkd(K_n^m)]$ and, among other things, resolve \cite[Conjecture 3.3]{KT21} and recover one of the main results in \cite{BR14}.
\begin{corollary}
\label{cor:p-space-corollary}
The following hold.
\begin{enumerate}
\item We have the isomorphism $\mc{P}(K_n^m)\cong_{S_n} \mathbb{Q}[\brkd(K_n^m)]$ of ungraded representations. In particular, the $\frob(\mc{P}(K_n^m))$ is $h$-positive.
\item The graded multiplicity of the trivial representation of $S_n$ in $\mc{P}(K_n^m)$ is given by the quantum DT invariant $\tilde{\Omega}_{(n)}(q)$.
At $q=1$ we obtain
\begin{align}
\label{eq:explicit_m_loop_quiver}
\dim(\mc{P}(K_n^m)^{S_n})=\mathrm{DT}_{Q,(n)}=
\frac{1}{mn^2}\sum_{d|n}(-1)^{mn+\frac{mn}{d}}\mu(d)\binom{\frac{(m+1)n}{d}-1}{\frac{n}{d}}.
\end{align}
\item We have $\grfrob(\mc{P}(K_n)\downarrow_{S_{n-1}}^{S_n})=\grfrob(\mathrm{PF}_{n-1})$, where $\mathrm{PF}_{n-1}$ is the parking function representation of $S_{n-1}$, with basis indexed by parking functions and grading given by the sum of entries in a parking function.
\end{enumerate}
\end{corollary}
\begin{proof}
The first statement is simply Theorem~\ref{thm:piecing_things}. The $h$-positivity is a consequence of the permutation action of $S_n$ on break divisors on $K_n^m$, which are lattice points in the permutahedron determined as the convex hull of the $S_n$-orbit of $(m(n-1)-1,\dots,m\cdot 1-1,0)$. Clearly, the stabilizer of any point is a Young subgroup, from which the claim follows.
The second statement is a consequence of Theorem~\ref{thm:graded_multiplicity_quantum_DT} for $G=K_{n}^m$. At $q=1$, we obtain the claimed expression because it equals the number of orbits under the $S_n$ action on $\brkd(K_n^m)$ \cite[Theorem 3.7]{KRT21}. The explicit expression for this specific numerical DT invariant was first computed by Reineke \cite[Theorem 3.2]{Rei12}.
The final statement was established in \cite[Thm. 2]{BR14}. We give an alternative proof.
We have the graded $S_n$-isomorphism $\mathbb{Q}[\bfx{n}]/\mc{I}(K_n)\cong \mc{P}(K_n)$.
By \cite{PS03} the left-hand side has a monomial basis $\{x_1^{a_1}\cdots x_{n-1}^{a_{n-1}}\}$ indexed by parking functions $(a_1,\dots,a_{n-1})$ of length
$n-1$.
Although the $S_n$-action on this basis is not easy to describe,
the $S_{n-1}$-action (permuting variables $x_1$ through $x_{n-1}$) is easily seen to be permutation action on parking functions.
Since the degree of a basis element is preserved, we get the graded isomorphism upon restriction as claimed.
\end{proof}
Corollary~\ref{cor:p-space-corollary} (3) may also be stated using symmetric function operators. Let $\langle -, - \rangle$ be the {\em Hall inner product}
on $\Lambda$ which declares the Schur basis to be orthogonal and let $s_1^{\perp}: \Lambda \rightarrow \Lambda$ be the degree $-1$ operator
which is adjoint to multiplication by $s_1$ under this inner product.
Corollary~\ref{cor:p-space-corollary} (3) is equivalent to
\begin{equation}
s_1^{\perp} \mathrm{grFrob}(\mc{P}(K_n);q) = (\mathrm{rev}_q \circ \omega) \nabla e_{n-1} \mid_{t \rightarrow 1}
\end{equation}
where
\begin{itemize}
\item
$e_{n-1}$ is the degree $n-1$ elementary symmetric function,
\item
$\mathrm{rev}_q$ reverses coefficient sequences of polynomials in $q$,
\item $\omega: \Lambda \rightarrow \Lambda$ is the involution interchanging $s_{\lambda}$ and $s_{\lambda'}$, and
\item $\nabla: \Lambda \rightarrow \Lambda$ is the eigenoperator on the basis $\{ \widetilde{H}_{\lambda}[X;q,t] \}$ of modified Macdonald polynomials
characterized by $\nabla: \widetilde{H}_{\lambda}[X;q,t] \mapsto q^{\sum (i-1) \cdot \lambda_i} t^{\sum (i-1) \lambda_i'} \cdot \widetilde{H}_{\lambda}[X;q,t]$.
\end{itemize}
Combinatorially, the grading on $s_1^{\perp} \mathrm{grFrob}(\mc{P}(K_n);q)$ corresponds to the coarea statistic when we think of parking
functions in terms of Dyck paths.
\begin{example}
\label{ex:motivation_for_more_DTs}
\emph{
Let us take $m=3$ and $n=4$. Then the ungraded $S_4$ module $\mc{P}(K_4^3)$ has Frobenius characteristic given by
\[
10h_{(1, 1, 1, 1)} + 15h_{(2, 1, 1)} + 3h_{(3, 1)}.
\]
This translates to the following Schur expansion:
\[
10s_{(1,1,1,1)} + 45s_{(2,1,1)} + 35s_{(2,2)} + 63s_{(3,1)} + 28s_{(4)}.
\]
From the coefficient of $s_{(4)}$, we infer that for the $4$-loop single vertex quiver $Q$ with dimension vector $\gamma=(4)$, we have
\[
\mathrm{DT}_{Q,\gamma}=28.
\]
}
\end{example}
As mentioned earlier, we do not yet know a combinatorial description for the Schur expansion of $\grfrob(\mc{P}(K_n^m))$. Even for the Schur expansion of $\frob(\mc{P}(K_n^m))$, one could derive an unconvincing expression involving Kostka numbers by appealing to the $h$-expansion.
This having said, the expansion for $\frob(\mc{P}(K_n^m))$ in the basis of monomial symmetric functions carries interesting information\textemdash{} if
$
\frob(\mc{P}(K_n^m))=\sum_{\lambda\vdash n}c_{\lambda}m_{\lambda},
$
then
\[
c_{\lambda}=\dim(\mc{P}(K_n^m)^{S_{\lambda}}).
\]
This given, one may wonder if there are quivers $Q$ for which $\mathrm{DT}_{Q,\lambda}$ equals $c_{\lambda}$. If so, then one may further ask for explicit expressions in the vein of ~\eqref{eq:explicit_m_loop_quiver}.
We answer these questions next.
\subsection{$\mathrm{DT}_{Q,\lambda}$ for quivers $Q$ and dimension vectors $\lambda$ so that $G_{Q,\lambda}=K_n^m$}
Fix positive integers $m$ and $k$. Fix a partition $\lambda=(\lambda_1\geq \cdots\geq \lambda_k>0)$.
Let $A$ be the $k\times k$ symmetric matrix with $a_{ii}=m+1$ for all $1\leq i\leq k$, and $a_{ij}=m$ for $1\leq i\neq j\leq k$.
Then $A$ determines a symmetric quiver $Q$ on $k$ vertices\footnote{This quiver is a subset of the class of \emph{almost $m$-regular quivers} \cite[Definition 6.3]{DFR21}.} with the property that the associated covering graph $G_{Q,\lambda}$ is $K_n^m$. Here $n=|\lambda|\coloneqq \sum_{1\leq i\leq k} \lambda_i$.
Our aim is to give explicit formulae for $\mathrm{DT}_{Q,\lambda}$ that generalize Reineke's formula in the $(m+1)$-loop quiver case.
By Theorem~\ref{thm:numerical_dt_break} we know that $\mathrm{DT}_{Q,\lambda}$ is the number of $S_{\lambda}$-orbits on $\brkd(K_{n}^m)$.
The polyhedral description of break divisors (as lattice points in trimmed permutahedra) does not lend itself well to a combinatorial analysis. To bypass this, we appeal to an alternative characterization for $\brkd(K_n^m)$ from \cite{KRT21} (building upon \cite{KST21,KT21}).
For $g\coloneqq g(K_n^m)$ consider
\begin{align}
\mc{D}_{m,n}\coloneqq \{(y_1,\dots,y_{n})\in \mathbb{Z}_{\geq 0}^n\;|\; y_1+\cdots+y_n=g(\!\!\!\!\!\mod mn), 0\leq y_i\leq mn-1\}.
\end{align}
Note that $\mc{D}_{m,n}$ carries a commuting $S_n \times \mathbb{Z}/n \mathbb{Z}$-action where the $S_n$-action is the natural one and the $\mathbb{Z}/n \mathbb{Z}$-action is given by adding $m$ modulo $mn$ to all coordinates.
As shown in \cite{KRT21}, break divisors of $K_n^m$ are distinguished representatives under the $\mathbb{Z}/n\mathbb{Z}$ action, and the number of $S_n$-orbits on $\brkd(K_n^m)$ can thus be computed by counting $S_n\times \mathbb{Z}/n\mathbb{Z}$ orbits on $\mc{D}_{n,m}$. This is precisely the strategy followed in \cite{KRT21}.
To compute $\mathrm{DT}_{Q,\lambda}$, we thus need to compute $S_{\lambda}\times \mathbb{Z}/n\mathbb{Z}$ orbits on $\mc{D}_{m,n}$.
We begin by recording some handy elementary number-theoretic facts that will play a crucial role in our analysis.
Let $\mu$ and $\phi$ denote the M\"{o}bius and Euler totient functions respectively.
Let $C_d(b)$ denote the Ramanujan sum as in \cite[\S 3]{KRT21}:
\begin{align}
C_d(b)\coloneqq \sum_{\substack{1\leq k\leq d\\ \gcd(k,d)=1}}e^{2\pi ikb/d}=\mu\left(\frac{d}{\gcd(b,d)}\right)\frac{\phi(d)}{\phi\left(\frac{d}{\gcd(b,d)}\right)}.
\end{align}
The following `orthogonality' result of Cohen \cite[Equation 1.2]{Coh59} (attributed to Carmichael) is pertinent.
For the reader comparing our approach here to that in \cite{KRT21}, we stress the fact that we did not need this property (and its consequences) in arriving at the results in \emph{loc. cit.}.
\begin{proposition}
\label{prop:cohen}
Fix positive integers $p$ and $q$.
Consider divisors $d$ and $e$ of $q$.
Then
\begin{align*}
\sum_{\substack{a+b=p(\!\!\!\!\! \mod q)\\ 0\leq a,b\leq q-1}}C_d(a)C_e(b)=\left\lbrace \begin{array}{ll}0 & d\neq e,\\ qC_d(p) & d=e.\end{array}\right.
\end{align*}
\end{proposition}
As an immediate corollary we obtain the following result that allows for substantial simplification of expressions involving Ramanujan sums.
\begin{corollary}
\label{cor:general_cohen}
Fix positive integers $p$ and $q$.
Consider a tuple $(d_1,\dots,d_k)$ of positive integers such that $d_i|q$ for all $1\leq i\leq k$.
Then
\begin{align*}
\sum_{\substack{a_1+\cdots + a_k=p(\!\!\!\!\! \mod q)\\ 0\leq a_i\leq q-1}}\prod_{1\leq i\leq k}C_{d_i}(a_i)=\left\lbrace \begin{array}{ll}q^{k-1}C_d(p) & d\coloneqq d_1=\cdots=d_k,\\0 & \text{otherwise.}\end{array}\right.
\end{align*}
\end{corollary}
\begin{proof}
The case $k=1$ is vacuously true. The case $k=2$ is Proposition~\ref{prop:cohen}. The remaining argument is a straightforward induction.
\end{proof}
We consider a slightly more general setup.
For $0\leq s\leq mn-1$, define
\begin{align}
\label{eq:general_dmnrs}
\mc{D}_{m,n,r,s}\coloneqq \{(y_1,\dots,y_{r})\;|\; y_1+\cdots+y_r=s(\!\!\!\!\!\mod mn), 0\leq y_i\leq mn-1\},
\end{align}
and let $
\mc{D}_{m,n,s}\coloneqq \mc{D}_{m,n,n,s}.$
Irrespective of $s$, the Young subgroup $S_{\lambda}$ acts on $\mc{D}_{m,n,s}$.
Denote the number of orbits under this action by $O_{m,\lambda,s}$.
We give a formula for $O_{m,\lambda,s}$ using Ramanujan sums.
\begin{proposition}
\label{prop:d_orbits}
Let $\gcd(\lambda)\coloneqq \gcd(\lambda_1,\dots,\lambda_k)$.
We have that
\[
O_{m,\lambda,s}=\frac{1}{mn}\sum_{d|\gcd(\lambda)}C_d(s)\prod_{1\leq i\leq k}\binom{\frac{mn+\lambda_i}{d_i}-1}{\frac{\lambda_i}{d_i}}.
\]
\end{proposition}
\begin{proof}
One may decompose $(y_1,\dots,y_n)\in \mc{D}_{m,n,s}$ as a concatenation of $k$ sequences: $(y_1,\dots,y_{\lambda_1})$, $(y_{\lambda_1+1},\dots,y_{\lambda_1+\lambda_2}),\dots$, $(y_{\lambda_1+\cdots+\lambda_{k-1}+1},\dots,y_{n})$.
Thus, abusing notation slightly, we may interpret $\mc{D}_{m,n,s}$ as being given by the disjoint decomposition:
\begin{align}
\label{eq:decompose_lattice_points}
\mc{D}_{m,n,s}=\displaystyle\bigsqcup_{\substack{a_1+\cdots+a_k=s(\!\!\!\!\!\mod mn)\\ 0\leq a_i\leq mn-1}}\displaystyle\bigsqcup_{1\leq i\leq k}\mc{D}_{m,n,\lambda_i,a_i}.
\end{align}
For any choice of $(a_1,\dots,a_k)$, the symmetric group $S_{\lambda_i}$ acts on the $\mc{D}_{m,n,\lambda_i,a_i}$.
The orbits under this $S_{\lambda_i}$-action on $\mc{D}_{m,n,\lambda_i,a_i}$ are indexed by multisets of cardinality $\lambda_i$ with elements drawn from $\{0,\dots,mn-1\}$ such that the sum of the elements in $a_i$ modulo $mn$. We know \cite[Lemma 3.1]{KRT21} that this quantity equals
\[
\frac{1}{mn}\sum_{d_i|\gcd(\lambda_i,mn)} \binom{\frac{mn+\lambda_i}{d_i}-1}{\frac{\lambda_i}{d_i}}C_{d_i}(a_i).
\]
From the decomposition in~\eqref{eq:decompose_lattice_points} it then follows that
\begin{align}
O_{m,\lambda,s}=\frac{1}{m^kn^{k}}\sum_{\substack{a_1+\dots+a_k=s(\!\!\!\!\!\mod mn)\\ 0\leq a_i\leq mn-1}}\sum_{\substack{(d_1,\dots,d_k)\\ d_i|\gcd(\lambda_i,mn)}}\prod_{1\leq i\leq k}\binom{\frac{mn+\lambda_i}{d_i}-1}{\frac{\lambda_i}{d_i}}C_{d_i}(a_i),
\end{align}
which by changing the order of summation may be rewritten as
\begin{align}
O_{m,\lambda,s}=\frac{1}{m^kn^{k}}\sum_{\substack{(d_1,\dots,d_k)\\ d_i|\gcd(\lambda_i,mn)}}\prod_{1\leq i\leq k}\binom{\frac{mn+\lambda_i}{d_i}-1}{\frac{\lambda_i}{d_i}}\sum_{\substack{a_1+\dots+a_k=s(\!\!\!\!\!\mod mn)\\ 0\leq a_i\leq mn-1}}\prod_{1\leq i\leq k}C_{d_i}(a_i).
\end{align}
\noindent By Corollary~\ref{cor:general_cohen} the inner summand simplifies and we get the desired expression.
\end{proof}
We record the result that we care about.
\begin{corollary}
\label{cor:more_DTs}
Let $\mc{D}_{m,n}\coloneqq \mc{D}_{m,n,g(K_n^m)}$.
Then we have the equality
\[
\mathrm{DT}_{Q,\lambda}=\frac{1}{mn^2}\sum_{d|\gcd(\lambda)}(-1)^{mn+\frac{mn}{d}}\mu(d)\prod_{1\leq i\leq k}\binom{\frac{mn+\lambda_i}{d}-1}{\frac{\lambda_i}{d}}.
\]
\end{corollary}
\begin{proof}
As argued earlier, the number of orbits under $S_{\lambda}$-action on $\brkd(K_n^m)$ equals $O_{m,\lambda,g}/n$.
By Proposition~\eqref{prop:d_orbits} this equals
\begin{align}
\label{eq:more general DT}
\frac{1}{mn^2}\sum_{d|\mathrm{gcd}(\lambda)}(-1)^{mn+\frac{mn}{d}}\mu(d)\prod_{1\leq i\leq k}\binom{\frac{mn+\lambda_i}{d}-1}{\frac{\lambda_i}{d}}.
\end{align}
Here we have used the equality $C_d(g)=(-1)^{mn+\frac{mn}{d}}\mu(d)$, implicit in \cite[Section 3]{KRT21}.
\end{proof}
Observe that the integrality of $\mathrm{DT}_{Q,\lambda}$ from the aforementioned expression is not obvious.
We can also straightaway derive a host of equalities that may be of independent interest.
\begin{enumerate}
\item If $\lambda=(1^n)$, then the quantity in \eqref{eq:more general DT} equals $m^{n-1}n^{n-2}$, as it should. Indeed this is the number of spanning trees in $K_n^m$, .
\item If $\lambda=(n)$, then the quantity in \eqref{eq:more general DT} equals the numerical DT-invariant of the $(m+1)$-loop quiver as in \eqref{eq:explicit_m_loop_quiver}.
\item If $\lambda=(n-1,1)$ for $n\geq 2$, then we are considering the $S_{n-1}\times S_1$ action on $\brkd(K_n^m)$.
The quantity in \eqref{eq:more general DT} only sees a contribution from $d=1$, and thus equals
\begin{align*}
\frac{1}{mn^2}\binom{mn+n-2}{n-1}\binom{mn+1-1}{1}=\frac{1}{n}\binom{mn+n-2}{n-1}
\end{align*}
When $m=1$, this becomes the $(n-1)$th Catalan number equaling $\frac{1}{n}\binom{2n-2}{n-1}$.
This is not surprising.
Indeed, by Berget--Rhoades \cite{BR14}, the restriction of the $S_n$ action on break divisors on $K_n$ to $S_{n-1}\times S_1$ recovers the classical parking function representation, whose orbit count is well known to be given by the Catalan numbers.
\item More generally, if $\lambda=(\lambda_1,\dots,\lambda_k)\vdash n$ is such that $\gcd(\lambda)=1$, then
\eqref{eq:more general DT} gives a product formula:
\[
\frac{1}{mn^2}\prod_{1\leq i\leq k}\binom{mn+\lambda_i-1}{\lambda_i}.
\]
\end{enumerate}
\begin{example}
\emph{
We return to Example~\ref{ex:motivation_for_more_DTs} to complete that link. The monomial symmetric function expansion for $\frob(\mc{P}(K_4^3))$ equals
\[
432m_{(1,1,1,1)} + 234m_{(2,1,1)} + 126m_{(2,2)} + 91m_{(3,1)} + 28m_{(4)}.
\]
Let us verify that the expression in Corollary~\ref{cor:more_DTs} does indeed match for $\lambda={(2,2})$. We get
\[
\left(\binom{12+2-1}{2}^2-\binom{7-1}{1}^2\right)/48=126,
\]
which agrees with the coefficient of $m_{(2,2)}$ in $\frob(\mc{P}(K_4^3))$.
}
\end{example}
\section*{Acknowledgements}
V.T. is extremely grateful to Matja\v{z} Konvalinka for earlier collaboration.
Thanks also to Spencer Backman, Chris Eur, Philippe Nadeau, Marino Romero, and Chi Ho Yuen for enlightening conversations/correspondence that have influenced, directly or indirectly, the results obtained in this work.
\bibliographystyle{hplain}
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
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The Attractive Man Academy
25-Apr-2018 by Toni Trusty
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Is it a serious video. why, then, have the editors. 8 things that make people attractive according to science. I think it's sometimes pure physical attraction and sometimes a status kind of thing. So far in this chapter about attraction, we've focused on some of the reasons that we like certain people more than others. Third… you can follow my proven, step-by-step system that will transform you into a confident and sexy man that has a presence so powerful, women will become sexually attracted, just by being around you. I was still super attracted to him. The attractive man academy the academy initial, we are going to eliminate any anxiousness or nervousness with ladies and transform that into rock-solid confidence. My dad doesn't at all fit the type i generally find physically attractive, and none of my boyfriends or even the guys i've crushed on have looked at all like him. Avoid constantly fidgeting with your hair or adjusting your clothes while talking to a man you are interested in, as these little acts show that you are self-conscious about your appearance. If it were working for me, i wouldn't be at this forum in the first place. Frustrating: having to explain what the heck song of fire and ice is. Make sure your eyebrows are neat – don't let them become old man shrubbery, or the dreaded unibrow, unless you're hoping to grow a zztop beard. You may have noticed other paintings by zipin. Likely to produce healthy offspring. Not just attracted to my. Several major league players have come out of the academy. Eva mendes – the most attractive female actor, model & singer. Yeah, bald is totally sexy. The appealing man academy the academy – initial, we are going to eliminate any anxiousness or nervousness with ladies and transform that into rock-solid self-confidence. But that's not a big deal – you can buy crest white strips on amazon and whiten your teeth that way, it's less expensive than a couple of haircuts. Same with the personal grooming tips – moisturize and get manicures and whatnot if you like it, but do it *for yourself*, not for any perceived change in your attractiveness. You can reach vendor's web site from this link directly: the attractive man academy. Most guys see how i'm traveling the world, dating beautiful women, and living the dream and they think that everything is so easy for me. If you do nothing else, be sure to smile around the man you are interested in romantically. Despite the vigorous exchanges, there was plenty of attractive football to admire as the teams put on an entertaining contest for the modest attendance of 252 dotted around the perimeter of the well-manicured pitch. Attractive to women, presumably because such features are a sign of health. Such strong self confidence makes one more attractive, sophisticated, and desirable. "it might seem remarkable that facial fa shows an equivalent effect on the two direct measurements of attractiveness, particularly considering that they are also influenced by different facial features. This course will take you step by step through a series of video lessons, exercises, templates and unique strategies for attracting any amazing woman. Since matt artisan released this monthly dating course, hundreds of men all over the world have used it to learn how to become confident to get any woman they want in just a few days. Many social theorists view rape not only as an. 'game' was an element in the past but a man who was from an honest family, worked hard, and looked like being a solid and permanent provider for a woman would get the nod from the father and mother. I've literally watched an entire cafe full of men form concentric circles of chairs around an attractive, articulate (taken) woman who was new to the environment. My legendary texting system that covers the basic fundamentals of texting girls and getting the date- all the way to advanced attraction and seductive texting. Regret came from davis, and she went. You will know exactly what to say to any girl you want to meet… and you will know exactly how turn her on and create attraction within the first 30 seconds. You will come out of this program a new man. Two texas cities make 'america's most attractive cities' list. Otherwise this stone would seem defaced. "that group of people got treated much differently. Pick up artist academy review – is matt's dating course useful. "wonderful man, and not bad to look at. Educational sports programme at weekends, during term time. The top 10 most attractive female celebrities in america. Do whiskers make a guy hotter or does it take away from a man's general clean-cut splendor. "the other great mae, mae west, said 'i'd rather be looked over, than overlooked,'" she said. I may be being too literal, but they don't match up very well, in my mind. Proper skin care will make you look younger, more alert and – importantly – more attractive. Man: the work that the speaker does in this poem, to arrive at that cerebral moment is important, but you get there by acutely paying attention to the thing. Then males were asked to rate the attractiveness of the participants from their pictures in a likert 10-point scale, where 0 is "not attractive at all" and 10 is "extremely attractive. And the point of this article is that these lifestyle changes will make you feel better and more attractive, which will build your confidence, which will make you more attractive to your gender of choice. I would say that if you're attracting the "wrong" women, it's sometimes worth thinking about why you're getting different results with them than with the "right" women and what those "right" women seem to be looking for in men. Needless to say, he grew back the soul patch 😉 i like it when guys experiment; it's like girls trying different hair styles and lengths when they get bored. "we asked, 'what face is the most attractive' and 'what face is the most aggressive looking,'" says scott. He's 9-years-old, and was just diagnosed in december, while he was living at ark-valley humane society in buena vista, colorado. First, the female participants reported an estimation of their own physical attractiveness in a 1-to-7 likert-type scale (1 was the lowest score and 7 the highest). Entrepreneurialism is still seen as a man's venture, and both men. And axe produces dreadful scents and worse commercials. So the next time you meet an introvert, don't assume they're being cold to you, it just takes time for them to break the ice with new people. The radio times, the academy award nominee said: "there are two sides to this coin. Well i live in the south. I think the whole world is in absolute uproar, i really feel that. In the case of the man i mentioned at the beginning of the piece, i cannot recall him ever pointing out the flaws of others or even comparing himself to others. One idea about how we rate physical attractiveness is based on the impact that different aspects of our bodies (like body fatness) have on evolutionary fitness. When a woman is ovulating -- and at the most fertile period in her cycle -- she's more likely to prefer a masculine man. Smiling is by far the most effective thing you can do to attract men. Studio executive (who asked not to be named) says he believes one of the main attractions of qingdao will be the way it makes official co-productions with china somewhat easier to greenlight. Men tend to have a more uniform definition of what they consider attractive while women's definitions tend to have more variability. Wearing red makes you more attractive. It's about how a man presents himself – the way he talks, the way he dresses and his attitude… and it's surprisingly easy to sabotage one's own attractiveness by accident. Of the 22 who started the academy in may but didn't graduate, some simply quit or were injured, she said. Professor john speakman added: "i am delighted to have been involved in this international collaboration that has revealed evolutionary aspects of what people regard as attractive across diverse cultures. "he was self-confident and very soft-spoken, believe it or not, at the time," added pitkow, who said he overlapped with trump for one year at the academy. So, if you you know someone looking to visit an attractive place, send them this way, and if you already live here, then congratulations. The painting is large, probably 48 x 36 and has very distinct bands of light technique. I do have to disagree on one point…. This one comes from statistics canada. If the teen got a high-stakes question right, they won $1. The attractive man academy can not be found on the internet without paying money. Figures were imported into lightwave 3d (v9. What's always interesting to me is that what i consider to be attractive (as in guys that i consider to be cute when i walk down the street) are not necessarily the guys that i date. The clincher was he was not particularly stunning looking himself. I have learned that women and men really do not measure "attractive" in the same way, but this is actually great news for men. "yes, i understand that i can cancel at anytime, no questions asked. Putting on the uniform doesn't make you attractive to women. , the retired colonel cradled an old album stuffed with black-and-white photos of young men posing in jodhpurs and shako hats, sitting on horseback, or just goofing around in t-shirts and shorts. Women are attracted to rich men with big muscles. The limpopo academy of private detection. Fatal attraction is a sultry, juicy thriller that's hard to look away from once it gets going. Plus… try out pua academy on me. You�ll discover the one question to ask her that will make her chase you� (she will instantly see you as a high status man after doing this). This result could be because perceived penis size was smaller when assessed relative to the height of a taller man; or because of general discrimination against short men irrespective of the value of other traits, so that even a larger penis did little to increase their net attractiveness. The attraction to these features can be supported from a biological perspective when it comes to mating. The penis and height values used stem from a large-scale study of an italian male population, but these values fit within the standard range for caucasians (reviewed in ref. The attractive man academy - the academy. Besides rape, the notal organ does not appear to have any other function. 2 and 3 we present data based on the relative attractiveness of the 343 figures. I don't disagree with anything you've said here. Gain access to women through looks, wealth or status. (they also have really great social responsibility as a company, and they encourage their employees toward those types of activities and charities as well. But i want women to be attracted to me". A woman with a 7:10 waist-to-hip ratio is the figure of health and peak fertility, so she is viewed as more physically attractive by men across all cultures. "why not take this character and have her participate in the 'action,' and what would that be for her values to come into play. I'm just glad i learned this early, because a weak back runs in the family, but apparently this is not something people naturally find out. And barnum & bailey circus this year, the timing seems apropos to shine the spotlight on the man who brought that idea to fruition. Ahahha, that picture never fails to amuse me 😀 ahhh, high school anime geeks. It doesn't matter if you brush and floss, and have reasonably okay teeth. I ended up creating the one and only program that literally has it all… and it's called "pick up artist academy. The attractive man academy … let's get started. A man who takes such a beautiful dog in must have the most beautiful heart.
The Attractive Man Academy By Matt Artisan
While i have yet to harness the magical formula for myself, here are a few things i have noticed after having spent time around the truly sexy. The gorgeous angelina is on the most attractive female celebrities in usa. How else to explain the academy's brief love affair with roberto benigni. Mma precious ramotswe: owner of the no. Facial attractiveness is related to women's cortisol and body fat, but not with immune responsiveness. "the cool thing is when guys come to me or my company, we've done all that trial and error and we know what works and what doesn't work," said artisan, noting he has approached at least 3,000 women in the last six years. You're basically taking away part of her free will. Beauty affects men's and women's brains differently. I dunno what you would call it. You'll uncovering the most powerful opener that sparks attraction together with industrial plant inward almost whatever situation. Man, have you read the back story on the mask. The effect of penis size on attractiveness varied with both height and body shape (fig. Something in the nature of a mustache and goatee would be dapper, or a well-trimmed elizabethan-style beard. If the fellow can actually grow a beard—and not some patchy, desperate jowl jacket—it can be super sexy and inviting. City officials told fox 4's matt stewart that the contracts have already been signed – so the vote to approve $4-million dollars in bonds to begin construction at parade park is expected to pass. If your an attractive guy that can get dates before the military you will continue to get dates in the military and after the military. The people who don't want to change i'd figure are just not thinking beyond the physical attraction. Our results also suggest that persuasiveness is moderated by male physical attractiveness: attractive males were particularly persuasive, whereas physical attractiveness did not matter among female entrepreneurs. To determine the repeatability of ratings of a figure's attractiveness across females, a repeatability analysis was performed for the 343 figures. "there was a time when women responded positively to gentlemen. The issue comes down to the differences between how men and women define "attractiveness". Man united's class of '92 is still having an impact on the club. Then women wanted sensitive, new age men, and what do you know. Had encountered reported having been beaten in excess of what was needed to. Beyond ratios and overall figures that are attractive for romantic reasons, the most important feature that determines attraction (especially platonic) is the face. Trust in me: trustworthy others are seen as more physically similar to the self. Her life has been one relationship disaster after another because she is totally clueless about selecting a decent man. Proper grooming and hygiene is so important for attractiveness, for both men and women. Second, to determine how figure attractiveness influenced response time, we calculated the pearson's correlation between the 53 attractiveness scores and log response time for each female. And i am trying to transition to my more academic side rather than my dragonriders of berk side. I really don't find blonde hair attractive in general, but i've dated two guys with blonde hair that i found attractive. Theodore dobias, a world war ii veteran and army colonel who was a training officer at the school, said in an interview that he recalled the young cadet needing time to acclimate to the rigors of academy life. The usa, the land of hollywood, most attractive female celebrities, victoria's secret angels, and sports illustrated swimsuit edition supermodels. Most attractive men and women was most likely basing it on a. The simple act of switching to clothes that fit you . But i don't think that's as likely to result in the same kind of emotional reaction as a conflict between the person who you really are and the kind of people who you think you want to date. It's about less quantifiable things like connection, trust, attraction, not just a ranking system. Your parents' looks affect what you're looking for. If you want to know how pick up artist academy works, keep reading the next part of this pick up artist academy review. You'll uncover the most powerful opener that sparks attraction and works in nearly any situation. Males with a larger penis were rated as being relatively more attractive. It's a pleasure to be around a guy who looks after his appearance and is at ease with himself. The attractive man academy review. Photo: noah berger / noah berger / special to the chronicle 2016. In a separate study they asked investors to listen to the same pitches delivered by a man or a woman. These values should capture ∼95% of the variation that females are likely to encounter, although they do not encompass the full range of variation, and the mean values are known to vary among different human populations. "about the height thing, it's true that some women look for men taller than them, but i also think it's worth noting that the average man is taller than the average woman, so it's easy to see couples where the man is taller. I actually think military guys are more attractive because of what y'all are doing with your lives. Introverts often look and dress like a model without all the flash. Learn how to use all types of plants: annuals, perennials, evergreens, shrubs and trees, and man-made items to bring these design basics to life. "we must move forward with every aspect of the academy and it starts with me taking over and moving forward. He was honoured that this great star was in. Our cabin in the woods. The difference between good looks and attractiveness. But at the same time – i've found other girls of the same height attractive and haven't had any of those negative feelings about it, so was it the height. Exactly what to say after you meet her so that you build instant attraction, keep the conversation flowing, and make her chase you. Prolonged breast-feeding and many years of child care if they were to ensure the. The first thing he says to me is i have a worm in my hair. Even though artisan's website boasts that he can turn men into casanovas through practicing the art of seduction, and he wrote a book called "how to turn her on through text," artisan said it's "all things girls want too. The proximate basis of the decisions leading to the reported attractiveness scores is unknown. The findings, published in the journal proceedings of the national academy of sciences, also suggest there is a glass ceiling for women in the corporate world because backers prefer presentations from men. They just weren't fully tested. A study by harvard university found that investors were more likely to put money into ventures if the man making the pitch is handsome. The men who are most invested in the idea that women only like guys who look like x often . This correlation is measure of the agreement among females in how they rate a figure's attractiveness. The projects that stand to gain the most from wanda's incentive are "films that would benefit from the location, developing china market access and local-partner relationships," agrees rance pow, chairman of asian film industry consultancy artisan gateway. "but with this london event happening [on wednesday], if that was a success - which hopefully it should be - one can imagine a london grand prix being pretty attractive to the liberty guys. We will mold you into a high value man that radiates enthusiasm and confidence. In the melodrama dangerous, davis played joyce. I have actually recently become very thin, as i been attending college on a limited budget. So, as you tried to say, attraction is subjective, but it is much more subjective then you say. "because every time i see someone i want to talk to i talk to them," artisan said. There was another time when women swooned at men in uniform, and hissed and booed at any man who thought the whole military patriotism thing was a load. So for example, if you are currently getting zero dates per month, you will be getting at least one date per week. Other than being a paying customer, i have no affiliation with girlschase, and i think it's a great site. The blonde bombshell toped the list of most attractive female celebrities. Courtesy of new york military academy buy photo. I'm a real person just like you and i'm excited to tell you the truth about this product and give you some insider information on the plan. We also welcome rock balancing artist, matt denault. Presumably served their interests by motivating them to identify the. At the premiere of "suburbicon" sunday night in los angeles, clooney addressed past sexual harassment cases, specifically those involving bill cosby and former fox news host bill o'reilly, which didn't ignite change quite the way they should have. "i found him such an attractive individual. Net expert team also give the attractive man academy a rating to indicate its relative merit. I think there's more universal agreement on this point than on long hair, at least among my friends. Matt artisan – the attractive man academy review | matt artisan – the attractive man academy download. Keep reading the review that introduces to you matt artisan's ultimate monthly dating course for men named pick up artist academy. Even just "lies about minor things to have sex," without otherwise being a particular asshole, isn't all that great either. Trump, who in 2012 offered $5 million for the release of president obama's college transcript and other documents, said he would not give the post permission to review his records from the military academy. As with penis size, the proportional increase in attractiveness declined as both male height and their shoulder-to-hip ratio increased. Remember that while men are men, they still know what makeup is. This observation confirms the importance of facial fa in determining attractiveness," wrote the researchers in their paper. Davis, trained for the theatre, saw. While they'll likely run and hide when . Behavior gives a man the right to rape her can be made with-out encouraging. The caption below his photo reads "ladies' man: trump. The multi talented scarlett johansson broke big with lost in translation and hasn't slowed down since. Now you're just being deliberately obtuse. The poem makes the leap for us that's like the experience, i think, of seeing the work of art. When a guy has a personality i really click with, and has other things about him i find attractive, i can overlook something that would otherwise turn me off. There have been decades when any man with pretensions to being an adult would have facial hair. Physical traits are more important to attraction than many of us would care to admit. Of food than almost anyone i know. A preference for a larger-than-average penis is qualitatively consistent with some previous studies (30⇓–32), but our results differ in showing that the most attractive size appears to lie more than 2 sds from the mean (i. I've tried more species, preparations, etc. All i can say is that if that's your primary issue, rather than people finding you physically or impersonally appealing, then you shouldn't take all of the recommendations here so much to heart. In 1968, the feud re-surfaced when. A team of researchers at the universidad autónoma de madrid in spain sought to explore the relationship between what both men and women perceive as attractive, along with a set of facial features. Being with matt was so easy, i remember thinking early on about how perfect he was and how everything just keeps falling together. Pick up artist academy is reliable, from the site vkool. The acts he's alleged to have perpetrated go way beyond horrifying. On being named sexiest man alive for a second time:. This program is dedicated to bringing you dating success at the core of being a man. Second, we used the same multiple-regression approach to calculate a unique fitness surface for relative attractiveness for each participant. He had plenty of a-list local support, too — matt damon, los angeles mayor eric garcetti and academy president cheryl boone isaacs all lent their voices to wanda's pitch during the glitzy gala at the los angeles county museum of art. Net experts has sufficient experience about the attractive man academy to comment on reliability and can suggest whether or not the attractive man academy delivers on its promises. It definitely did not detract from my attraction to him then. Perhaps my inexplicable attraction just confirms that i was either born about forty years too late or i should be living in a cabin in the pacific northwest. The aim of this review is to evaluate the attractive man academy for the user who may have a desire to buy. Showing you the one thing to do that will generate sexual attraction right even before you open your mouth. But don't count on all your efforts holding much currency for long. In her youth, she married a musician who was cruel to her. Men and women perceive it so differently. You'll uncover the 1 query to ask her which will make her chase you' (she will instantly see you as a higher status man after doing this). The pill may make unattractive guys look hotter to you. Where to take a girl on a date and what to talk about so that she feels deeply attracted to you. The study was coordinated by professor john speakman, of the institute of genetics and developmental biology, chinese academy of sciences, beijing and the institute of biological and environmental sciences at the university of aberdeen in scotland. You will learn what "bad boys" do to give women a rush of adrenaline and keep her craving for more and how you can use it without being an "asshole. At some point, a bunch of friends had put on love, actually, and the guys in the group were all asking which actor the women though was most attractive. New york military academy was founded in 1889 by civil war veteran charles jefferson wright. Female) × 2 (entrepreneur physical attractiveness: high vs. As a senior at the new york military academy in 1964, trump was named a captain. Personally, i would take a bald guy over a guy with long hair in a ponytail any day. Symmetry signals good genes for reproductive health. Im in the british army and to be honest one squaddy does something wrong we all get a bad name you can't judge every military man because your ex treated you like crap at the end of day we are people and we do have feelings were all different. After all, short of painful surgeries, there's not much a man can do about the shape of his face or his height. But, how important do you think physical attractiveness is when determining if we like someone either romantically or platonically. Avoid being overly dramatic or emotionally sensitive. Triple your dates is just a few months. Of the three women there, for each dude, only two of us agreed he was hot (you know, beyond the general this is a hollywood production and therefore everyone is implausibly attractive) and the third didn't. He'll be working throughout the day in the gardens and waterfalls. Then it is only $67/month and you can cancel at any time. Even with a widened, more inclusive field of best picture nominees, there's unlikely to be a weinstein company release among them. Inducing the young men to acknowledge the power of their sexual impulses, and. On whether he'll ever have children:. I'm sure good military men wouldn't appreciate being judged based off of a few bad apples just as i wouldn't appreciate being judged based off of how most navy girls act. Each attractive in her rose-and-blue striped dress (oh. 5 key categories to become a pick up artist such as conquer the approach, alpha mindset for effortless attraction, communicating persuasively, sex & relationships, and sex & relationships. "sometimes having "scruff" can make a guy with more of a baby face look more mature, which can = more attractive even if it isn't the nicest looking scruff ever. George clooney has been named people's sexiest man alive for 2006 – joining his pal pitt as a two-time honoree. Leveling up: how to be more attractive in 5 easy steps. Granted, i'm sure he was aware of his physical shortcomings just like the rest of us, but he didn't feel the need to point them out. In reality, being attractive to women is a combination of a host of factors, coming together to build a holistic version of desirability that's based on more than just whether or not one has scandinavian cheekbones and piercing blue eyes. If the industry supports me, that is all i need. Next found matt, to ask what he thinks about all this. Within minutes, i understood completely why this man had managed to charm my friend and so many other women: he seemed instinctively in tune to the fact that the. Fanwell: the younger of the two assistants, who has completed his apprenticeship. Sort of see their point, but my fundamental question was, how does such a relationship even get started before you have that shared history. Artisan said that while dating apps can help make the initial connection, his workshops teach men what to do after meeting a woman. Apparently, this man had his pick of many women, most of whom were very physically attractive. One month into the academy i broke my ankle, i was so upset but i wasn't going to be sent through the next one; so i sucked it up and did what i had to do to make it through with the class i started this journey with. That might mean concentrating on other aspects of your life or trying to make new friends, while being open to dating if someone does happen to come along. In our culture that, even today, both male and female investors. Smiling might not make you more attractive. What is the value of learning the exact, step-by-step, blueprint that i've used to meet, attract and date hundreds of beautiful women. If an already attractive human were to be transformed, their physical beauty would be "beyond breathtaking", for example dimitri. Com, i made a full pick up artist academy review, based on james quek's sharing, a real customer and other customers' sharing, to show you everything about it. Placement: 'interstitial gallery thumbnails 70',. And which two agreed was pretty much a crap shoot. He also noted that trump, when he commanded a company, seemed friendlier than other high-ranking students. This course will help you be a high value man so that girls will be magnetically drawn to you without consciously knowing why. Critics were enthusiastic about the film, and it received six academy award nominations, including best picture (which it lost to. To keep them from functioning, the males cannot rape. However, the drop in the corporate income tax rate to 21 percent from 35 percent would dim the attraction of munis for banks and insurance companies. You're missing out on lots of opportunities if you're not talking to them. Apparently though, we're attracted to other people because of. It's a pretty silly phrasing to – *of course* if i'm putting time into how i look – it's target is other people, and a perceived change in attractiveness. But my personal preference is long hair, and some version of a beard and mustache. That what is biological is somehow right or good, would be to. A comprehensive guide showing you how to attract the woman you want. Their energies attracting, wooing and securing sexual partners. He is chaotic evil to the point where he makes belkar bitterleaf look like a saint. It's the relationship that's hard to get. Motholeli: one of two foster children being raised by mr. young women should be informed. The most essential thing among all, this product has 100% money back guarantees if you aren't happy about it. The one question to ask her that will make her chase you… (she will instantly see you as a high status man after doing this). Biology letters found the face can signal different things in both men and women when it comes to attraction. and there are many ways for a man to make himself more attractive. Violet sephoto: low scoring but attractive student at the secretarial college when grace makutsi attended it. It also reflects a sense of confidence, which both men and women find extremely rare and attractive. But realize this… that every competent person in the world, earned his confidence by working on it either consciously, or unconsciously. Used to be if there's a british guy and he was a villian he always had "perfect" teeth. I agree that nobody (or the great majority of people, since you never know what some folks may be into) likes severely discolored teeth, but as long as they are healthy and taken care of, i don't think it poses a problem. You'll be surprised by the facial features men perceive as most attractive in women and why they're considered desirable features in a potential partner. They objectify women, they clearly objectify woman," he said, adding that those companies teach that "it's not about getting to know her, it's not about connection, it's about the fastest way to meet her and have sex with her. In the meantime, if you have to be around one of these rare souls, study and observe them the way an apprentice would a master artisan. One friday after the academy we were at the gym and matt asked me what i was doing that night. Rehabilitate the fallen star, was the tall, dark and attractive 30-year-old actor franchot tone, born into a well-off new york family. You don't have to go out and get a mani/pedi (but i do recommend it) but you want to keep your nails neatly trimmed (not bitten) and filed with care to avoid points or raggedy edges.
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{"url":"https:\/\/socratic.org\/questions\/please-answer-the-given-question","text":"Feb 10, 2018\n\nGiven that in $\\Delta A B C , A B = A C$\n\n$B X \\mathmr{and} C Y$ are bisectors of $\\angle A B C \\mathmr{and} \\angle A C B$ respectively.\nSo $\\angle A B C = \\angle A C B$\n$B Y = 4 c m$, we are to find out length of $A X$\n\nwe have\n\n$\\angle A B C = \\angle A C B$\n$\\implies \\frac{1}{2} \\angle A B C = \\frac{1}{2} \\angle A C B$\n\n$\\implies \\angle A B X = \\angle B C Y$\n\n( since $B X \\mathmr{and} C Y$ are bisectors of $\\angle A B C \\mathmr{and} \\angle A C B$ respectively )\n\nAs we have $\\implies \\angle A B X = \\angle B C Y$, the two circumferential equal angles of same circle, the length of the arcs on which these angles stand will be same .\n\nHence $a r c B Y = a r c A X$ and so chord$A X =$chord $B Y = 4 c m$","date":"2019-01-18 11:22:14","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 15, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8442261219024658, \"perplexity\": 1219.1067202276427}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2019-04\/segments\/1547583660070.15\/warc\/CC-MAIN-20190118110804-20190118132804-00497.warc.gz\"}"}
| null | null |
Neferu I, esposa de Mentuhotep, mare d'Antef I i Antef II, dinastia XI
Neferu II, filla d'Antef III, dinastia XI, esposa principal i germana de Mentuhotep II (III) i mare de Mentuhotep III (IV).
Neferu III, filla d'Amenemhet I i esposa de Sesunret I dinastia XII
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 7,846
|
<?php
namespace Illuminate\Routing;
use Closure;
use BadMethodCallException;
use InvalidArgumentException;
class RouteRegistrar
{
/**
* The router instance.
*
* @var \Illuminate\Routing\Router
*/
protected $router;
/**
* The attributes to pass on to the router.
*
* @var array
*/
protected $attributes = [];
/**
* The methods to dynamically pass through to the router.
*
* @var array
*/
protected $passthru = [
'get', 'post', 'put', 'patch', 'delete', 'options', 'any',
];
/**
* The attributes that can be set through this class.
*
* @var array
*/
protected $allowedAttributes = [
'as', 'domain', 'middleware', 'name', 'namespace', 'prefix',
];
/**
* The attributes that are aliased.
*
* @var array
*/
protected $aliases = [
'name' => 'as',
];
/**
* Create a new route registrar instance.
*
* @param \Illuminate\Routing\Router $router
* @return void
*/
public function __construct(Router $router)
{
$this->router = $router;
}
/**
* Set the value for a given attribute.
*
* @param string $key
* @param mixed $value
* @return $this
*
* @throws \InvalidArgumentException
*/
public function attribute($key, $value)
{
if (! in_array($key, $this->allowedAttributes)) {
throw new InvalidArgumentException("Attribute [{$key}] does not exist.");
}
$this->attributes[array_get($this->aliases, $key, $key)] = $value;
return $this;
}
/**
* Route a resource to a controller.
*
* @param string $name
* @param string $controller
* @param array $options
* @return \Illuminate\Routing\PendingResourceRegistration
*/
public function resource($name, $controller, array $options = [])
{
return $this->router->resource($name, $controller, $this->attributes + $options);
}
/**
* Create a route group with shared attributes.
*
* @param \Closure $callback
* @return void
*/
public function group($callback)
{
$this->router->group($this->attributes, $callback);
}
/**
* Register a new route with the given verbs.
*
* @param array|string $methods
* @param string $uri
* @param \Closure|array|string|null $action
* @return \Illuminate\Routing\Route
*/
public function match($methods, $uri, $action = null)
{
return $this->router->match($methods, $uri, $this->compileAction($action));
}
/**
* Register a new route with the router.
*
* @param string $method
* @param string $uri
* @param \Closure|array|string|null $action
* @return \Illuminate\Routing\Route
*/
protected function registerRoute($method, $uri, $action = null)
{
if (! is_array($action)) {
$action = array_merge($this->attributes, $action ? ['uses' => $action] : []);
}
return $this->router->{$method}($uri, $this->compileAction($action));
}
/**
* Compile the action into an array including the attributes.
*
* @param \Closure|array|string|null $action
* @return array
*/
protected function compileAction($action)
{
if (is_null($action)) {
return $this->attributes;
}
if (is_string($action) || $action instanceof Closure) {
$action = ['uses' => $action];
}
return array_merge($this->attributes, $action);
}
/**
* Dynamically handle calls into the route registrar.
*
* @param string $method
* @param array $parameters
* @return \Illuminate\Routing\Route|$this
*/
public function __call($method, $parameters)
{
if (in_array($method, $this->passthru)) {
return $this->registerRoute($method, ...$parameters);
}
if (in_array($method, $this->allowedAttributes)) {
return $this->attribute($method, $parameters[0]);
}
throw new BadMethodCallException("Method [{$method}] does not exist.");
}
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 7,966
|
Gerd Koenen (born 9 December 1944 in Marburg) is a German historian and former communist politician.
Life and work
Koenen grew up in Bochum and Gelsenkirchen and studied Romance languages, history and politics in Tübingen. There, he joined the Sozialistischer Deutscher Studentenbund (Socialist German Student Association) in the wake of the shooting of Benno Ohnesorg by the police. In 1968 he moved to Frankfurt, where in 1972, he completed the state exam in history and politics.
In 1973, he joined the newly founded Communist League of West Germany (KBW). Under the influence of his party he gave up his 1974 doctoral dissertation, preferring instead to devote himself to the "revolutionary factory work" and from 1976 to edit the Communist People's Daily of KBW.
As of 1982, Koenen distanced himself from KBW and was disillusioned with his study of the Polish antisoviet movement Solidarity. A number of Koenen's publications are devoted to the history of communism and its perception in Germany, a subject on which he finally received his doctorate in Tübingen in 2003. From 1988 to 1990, he was editor of the magazine Pflasterstrand ("Paved Beach") along with Daniel Cohn-Bendit).
Koenen's 2001 book Das rote Jahrzehnt ("The Red Decade") became well-known and due to the discussion of the radical leftist past of foreign minister Joschka Fischer, and the importance of the '68 movement in the history of the Federal Republic.
Unlike some other intellectuals with communist pasts, Koenen so far has not absolutely condemned all left positions in a reversal of position. In a 2001 edition of the Joscha Schmierer-edited magazine Commune, Koenen inveighed against the "trial of the young seniors of the Free and Christian Democracy, a rhetoric of universal suspicion of their way of Resolute conformism as the only possible way of socialization ex post yet to establish".
Articles by Koenen also appeared in Der Spiegel, Die Zeit and many national newspapers. In addition, Koenen is author or co-author of several radio and television broadcasts.
Koenen got his doctorate in 2003 from the University of Tübingen with his thesis Rom oder Moskau – Deutschland, der Westen und die Revolutionierung Russlands 1914–1924 ("Rome or Moscow: Germany, the West and the revolutionization of Russia 1914–1924"). From 2008 to 2010, Koenen researched the history of communism at the Freiburg Institute for Advanced Studies, FRIAS.
Books
with Krisztina Koenen und Hermann Kuhn: Freiheit, Unabhängigkeit und Brot. Zur Geschichte und den Zielen der Arbeiterbewegung in Polen. Sendler, Frankfurt am Main 1981, .
with Barbara Büscher, Ruth-Ursel Henning, Dorota Leszczynska, Christian Semler, Reinhold Vetter: Solidarność. Die polnische Gewerkschaft 'Solidarität' in Dokumenten, Diskussionen und Beiträgen. Bund-Verlag, Köln 1983, .
Der unerklärte Frieden. Deutschland – Polen – Rußland. Eine Geschichte. Sendler, Frankfurt am Main 1985, .
Die großen Gesänge: Lenin – Stalin – Mao Tsetung. Führerkulte und Heldenmythen des 20. Jahrhunderts. Eichborn Verlag, Frankfurt am Main 1987 (2. Auflage 1991), .
Unheilige Allianz. Rußland und Deutschland. Eine 400jährige Faszination in Freundschaft und Feindschaft. Eichborn Verlag, Frankfurt am Main 1990, .
with Karla Hielscher: Die schwarze Front. Der neue Antisemitismus in der Sowjetunion. rororo, Reinbek bei Hamburg 1991, .
with Lew Kopelew (Hrsg.): Deutschland und die russische Revolution 1917–1924; West-östliche Spiegelungen Serie A, Bd. 5; Fink, München 1998, .
Utopie der Säuberung. Was war der Kommunismus?. Alexander Fest Verlag, Berlin 1998, .
Das rote Jahrzehnt. Unsere kleine deutsche Kulturrevolution 1967–1977. Kiepenheuer & Witsch, Köln 2001, .
Vesper, Ensslin, Baader. Urszenen des deutschen Terrorismus. Kiepenheuer & Witsch, Köln 2003, .
Der Russland-Komplex. Die Deutschen und der Osten 1900–1945. C.H. Beck, München 2005, . (Leipziger Buchpreis zur Europäischen Verständigung 2007)
Traumpfade der Weltrevolution. Das Guevara-Projekt. KiWi, Köln 2008, .
with Andres Veiel: 1968. Bildspur eines Jahres. Fackelträger, Köln 2008, .
Was war der Kommunismus? Vandenhoeck & Ruprecht, Göttingen 2010, (FRIAS Rote Reihe, Band 2).
References
Living people
1944 births
Historians of communism
Historians of fascism
University of Tübingen alumni
21st-century German writers
21st-century German male writers
20th-century German historians
German male non-fiction writers
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 7,515
|
<?php
namespace backend\modules\fix\models;
use Yii;
/**
* This is the model class for table "fix_poin_detail".
*
* @property integer $id
* @property integer $project_id
* @property integer $site_id
* @property integer $prin_id
* @property integer $prin_detail_id
* @property integer $inventory_id
* @property string $inventory_name
* @property double $qty
* @property integer $unit_id
* @property integer $unit_name
* @property double $price
* @property integer $status
* @property integer $vendor_id
* @property integer $home_id
* @property integer $job_list_id
* @property string $job_name
* @property integer $is_deductions
*/
class PoinDetail extends \yii\db\ActiveRecord
{
/**
* @inheritdoc
*/
public static function tableName()
{
return 'fix_poin_detail';
}
/**
* @inheritdoc
*/
public function rules()
{
return [
[['project_id', 'site_id', 'poin_id', 'prin_detail_id', 'inventory_id', 'unit_id', 'status', 'vendor_id', 'home_id', 'job_list_id', 'is_deductions'], 'integer'],
[['qty', 'price'], 'number'],
[['inventory_name', 'job_name'], 'string', 'max' => 255],
[['unit_name'], 'string', 'max' => 50],
];
}
/**
* @inheritdoc
*/
public function attributeLabels()
{
return [
'id' => 'ID',
'project_id' => 'Project ID',
'site_id' => 'Site ID',
'poin_id' => 'poin_id ID',
'prin_detail_id' => 'Prin Detail ID',
'inventory_id' => 'Inventory ID',
'inventory_name' => 'Inventory Name',
'qty' => 'Qty',
'unit_id' => 'Unit ID',
'unit_name' => 'Unit Name',
'price' => 'Price',
'status' => 'Status',
'vendor_id' => 'Vendor ID',
'home_id' => 'Home ID',
'job_list_id' => 'Job List ID',
'job_name' => 'Job Name',
'is_deductions' => 'Is Deductions',
];
}
public function getUnit()
{
return $this->hasOne(Unit::className(), ['id' => 'unit_id']);
}
public function getInventory()
{
return $this->hasOne(Inventory::className(), ['id' => 'inventory_id']);
}
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 4,448
|
We're getting an error message that seems to say "You took too long on filling out the form" (paraphrasing). Even when we just take 30 seconds to complete then hit register. Can you help? Hosting is with Siteground.
You will likely need to deactivate the SiteGround caching plugin to avoid that error. The Siteground caching plugin is known to delete the session transient prematurely.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 5,816
|
# On a Shoestring to Coorg
_An experience of southern India_
DERVLA MURPHY
_To Rachel and her father with love and gratitude_
It may yet be found that the traveller who tosses up at every crossroads will arrive first at the goal.
from _The Thoughts of Wi Wong_ by Arland Ussher
# _Contents_
1. Title Page
2. Dedication
3. Epigraph
4. _Acknowledgements_
5. _Map_
6. _Prologue_
7. 8. 1 Initiation in Bombay
9. 2 Hippies in Goa
10. 3 Tibetans in Mundgod
11. 4 Discovering Coorg
12. 5 Musings in Mysore
13. 6 Andanipura Farm
14. 7 The Huthri Festival
15. 8 A Glance at Kerala: Cochin's Kathakali Dance
16. 9 Pilgrims at Cape Comorin: Family Life in Tamil Nadu
17. 10 On the Coast of Coromandel
18. 11 Fever in Madurai: Wildlife in Periyar
19. 12 Ancestor Veneration in Devangeri
20. 13 Caste in Coorg
21. 14 Forest Funeral
22. 15 A Naming Ceremony and a Wedding
23. 16 Praying and Dancing
24. 25. _Epilogue_
26. _Select Bibliography_
27. _About the Author_
28. Copyright
# _Acknowledgements_
My thanks must go in many directions: to A. C. Thimmiah and Dr Chengappa of Virajpet, who made it possible for us to settle in Coorg; to the Bernstorffs of New Ross, who had us to stay for three months while I was writing this book and created a perfect background atmosphere of sympathetic encouragement; to Alison Mills and Karen Davenport who gallantly typed from an almost illegible manuscript without error or complaint; to Diana Murray who tactfully but relentlessly de-purpled many passages, and provided endless inspiration and comfort during the darkest hours of Revision; to Jane Boulenger and John Gibbins who helped prepare a chaotic typescript for the printer; to Patsy Truell who helped with the index and with correcting the proofs and to the editors of _Blackwood's_ _Magazine_ and _The Irish Times_ in which some extracts first appeared.
# _Prologue_
In August 1973 it was exactly five years since I had been outside Europe. Therefore feet and pen were equally itchy and I decided that this was the moment – before schooling started in earnest – to share with my daughter Rachel the stimulation of a non-European journey. Already she had twice proved, on European testing-grounds, that she could enjoy short bouts of travelling rough: but I did realise that no five-year-old could be expected to proceed as speedily as my faithful bicycle or as sturdily as my Ethiopian mule.
A period of happy dithering followed; I consulted the atlas almost hourly and received much conflicting advice. One friend, a political journalist, thought International Harmony badly needed a book on China by D. M. and urged me to write to the Chinese Embassy in London. I obeyed, ingratiatingly quoting a pro-Mao passage from my book on Nepal, but there was no reply. From Australia, another friend who works in god-forsaken mines wrote that the outback has much more to it than Europeans imagine; that the animal life and landscapes are fantastic; that if I avoided all cities I would adore the place and could write a pornographic classic about the mining subculture. From Kuala Lumpur, a friend's daughter who had been teaching in Malaysia for two years almost succeeded in persuading me that it is the _only_ country worth an intelligent person's attention; and another friend was adamant that anybody who has neglected to walk through the Pindus Mountains knows nothing of the more sublime joys of travel.
Most tempting of all, however, were the letters from a charmingly eccentric millionaire who repeatedly invited us out to explore the mountains of Central Mexico. His Mexican estate is embedded in primeval jungle and the nearest town of any size is many miles away. I liked the sound of all this, and one does not have to be a nasty calculating bitch to appreciate the advantages of a tame millionaire in the background.
Meanwhile, my publisher (who is Rachel's godfather and takes his duties seriously) was expressing the opinion that for me there is a book in Scotland. And left to myself I rather fancied Madagascar or New Guinea – though neither, I realised, is the ideal country in which to blood a five-year-old.
In the end I settled for Mexico, under the influence of the superb photographs that arrived in the post at least once a month. Included were views of a Gothic-style temple recently built in the middle of a mountain torrent for a colony of tame ducks who had found the surrounding terrain uncomfortable. One day I showed these pictures to an imaginative friend who said, 'If that's what he's built for his ducks, what will he build for you?'
Everybody was suitably impressed/censorious/envious/incredulous when I announced that soon I was going to Mexico to live with a millionaire in a jungle. But then a friend came to stay, who had just returned from India, and as we talked a most delightful feeling took possession of me.
I recognised it at once, though some years had passed since I last felt it. It was an excitement amounting almost to intoxication, a surging impatience that quickened the pulse. It was a delicious restlessness, a stirring of the imagination, a longing of the heart, a thirst of the spirit. It meant that I did not want to go to Thailand, Greece, Kenya, Australia, Malaysia, Dhagestan, Tanzania, Scotland, Madagascar, New Guinea, Mexico or anywhere other than India. It was absurd – and, at that stage of my planning, downright inconvenient. But I welcomed it.
My choice of Mexico had been quite arbitrary. All the other possibilities had seemed equally attractive and just as likely to bear readable fruit; and this detachment had been, I now realised, a bad omen. If travel is to be more than a relaxing break, or a fascinating job, the traveller's interest, enthusiasm and curiosity must be reinforced by an emotional conviction that at present there is only one place worth visiting.
Initially I felt bewildered by this effervescence of what must have been fermenting for years in hidden corners of my mind. Far from having fallen in love with India during previous visits I had been repelled by some aspects of Hindu life, irritated by others, uneasily baffled by most and consciously attracted by very few. On balance I had found the Indians less easy to get on with than the Pakistanis and Nepalese – to say nothing of the Afghans and Tibetans – and by making this fact too plain in my first book I had deeply offended a number of people.
Why, then, my compulsion to go back? I had no quasi-mystical ambition to improve my soul by contact with Hindu spirituality, nor had I forgotten the grim details of everyday Indian life – the dehumanising poverty, the often deliberately maimed beggars, the prevaricating petty officials, the heat, the flies, the dust, the stinks, the pilfering. Is it, perhaps, that at a certain level we are more attracted by complexities and evasions, secrets and subtleties, enigmas and paradoxes, unpredictability and apparent chaos, than by simplicity, straightforwardness, dependability and apparent order? It may be that in the former qualities we intuitively recognise reality, and in the latter that degree of artificiality which is essential for the smooth running of a rationalistic, materialistic society.
Certainly I had always been aware – without always being prepared to admit it – that my more unsympathetic responses to Hindu culture exposed a personal limitation rather than the defects of Indian civilisation. In other words, India represented a challenge that I, like countless other Europeans, had run away from. However, unlike the impregnably self-assured Victorian imperialists I could not convince myself that a failure to appreciate India was a mark of virtue. So perhaps it is not really surprising that as the time-gap widened between India and me the pull to return to the scene of my defeat and try again operated like an undertow in the unconscious – growing steadily stronger until, on that September evening, it took command.
By next day, however, my euphoria had ebbed slightly and I was seeing this return to India as a dual challenge. Apart from the subtle, impersonal challenge of India itself, there would be the personal challenge posed by trying to achieve a successful fusion of two roles: mother and traveller. It seemed those roles must inevitably clash and at moments I doubted if they could ever be made to dovetail. Then I realised that from the outset one role had to be given precedence: otherwise the whole experience would be flawed, for both of us, by my inner conflicts. So I decided to organise our journey as Rachel's apprenticeship to serious travelling.
In effect, this decision meant not organising it; we would fly to Bombay and slowly wander south to Cape Comorin, planning our route on a day-to-day basis. As things turned out, these inconsequential ramblings had the happiest results. In South West India, between the Malabar Coast and the Carnatic, we both fell in love with the little-known province of Coorg. And there we stayed for two months.
At Heathrow there was a cheerful man behind the weighing-machine and I felt rather smug when he said – 'So you're off to India for a short weekend?'
I think I can claim to have perfected the art of travelling light. Neither my medium-sized rucksack nor Rachel's mini-rucksack was quite full, yet no essential had been left behind. We were even carrying some luxuries; seven minute rubber animals in a tin box: crayons and felt pens: a favourite furry squirrel: one storybook (a Rupert Bear annual – not my choice) and half a dozen schoolbooks. For four months in South India one needs much less kit than for four weeks in Europe. From November to March the weather is warm and dry, and light clothing costs so little in the bazaars that our wardrobe consisted only of a change of underwear. Rachel's pack held _Squirrel Nutkin_ , our sponge-bag and our first-aid kit, water-purifying pills, antiseptic ointment, Band-Aids, multi-vitamin capsules and antidysentery tablets. My pack held a bathing-costume, our sleeping-bags, books, notebooks and maps.
As our plane took off Rachel plunged into conversation with an amused gentleman from Kerala and I suddenly became conscious of having embarked on an adventure that would demand mental rather than physical stamina. This was to be my first long journey with a human travelling-companion, and I am a person who needs solitude. Yet there were obvious compensations. I regard other adults – however congenial – as a form of insulation against the immediate impact of travelling experiences; but small children form links, not barriers. And I was enjoying a delightful 'holiday feeling', knowing this to be the start not of an endurance test but of a carefree journey 'as the spirit moved us'.
CHAPTER ONE
# _Initiation in Bombay_
## NOVEMBER 16TH. YWCA HOSTEL, BOMBAY
Somewhere Apa Pant has remarked that air-travellers arrive in two instalments and for me this is Disembodied Day, that dreamlike interval before the mind has caught up with the body; and because a natural parsimony compels me to eat all the meals served en route the body in question feels so overfed I wish it could have been left behind, too.
Oddly enough, Rachel seems immune to jet-lag, despite having had less than three hours' sleep. I chose to stay in this hostel for her sake, thinking it would serve as a not too unfamiliar halfway house between Europe and Asia. But such solicitude was soon proved needless and I last saw her disappearing up the street with two new-found Indian friends. It seems she has gone to lunch with someone; I felt too exhausted to find out exactly with whom or where.
Of course even I was buoyed up, for the first few hours after our landing at seven a.m., by the simple fact of being back in India. Emerging from the cool plane into warm, dense air (72 ºF., according to official information) I was instantly overwhelmed by that celebrated odour of India which I had last smelt many hundreds of miles away, in Delhi. It seemed to symbolise the profound – if not always apparent – unity of this country. And it is not inappropriate that one's first response to India should involve that sensual experience least amenable to analysis or description.
Outside the airport buildings the scores of waiting taxi-wallahs made little effort to capture us – no doubt they understand by now the financial implications of a rucksack – and with the roar of jets in the background we walked for the next forty minutes through scenes of poverty, filth and squalor which make exaggeration impossible. On flat stretches of wasteland dozens of men were performing their morning duty, unselfconsciously squatting, with rusty tins of water to hand and sometimes a hopeful pig in the background. The Hindu opening his bowels must be the world's greatest mass-manifestation of the ostrich-mentality. Your average Hindu is an extremely modest man, but because he can't see you, having his gaze fixed on the ground, he will serenely evacuate while hundreds of people pass to and fro nearby.
So we proceeded, with bougainvillaea gloriously flourishing on one side of the highway and the stench of fresh excrement drifting to us from the other. All around were uncountable thousands of homes – many no bigger than small tents – constructed of bamboo matting, or driftwood, or beaten kerosene tins. Between and in these shelters people seethed like so many ants, and diseased pi-dogs nosed through stinking muck, and shrivelled-looking cattle were being driven on to the dusty, grey-green wasteland to eat Shiva-alone-knows-what. After some time Rachel observed dispassionately, 'I must say this place seems rather shattered' – a tolerably graphic description of the outskirts of Bombay. Yet I was not overcome by that nauseated depression which similar scenes induced ten years ago. Perhaps I am no longer quite sure that India's dire poverty is worse than the dire affluence through which we had been driving twelve hours earlier in London.
Outside one sagging bamboo shelter at the edge of the road a graceful, dark-skinned young woman was washing her feet, using water taken from a stagnant, reeking pond with a lid of bright green scum. She looked up as we passed, and met my eyes, and smiled at us: and her smile had a quality rarely found in modern Europe. It recalled something I had read on the plane, in Dr Radhakrishnan's essay on 'Ethics'. 'When the soul is at peace, the greatest sorrows are borne lightly. Life becomes more natural and confident. Changes in outer conditions do not disturb. We let our life flow of itself as the sea heaves or the flower blooms.'
Presently a taxi slowed beside us and the driver suggested – 'You go Gateway of India for only Rs.40?'* He dropped abruptly and unashamedly to Rs.10 on realising I was no newcomer to India. Then, when I still shook my head, he looked sympathetic and advised us to board an approaching city-bound bus. The fare, he said, would be only forty paise for me and twenty paise for 'the baby'.
The bus was crammed and we were nowhere near a scheduled stop. Yet the driver obligingly halted and the conductor curtly ordered a barefooted youth with dirty, matted hair – probably a tribal outcaste – to give up his seat to the foreigners. The youth obeyed at once, but sullenly; and his resentful glare so embarrassed me that I remained standing beside him while Rachel sat down. Then another young man, weedy-looking but neatly dressed, offered me his seat, told me his name was Ram and asked, 'Where is your native place?' He thought Glasgow was the capital of Ireland but claimed to be a _Times of India_ staff reporter.
A cool breeze freshened the windowless bus as we slowly jolted through mile after mile of slums, semi-slums and swarming bazaars. Rachel was fascinated to see bananas growing on trees, cows lying on city pavements and a crow boldly swooping down to steal a piece of toast off a street-vendor's stall. And I was relieved to feel myself rejoicing. On the plane it had suddenly occurred to me that this return could prove a dreadful mistake. But now, looking affectionately out at India's least attractive urban-slum aspect, I knew it was no such thing.
Ram followed us off the bus and spent over two hours – 'It is my duty...' – helping us to locate this hostel. I can never come to terms with his type of doggedly helpful but obtuse Indian. To us such people seem too self-consciously altruistic as they offer help or hospitality, though in fact this is a gross misinterpretation of their state of mind. Nevertheless, the _mleccha_ – the foreigner – is usually helped by Indians like Ram not because the Indian cares about the individual's fate but because he regards the needful stranger as an incidental source of religious merit, a messenger from the gods who, if given aid, will act as a channel for valuable blessings. Granted, this is a nice idea: but from the _mleccha_ 's point of view it tends to stunt many of his relationships with Indians. Few Westerners enjoy being discounted as individuals; and most travellers like to be able to feel that each new acquaintance is potentially a new friend.
This morning I would have much preferred to find my own way and we might well have got there sooner without a guide who refused to admit that we were repeatedly being sent astray. Everyone of whom we sought assistance gave us a different set of wrong directions with complete assurance. I had forgotten the Indians' propensity for being ultra-dogmatic when in fact they haven't a clue; and on a hot day in a big city with a small child after a sleepless night I found it excessively trying. Moreover, because Ram meant so well, and yet was being so stupid and obstinate, I felt increasingly irritated and ungrateful and therefore guilty. It is on such trivia that everyday Indo–European relations most often founder.
When at last we arrived here Ram held out his hand to say a Western-style goodbye and fixed his gaze on a box of cigars sticking out of my bush-shirt pocket. 'Give me those cigars,' he requested, in an oddly peremptory tone. I stared at him, nonplussed by the strength of my disinclination to reward him for all his efforts. Then I opened the box and handed him one cigar. He could see there were four others, but he seemed not to resent my meanness. Turning away from him I realised something was out of alignment, though I couldn't quite determine what. Perhaps because of this being Disembodied Day, the whole incident made me just a little apprehensive. It seemed to conceal a warning of some sort, possibly to the effect that it is perilously easy for Indians and Europeans to bring out the worst in each other.
It is now two p.m., so Rachel should be back soon from her luncheon party. I had planned to sleep while she was out, but I seem to have reached that point of exhaustion at which sleep eludes one. Why do people regard flying as an _easy_ way to travel?
_Later_. My philosophical acceptance of Indian destitution did not survive this afternoon's stroll around Bombay. Men with no legs and/or arms were heaped in corners or somehow propelling themselves along pavements; lepers waved their stumps in our faces or indicated the areas where their noses had been; deformed children frantically pleaded for paise and hung on to my ankles so that, as I tried to move away, their featherweight bodies were dragged along the ground; and – in a way worst of all – perfectly formed children, who could be like Rachel, sat slumped against walls or lay motionless in gutters, too far beyond hope even to beg. One pot-bellied, naked toddler stood quite alone, leaning against the pillar of a shopping arcade with a terrible expression of resignation, and mature awareness of misery, on his pinched, mucus-streaked face. Should he survive he will doubtless end up resembling the next wreck we passed – an ancient, armless man, wearing only a token loincloth and sitting cross-legged beneath the arcade, his shaven head moving all the time slightly to and fro, like a mechanical toy, and his hardened, sightless eyeballs rolling grotesquely.
Around the next corner we came on a small girl who had festering scurvy sores all over both legs and was sitting on the edge of the pavement with her baby brother (I suppose) in her lap. He lay gasping, his mouth wide open, looking as if about to expire. He weighed perhaps ten or twelve pounds but, judging by his teeth, must have been at least a year old. Nearby, a young woman with the dry, lined skin of the permanently hungry lay stretched full length in the shadow of a wall. Her skeletal torso and flaccid breasts were only half-covered by a filthy cotton wrap and her eyes were partially open though she seemed to be asleep. She may have been the children's mother. None of the passers-by took any notice of her. One five-paise piece lay in the tin begging-bowl by her side and a small glass of tea now costs at least twenty paise. As I dropped fifty paise into the bowl I was ravaged by the futility of the gesture. Of course one has seen it all before, and read about it, and heard about it, and despairingly thought about it. Perhaps it is too commonplace, too 'overdone', to be worth talking or writing about again. Perhaps the tragedy of poverty has lost its news-value. Yet it has not lost the power to shatter, when one comes face to face with fellow-humans who never have known and never will know what it feels like to eat enough.
This evening I find another of Dr Radhakrishnan's comments more pertinent than the one I quoted earlier. 'There was never in India a national ideal of poverty or squalor. Spiritual life finds full scope only in communities of a certain degree of freedom from sordidness. Lives that are strained and starved cannot be religious except in a rudimentary way. Economic insecurity and individual freedom do not go together.'
In the bed next to mine is an Iraqi woman journalist who also arrived today to report on India's reaction to the oil-crisis. She admitted just now to feeling no less shattered than I am, though during the 1960s she worked in Bombay for four years. 'One forgets,' she said, 'because one doesn't want to remember.'
'And _why_ doesn't one want to remember?' I wondered.
She shrugged. 'It serves no purpose to clutter the mind with insoluble problems. Tonight, as you say, we are shattered. And in what way does that help anybody? It simply boosts our own egos, allowing us to imagine we have some vestige of social conscience. It's only when the Mother Teresas feel shattered that things get done. Now I must sleep. Good-night.'
A forceful lady – and a realist.
## NOVEMBER 17TH. YWCA HOSTEL, BOMBAY
Most of the young women here seem to be Christians from Kerala or Goa. They speak intelligible though not fluent English and work as teachers, secretaries, clerks, receptionists or shop-assistants. By our standards the majority are outstandingly good-looking, though too many have bewilderment, loneliness – and sometimes disillusion – behind their eyes. Transplanted from sheltered, gregarious homes to this vast and callous city of six million people, their lives must be dreary enough. Overprotected upbringings will have done nothing to prepare them to make the most of their stay in what is – much as I dislike the place – India's premier city and an important centre of every sort of social and cultural activity.
None of those to whom I have spoken has any relative or friend in Bombay: if they had they would not be staying in a hostel. Yet they consider themselves lucky to have got into the YWCA and one can see their point; the place is clean and spacious, though gloomy with the endemic gloom of institutions, and the charges are reasonable. We are paying only Rs.25 per day for four meals each – as much as one can eat – and two beds in a six-bed, rat-infested dormitory. To Rachel's delight, pigeons nest in the dormitory rafters (hence the rats, who appreciate pigeon eggs) and cheeky sparrows by the dozen hop merrily around the floor. The walls are decorated with large, violently coloured photographs of the girls' favourite film stars and four ceiling fans keep the temperature comfortable.
In India the establishment of even the simplest facts can take several hours and it was lunchtime today before I could feel reasonably certain that tomorrow at eight a.m. we may board a steamer to Panaji (Goa) from the Ballard Pier. However, our misdirected wanderings in search of this information were enjoyable enough and at one stage took us through the narrow, twisting streets and lanes of the old city, where many of the Gujarati houses have carved wooden façades, recalling Kathmandu. Rachel was thrilled to see craftsmen at work behind their stalls – sandalwood carvers, tortoise-shell carvers, brass-smiths, coppersmiths – and when we passed the unexciting eighteenth-century Mombadevi Temple she said she wanted to 'explore' it. But a rather truculent priest demanded Rs.10 as an entrance 'offering' so I suggested she postpone her study of Hindu architecture until we reached some more spiritual region.
In the enormous, high-ceilinged hostel refectory we lunched at the matron's table by an open window and, as we ate our rice and curried fish, watched a kite eating a rat (ex-dormitory?) in the topmost branches of a nearby fig tree. Then Rachel got into conversation with two friendly Peace Corps girls, on their way home from Ethiopia, who invited her to accompany them to Juhu beach. She accepted delightedly and, as an afterthought, suggested that I might come, too.
Juhu is only ten miles from the city centre but it took us two hours to get there. Today Bombay's taxis are on strike, in protest against the government's suggestion that auto-rickshaws should be introduced into the city to conserve fuel, so the buses were impossibly crowded and we had to walk to the railway station.
Even when the suburban train was moving, agile urchins constantly leaped in and out of our carriage, hawking a wide variety of objects, edible or decorative. The little girls were no less daring and strident than the little boys and Rachel became quite distressed lest one of them might fall under the train. (She herself is by nature extremely cautious, with a tendency to pessimism which can be exasperating: but at least it means I need never worry about her doing reckless deeds.) There is an enormous difference between the children of the truly destitute, who are past trying, and these ragged but enterprising youngsters with their mischievous eyes, wide grins and flashing teeth.
Juhu beach is lined with tall palms, expensive hotels and the homes of the rich. Where we approached it, through a gap between the seafront buildings, a large notice said 'Danger! Bathing Forbidden!' The sand stretched for miles and was unexpectedly deserted, apart from a few servants of the rich exercising a few dogs of the rich, yet within seconds of our beginning to undress a score of youths had materialised to stand and stare.
The Americans decided simply to sunbathe, because of the above-ground sewage pipes we had passed on the way from the station, and to avoid whatever the danger might be I kept close to the shore, where the water was shallow, tepid and rather nasty. I couldn't even feel that I was being cleaned, since my own pure sweat was obviously being replaced by something far less desirable. I soon got out but Rachel refused to emerge until the huge red balloon of the sun had drifted below the horizon.
Back on the road, we stopped at a foodstall to buy deliciously crisp, spiced potato-cakes, stuffed with onions and freshly cooked over a charcoal fire that flared beautifully in the dusk. Then we stood at a bus stop for thirty-five minutes, during which time seven alarmingly overcrowded buses lurched past without halting. The eighth and ninth did stop, but took on only the more belligerent members of the assembled mob, so before the tenth appeared I requested the girls to fight their way on, take Rachel from me and, if I got left behind, cherish her until we were reunited. In fact neither the tenth nor the eleventh stopped, but we successfully assaulted the twelfth.
The narrow streets of the Ville Parle bazaar were lit by a golden glow from hundreds of oil-lamps hanging over stalls heaped with every sort of merchandise: bales of shining silks and vividly patterned cottons, stacks of gleaming copper pots and stainless steel ware, round towers of glittering glass bangles, pyramids of repulsively Technicolored sweetmeats, acres of fresh fruit and vegetables, mountains of coconuts, molehills of cashew-nuts, hillocks of melons, forests of sugar-cane and gracefully overflowing baskets of jasmine-blossom. Mingling with the dreamy richness of the jasmine was that most characteristic of all Indian evening smells – incense being burned in countless homes to honour the household gods. (Foul gutters and festering sores, jasmine and incense: India in a nutshell?)
Through the jostling, noisy crowd – uninhibitedly abusing, joking, arguing, gossiping, chiding, haggling: no sign here of Hindu inertia – through this pulsating crowd moved creaking ox-carts and hooting buses, chanting sadhus and yelling balloon-sellers, thoughtful-looking cows and overloaded handcarts, cursing cyclists and battered trucks, hoarse lottery-ticket sellers and faceless Muslim housewives carrying so many purchases beneath their _burkhas_ that they looked pregnant in the wrong places. 'It's fun here,' said Rachel, 'but you must be careful not to lose me.' She fell asleep on the train and had to be given a piggyback home from Churchgate Station.
* One rupee equals five pence and there are one hundred paise to the rupee.
CHAPTER TWO
# _Hippies in Goa_
## NOVEMBER 18TH. AT SEA BETWEEN BOMBAY AND PANAJI
The deck-area of our steamer is not too crowded and after Bombay one appreciates sea-breezes, even when adulterated by clouds of hash; forty or so of our fellow deck-passengers are hippies on their annual migration from Nepal, or the north of India, to Goa.
In affluent Europe I find it easy enough to understand an individual hippy's point of view, but on seeing them massed against an Indian background of involuntary poverty I quickly lose patience. Several of those within sight at this moment are emaciated wrecks – the out-and-outers, travelling alone, carrying no possessions of any kind, clad only in tattered loincloths, their long sadhu-style hair matted and filthy, their bare feet calloused and cracked, their legs pitted with open scurvy sores, their ribs and shoulder-blades seeming about to cut through their pallid skins, their eyes glazed with over-indulgence in Kali-knows-what and their ability or will to communicate long since atrophied. This is dropping-out carried to its terrible conclusion – but dropping into what, and why? Certainly these wrecks will soon drop into a nameless grave, and for their own sakes I can only feel the sooner the better. One agrees when hippies criticise the essential destructiveness of a materialist society, but what are they offering in its place?
All day we sailed south under a cobalt sky, within sight of the mountainous Maharashtrian coast, past dark-sailed fishing-boats that have scarcely changed since pre-Aryan times. The deck, shaded by a vast tarpaulin, never became too hot and now the night breezes feel deliciously cool.
This afternoon, while Rachel was bossing three shy little Goan boys into playing her sort of game, I was talked at by a young engineer from Poona who proved to be a compulsive statistics quoter. He told me that Maharashtra makes up one-tenth of India's territory, that two out of every five industrial workers employed in India are Maharashtrians, that the Indian film industry, most of the defence factories and two-thirds of the textile and pharmaceutical industries are in Maharashtra, that that State contributes more than one-third of India's revenues and that its per capita consumption of electricity is more than twice the all-India average.
At this point the plump, amiable young Goan who was sitting on my other side – father of Rachel's current boy-friends – remarked thoughtfully, 'And in the capital of Maharashtra more than a lakh people sleep on pavements every night.'
The Maharashtrian glared. 'At Nhava Sheva a second Bombay is to be built soon,' he said coldly.
'How soon?' wondered the Goan mildly, his eyes on the Western Ghats.
'Sooner than anything is likely to be built in Goa!' snapped the Maharashtrian.
The Goan continued to gaze at the mountains. 'But I don't think we _need_ new buildings,' he said. 'Not many, anyhow. We are content.'
' _Content!_ ' sneered the Maharashtrian. 'Do you not know that after 450 years of Portuguese ruling not one village had electricity? Now after eleven years of the Indians' ruling, most villages have it.'
The Goan looked from the mountains to me and smiled very slightly. 'But for a lot of those four hundred and fifty years no village anywhere had electricity,' he observed.
Then he and I stood up and went to make sure our respective offspring had not flung each other overboard.
At about five-thirty we altered course, making for Ratnagiri harbour, and the sun was swiftly sinking as we sailed between high headlands, covered with long red-gold grass that glowed like copper in the slanting light. A romantically ruined fort and a small white temple crowned the cliffs to starboard – lonely against the sky, looking out to sea. 'It is a very holy temple,' my Roman Catholic Goan friend told me. A civilised respect for all religions has rubbed off on to many Indian Christians from their Hindu neighbours.
In Ratnagiri's wide lagoon little craft sped towards us like waterbeetles and briefly the western sky was a flaring expanse of scarlet and purple, orange and violet. Then the sun was gone, but still I stood enchanted, gazing across the dark green waters of the bay to where distant flecks of firelight marked the many thatched huts on the lower slopes of the steep encircling hills.
A steamer puts in at Ratnagiri every evening, except during the monsoon, yet our arrival caused such excitement we might have been calling at Pitcairn. The unloading and loading of passengers and cargo took over an hour, but unfortunately Rachel missed the fun – having gone to sleep, almost literally on her feet, at four o'clock. A Spartanish upbringing is now paying off: she thinks nothing of lying down on a filthy deck amidst scores of talking, eating, praying or copulating Indians. Yet she cannot – positively cannot, without retching – tolerate the deck-class loo and I have had to show her the way to the first-class lavatories. No amount of Spartan brainwashing can reasonably be expected to eradicate this sort of inherent fastidiousness.
A hazard I had overlooked was the degree of spoiling to which a small child would be exposed in India. During these first few days it has perhaps helped to give Rachel confidence in relation to her new surroundings, but I hate to think what four months of it will do to her.
Indian reactions to the very young can be most trying from a European's point of view. While we were unloading at Ratnagiri Rachel slept deeply, undisturbed by hundreds of people – passengers, crew and coolies – running, leaping and shouting all around her. Yet, despite her being so obviously exhausted, at least a dozen women had to be physically restrained from trying to fondle, play with and talk to her. I fear a few of them misunderstood my motive and fancied I was operating some _mleccha_ caste taboo. In a country of overcrowded joint-family dwellings there can be no conception of a child's need for long hours of unbroken sleep. In other respects, too, the tendency is to treat Rachel as an animated toy rather than a human being. Most of the Indians we have met so far are complimentary about her in her presence, recklessly provoke her to show off (little provocation is needed) and allow her to interrupt their conversations with impunity. All this naturally aggravates her bumptiousness, which trait seems to me the chief distinguishing mark of small female humans. But perhaps I should have said 'Western humans', since most Indian children are evidently immune to it. The Indian tradition discourages the development of a child's self-reliance and no doubt counteracts what to us is 'spoiling'. One can afford to be tolerant of bad manners and constant demands for attention, and effusive about a child's allegedly winning ways, if one has no real regard for him as a unique human personality.
Another minor problem at present is how to take Rachel's occasional harsh criticisms of the behaviour of certain Indians. For instance, early this morning our half-empty bus twice sped away from bus stops, leaving several would-be passengers behind, and she asked, 'Why didn't the driver give these people time to get on? He's being cruel.'
Not wishing her to become the sort of habitually condemnatory traveller one too often meets in India, I muttered something about 'thoughtlessness rather than cruelty'; but I could see she was not impressed by this. Our bus-driver's behaviour was most probably a result of his enjoyment of power, but it would have been both absurd and unwise to try to explain to Rachel that recently urbanised young Indians, in positions of petty authority, often become bullies for complex reasons connected with the structure of the Hindu family. Therefore, to avoid confirming her deduction that many Indians are callous louts, I had fallen back on the sort of waffling she so rightly scorns. The snag is that small children have their own black and white code and to try to make them focus on the grey areas too soon would impose an unfair strain. Against one's own cultural background one manages this situation without even thinking about it, but given the added complication of an alien set of values it can become decidedly awkward.
I have been advised that the best and cheapest place to relax in Goa is Colva beach, where the hippy colony is small, the beach long and the absence of man-eating insects makes sleeping out feasible. Although Goa has a lot to offer I don't plan to explore: we are pausing there solely to give Rachel a few days' rest while she completes her adjustment to the time-change.
## NOVEMBER 19TH. COLVA BEACH
We berthed at Panaji two and half hours late; I'm not sure why, but who cares anyway? Today I have been quite overcome by Indian fatalism plus European sybaritism. This beach really is everyman's dream of a tropical paradise.
Our night on the boat was imperfectly restful; during the small hours we stopped twice at obscure ports and the usual pandemonium ensued by the light of the moon and a few Tilly lamps. Soon after five o'clock both Rachel and I gave up the attempt to sleep and sat looking over the side at the tender beauty of moonlight on water. Then gradually came a dove-greyness to the east; and then a lake of bronze-green light widening behind the Western Ghats; and finally a sudden reddening and a radiant arc above the night-blue mass of the hills. That was a sunrise to remember.
We sailed up the palmy, balmy Aquada estuary through schools of frolicking porpoises, yet despite its lovely setting I was not impressed by Panaji which is being developed with more haste than taste.
Goa has traditionally enjoyed a standard of living higher than the Indian average, but recently new industries fostered by Delhi have attracted thousands of landless peasants, from Andhra Pradesh, UP and Mysore, and many have been unable to get the jobs they hoped for. Therefore the scene as we berthed was not quite what the tourist literature leads one to expect of dreamy, easy-going, old-world Goa. Some fifty or sixty porters were grouped on the quay and they fought each other like tigers for access to the boat and an opportunity to earn the equivalent of two and a half pence. In some places such _mêlées_ are no more than a local sport; here the frantic desperation on these men's faces made one realise that carrying a load could mean the difference between a meal and no meal.
Panaji's best buildings line the quay – the Old Fort, Government House and the Palace of the Archbishop, who is Primate of the Roman Catholic Church in India. (Since reading Desmond Morris I cannot use that phrase without visualising a gorilla in cardinal's robes.) Having strolled past these and other handsome façades we spent half an hour wandering through the narrow but astonishingly neat and clean lanes of the old, Iberian-flavoured quarter of Fontainhas. During Portuguese times every urban householder was compelled by law to paint the outside of his house annually, after the monsoon, and it seems the Goans have not yet abandoned this habit.
From Panaji one can take a motor-launch to Rachol, en route for Colva beach, but wishing to glimpse the countryside we went by bus – a roundabout journey, because of Goa's many rivers and estuaries. For two hours we jolted slowly between still, palm-guarded paddyfields, or over steep hills entangled in dense green jungle, or past tidy hamlets of red-brown thatched cottages, or over wide, slow rivers serenely reflecting a deep blue sky. I couldn't help longing to be on foot, with a pack-animal to carry my kit; but another year or so must pass before I can revert to that way of life.
In four and a half centuries the Portuguese naturally made a much deeper impression on Goa (area 3,800 square kilometres: population 837,180 in 1971) than the British could make on their unwieldy empire in less than half that time. Margao is emphatically not an Indian town – not even to the extent that the British-built hill-stations now are – but neither is it Portuguese, despite a few imposing buildings with Moorish touches. Like the rest of Goa, it has its own unique, unmistakable character.
One immediately senses the effect on local attitudes of the hippy influx. The Goans are by nature welcoming and warm-hearted, and not unduly disposed to take financial advantage of the tourist, but many do now feel it necessary to be politely on guard with outsiders. Much hippy behaviour grossly offends Indians of every sort, though this country's high standards of tolerance and hospitality usually preserve the offenders from being made to feel uncomfortable or unwelcome. In Goa, however, with its strong Christian minority, I had thought people might be less temperate in their reactions to such hobbies as nudity and drug-taking; but apparently this is not so.
When we got down from our bus it was two o'clock, and hot and still in the streets of Margao. Most of the shops were shut – I was looking for a liquor store – so we sat drinking tea under a tattered awning, watching a couple of American hippies rolling a joint. When someone beckoned from the tea-house door the young man jumped up with more alacrity than hippies are wont to display and hurried round to the side of the building. His companion then looked at us, smiled hazily and asked, 'You want some grass?'
'No thank you,' I said, 'my vices are of another generation. I'm looking for a liquor store. But it seems they're all closed.'
The girl stood up. 'I'm Felicity,' she said, shaking pastry-crumbs out of the folds of her voluminous ankle-length robe. 'Come, I'll show you – there's always one open down here.' And she took the trouble to guide us for half a mile through dusty, sun-stricken streets. At the door of the shop she nodded and turned away, having given a perfect example of the sort of disinterested kindness practised by many hippies but for which the tribe gets too little credit.
Colva is a scattered settlement, rather than a town or village, and my heart sank when the bus stopped on the edge of the beach beside a shack in which Coke and other such fizzy potions are sold. The place seemed to be infested with foreigners. Not less than ten were visible at a glance, including a flaxen-haired youth who was strolling under the near-by palms, stark naked, his eyes fixed raptly on the horizon as though it were vouchsafing him some vision not normally granted to man – as, indeed, it doubtless was. Rachel considered him closely for a moment and made an unprintable judgement before turning her attention to the camping possibilities of the terrain.
As we walked on to the beach it became apparent that Colva is not, after all, too seriously infested; pale, smooth sands stretch for many miles with no trace of development and away from the bus stop there are few people to be seen. Close to the sea, palms flourish on low, scrubby sand-dunes where I reckoned it should be possible to camp comfortably; but first we would bathe, and then return to the settlement to eat before looking for a sleeping-spot. Floating in clear green water, listening to pure white surf singing on golden sands beneath an azure sky, I felt as unreal as a figure in a travel brochure for millionaires.
The local fisherfolk – whose boats and nets are strewn all over the beach – seem very shy, though willing to be friendly with Rachel. They are almost black-skinned, quite tall and beautifully proportioned. (Good advertisements for a fish and coconut diet.) The women wear gay blouses and swirling skirts, the men only a codpiece attached to a string around their waist, or sometimes to a belt of silver links. As we bathed they were constantly passing to and fro, the women and girls carrying on their heads enormous circular wicker baskets, or earthenware or brass jars. Twice we saw crews loading elaborate nets into heavy boats, which were then pushed on rollers into the sea. It delighted me to watch these men – all grace, strength and skill – performing a ritual unchanged for millennia. As they worked they chanted a slow, haunting song and seemed to be thoroughly enjoying themselves. These aboriginal inhabitants of Goa have never interbred with invaders.
Back at the settlement we met a pathetic American youth named Bob who had the unmistakable appearance of one suffering from chronic dysentery. When I explained that we were going to sleep out he jumped like a shot rabbit and told us that a hippy sleeping on the dunes had had his throat slit three nights ago. The naked body was found only this morning and has not yet been identified, nor have the police any idea who the killer might be, so we are now installed in a typical Goan fisherman's hut at Rs.5 a night. It is half-full of nets and other equipment, with a roof and walls of palm-fronds, interwoven with palm-trunks, and a floor of loose, fine sand. The beds are strips of coir laid on the sand and since there is no door the place has its limitations as a protection against throat-slitters. However, our landlord's cottage is scarcely thirty yards away and his pi-dogs are large, fierce and vociferous.
From our non-door we have a splendid view of the sea; I threw a stone to see if the waves were within a stone's throw and if I were a better stone-thrower they would be. Rachel rejoices in the innumerable small black pigs and minute piglets, and in the brown-and-cream goats and mangy pi-dogs (too much fish produces mange) who roam around nearby. The whole beach is permeated by a strong but pleasant fishy smell: noisy flocks of gulls and crows see to it that no fish rots. Slightly less pleasant-smelling is my present form of illumination – a wick floating in a small tin of shark's oil.
## NOVEMBER 20TH. COLVA BEACH
This has been an extremely idle day: I can think of none other quite like it in my entire life. Yet now my muscles are reminding me that 'idle' is not the mot juste; since morning I must have swum seven or eight miles, up and down, parallel to the beach.
I am writing this sitting in the doorway of our hut, with a glass of Feni (the local spirit, distilled from cashew-nuts) beside me, and through a fringe of palms, stirring in the evening breeze, I can see a fleet of ancient fishing-boats sailing away into the gold and crimson sunset. But this is a place and a time for purple prose, so I must exercise restraint.
A coconut-picker has just been distracting me: I delight in watching them as they swarm up these immensely tall trees, with no aid but a few shallow footholds cut in the bark, and send huge nuts thudding on to the sand. Nuts are now seventy-five paise each – a few years ago a rupee bought half a dozen – but one nut provides a full meal for two.
A ripple of morbid excitement went through the settlement today as the police from Margao man-hunted. They have apparently established that the murdered man was a German – good detective work since he wore nothing, carried no documents and had communicated with nobody during his fortnight or so amongst these dunes. Such a degree of withdrawal is common at a certain stage of drug-addiction, when the victim himself hardly knows who he is, but the Goan police do not realise this and clearly suspect Colva's foreign colony of an unhelpful conspiracy of silence.
## NOVEMBER 21ST. COLVA BEACH
The hazards of tropical life are upon us. This morning Rachel trod on a malevolent dead fish with a frill of four-inch spikes around its neck. One spike penetrated far into her right foot, which bled profusely, but prolonged immersion in sea-water seems to have cured it.
When I looked up just now I saw a line of five young women walking by the edge of the waves, balancing enormous wicker fish-baskets on their heads. They moved with marvellous grace and against a turquoise sea their full-skirted gowns – orange, blue, pink, yellow, red, green, mauve – billowed and glowed brilliantly. Life on Colva beach is full of such pictures, making the ugliness and suffering of Bombay seem not part of the same human existence. But the snag about even a rudimentary tourist industry is that it inexorably raises barriers between travellers and residents. Here the Us and Them atmosphere is already so strong that one can only admire the locals from a distance.
This is being another slightly unreal day; it is just too idyllic to waken on golden sand in a palm-leaf hut, and to look through a non-door at a milky blue early sky, and to hear the gentle hiss of the surf behind the shrieking of parrots and the immemorial chanting of fishermen beaching their boats.
_Later_. The first disaster of the trip: despite all my security precautions someone stole between five hundred and six hundred rupees while we were having our sunset swim. As usual I had put my purse – containing watch, cash and traveller's cheques – in the pocket of my shorts, which were left close to the water with my boots on top to make an easily watched pile. I could have sworn I never took my eyes off that pile for more than thirty seconds and it was a nightmarish moment when I put my hand into my empty pocket. To be without one paise some 6,000 miles from home is not funny. Immediately I found myself thinking, 'Thank God it's a hippy colony!' for in such situations the less way-out type of hippy may be seen at his concerned best.
On the way back to our hut I paused to ask a young Australian couple – camping under the palms in a tiny tent – if they had noticed anything suspicious. They had not, but instantly offered to lend me Rs.10 and to babysit Rachel while I went to the police in Margao. (Here there is neither policeman nor telephone.) No one believed the police would even pretend to attempt to recover the money – responsible Indians themselves admit the rule of law has virtually collapsed since the British left – yet the average European's first reaction to any crime is to report it to the police. Though one may know this exercise to be pointless it still has a therapeutic effect, probably because it is our way of sublimating a primitive longing for revenge.
Leaving Rachel with the Australians, I hurried between the palms to our hut – and saw my purse lying on the floor the moment I stepped through the doorway. My first thought was that it must have slipped out of my pocket before we went for our bathe, but all the cash had been taken, including the coins, though all the cheques and my watch have been returned. So I feel certain the thief was not an Indian, who could use traveller's cheques as currency notes and to whom a Swiss watch would seem a treasure beyond price – even one bought for thirty shillings in Kathmandu eight years ago. It is, however, easy to imagine a destitute hippy lurking among the palms, or behind a beached boat, and being irresistibly tempted to solve his pressing financial problems at my expense. The hippy conscience is a curious, unpredictable thing and it does not surprise me that such a thief would go to some trouble to return unwanted loot. Very likely if the same young man – or woman – suddenly inherited a fortune they would give most of it away.
This is Colva's third major robbery from a foreigner in ten days. Last week an unfortunate English girl, on the way home from a working holiday in Tokyo, was robbed of £400, a gold watch and her passport. (British passports are currently fetching £300 each in India.) Such a calamity makes our loss look pretty insignificant and when I heard about it my lust for vengeance ebbed and I decided not to bother trekking to and from Margao police station.
## NOVEMBER 22ND. KARWAR
Last night four sympathetic fellow-foreigners arrived at our hut to cheer me with a mixture of Feni and Arlem beer and their mission was entirely successful. We sat happily on the sand, beneath a black sky that was lively with the golden blazing of tropical stars, and soon I had decided that money-losses were of no consequence and that all was right with my world. But I woke this morning feeling dreadfully otherwise. Clearly the aforementioned mixture is injudicious and the thought of our stolen money seemed the last straw.
Then our landlord's toothless wife called, as usual, with a little present for my breakfast – a thick, cold, moist slab of slightly sweetened rice-bread flavoured with coconut. Despite its promising ingredients, this bread is repulsive beyond anything I have ever eaten: but, because its cook always sat smiling in the doorway to observe my enjoyment of her gift, I had hitherto forced myself to masticate gallantly while looking as though taking an intelligent interest in her rapid Konkani monologue. This morning, however, being past such well-mannered heroism, I implied that I was hoarding the choice morsel for consumption on the bus. Whereupon our friend hastened away to return half an hour later, beaming, with two more slabs.
After our early swim I left Rachel digging a canal with a Swedish hippy and sought a large pot of tea in the recently built tourist restaurant – a small, inoffensive building. For obvious reasons I retired to the least bright corner but was soon pursued by the only other breakfaster, a bustling Bombay whizz-kid who even at the best of times would have done my equilibrium no good. He informed me that he was 'associated with the Taj Group of hotels' and had come to Colva to plan another excrescence to match that now being built near Calangute beach on the once-magnificent ramparts of an old Portuguese fortress. He was full of contempt for the shiftless Goans who, he claimed, were simply not interested in the profitable development of their territory. However, he assured me that things are about to improve. Apart from his own present endeavours, a hotel complex (which sounds like what I've got, but must mean something quite different) is being built near Colva by a Goan company; and Goan millionaire mine-owners are planning a five-star hotel at Siridao; and a Bombay travel agency is planning another five-star hotel at Bogmalo beach. And so 'the death of the goose' is being as ruthlessly and obtusely organised in Goa as in Ireland.
At our present pace it will not take humanity many more years to obliterate every trace of natural beauty on this planet; then people will look back on the Landscape Age as we look back on the Ice Age, believing it once existed yet unable to imagine it.
From Margao to Karwar is only forty-five miles but the journey took three and a half hours; Indian buses are probably the world's least frustrating motor vehicles. They always arrive (unless they crash, instantly killing everyone on board), yet they move so slowly, and stop so often for so long, that one can observe quite an amount of local life from a well-chosen seat.
This afternoon we passed first between newly harvested, golden-brown fields where pillars of blue-grey smoke marked bonfires of burning maize stalks. Then for miles our road twisted through lonely mountains covered in dense, shadowy jungle, or plantations of teak or eucalyptus – the last popular as quick-growing firewood. A few brown rhesus monkeys sat or sauntered by the roadside but Rachel missed them. In buses I refrain from pointing out things of interest, feeling she must be left to observe and absorb at her own pace. There is so much – details I take for granted – to delight and amaze her: full-grown bulls gently wandering between the benches in a bus stand waiting-room; cows with brilliantly painted horns wearing silver necklaces or garlands of flowers; flocks of bright green parakeets flying parallel with the road, racing the bus and, not surprisingly, overtaking it; petite women-coolies carrying great loads of earth or bricks or timber beams on their heads and babies on their hips; elaborately carved wayside temples; gigantic banyan trees like bits of Gothic architecture gone wrong; cascades of bougainvillaea and poinsettia; demented-seeming, nearly naked _sadhus_ moaning mantras as they hold their begging-bowls under one's nose.
A group of slim, ebony-skinned tribal people boarded the bus for a short time in the mountains but kept aloof from the other passengers. The men wore only the most meagre of loincloths and the barebreasted young women were laden with necklaces of tiny black beads – each necklace must have weighed at least two pounds – and with large golden ornaments in their noses and ears. They also wore countless tinkling glass bangles on their slender arms and many silver rings on their toes.
At the State border two armed military policemen came aboard to check all the luggage. Then they beckoned to three men who left the bus and followed them behind a small palm-frond shelter. A few moments later the men returned, openly replacing their rolls of rupees in their shirt pockets. Goa has long been a notorious smugglers' colony and since the Government of India banned the import of luxury articles the Goans have been supplying foreign status-symbol goods to both the newly rich, who want to flaunt their new riches, and the traditionally rich, who want to maintain their normal standard of living. Nor do the State police on either side of the border overlook the opportunities thus provided. Also, alcohol is sold throughout Goa for about half the price demanded in heavily taxed Mysore State. So it was tactful of the police to ignore my rucksack.
Over the border, we were still in unpeopled, heavily forested country, but the well-kept Goan road was replaced by a rough dusty track. Then we came to a village – to a town – to more villages – and were back in the 'teeming millions' belt. As the sun set I could see tiny lamps burning before crude shrines in domestic courtyards on the edge of the darkening forest.
At last the bus stopped, its front wheels only feet away from the lapping waters of the Kalinadi river estuary. Boarding the antique, overcrowded ferry-boat, I took Rachel on my knee and admired the ribbons of pink and gold cloud reflected in the wide waters. Then, turning to look towards the open sea, I saw a picture of unforgettable loveliness. The dark expanse of the estuary was catching the last russet-and-green sunset tints on its ripples, and to the north palms were etched black against a royal blue sky, and to the west, silhouetted superbly against the final fiery band above the horizon, a solitary, slim boatman stood astride his loaded craft, leaning on a long pole, straining to push off.
In India one rarely sees an ugly face but beside us on the bus today sat one of the ill-favoured minority who also suffered, poor lad, from severe acne. He passed the time by picking obsessively at his pimples and talking pidgin English to me, despite the evident impossibility of my being able to hear him above the rattling and roaring of our vehicle. On arrival at the ferry he solicitously helped us on to the boat, and off again at the other side, and then he insisted on taking us to the dak-bungalow in an auto-rickshaw. While I was thanking him, he predictably murmured 'It is my duty' and faded away into the night. Unfortunately the dak-bungalow was full; so, because of our spotty friend's conviction that a dak-bungalow is the only suitable accommodation for foreigners, we found ourselves stranded two miles from the town's hotels. While we were discussing what to do next an engineer from Bangalore introduced himself and as he knew Karwar well we gladly joined him in the search for rooms. A short, stout, middle-aged man, he spoke excellent English. I wondered if he would prove sufficiently Anglicised to offer to carry my water-bottle or foodbag but, though himself carrying only a fat briefcase, he made no attempt to share the white woman's burden.
For Rachel's sake, this was the sort of situation I had hoped to avoid, since I believe a small child can be expected to rough it only if allowed enough sleep at regular hours. However, she was thoroughly enjoying being out under the stars as we pushed our way through the noisy, crowded bazaar from one full hotel, or doss-house, to another. Children usually revel in unalarming crises which prove that grown-ups are not always able to organise things exactly as they want them.
Eventually we gave up and went to a vegetarian restaurant where we sat by open windows in the purdah compartment and much astonishment was expressed at the speed with which I – having eaten nothing all day – dispatched a moderately hot curry and a foot-high mound of rice. In South India food is served either on a large circular metal tray – usually, nowadays, of stainless steel – or, more sensibly, on a large square of banana-leaf. No cutlery is used and every restaurant is provided with hand-basins for the rinsing of hands and mouths before and after meals; if running water is not available a barrel or water-jar and several dippers will be placed beside the basins. The majority of South Indian restaurants are owned and run by Brahmans, since food cooked by the highest caste may be eaten by most Hindus. Usually in such establishments the floors are not very well swept, the tables are a trifle grubby, the walls are badly in need of paint, the hand-basins are fairly revolting and the latrines are quite unspeakable – but in the kitchens all will be well. Probably, in fact, a lot better than in most European hotel kitchens.
When we stood up to leave, our friend abruptly announced that he had decided to take us to the Government Polytechnic College, where the warden – a friend of his – would certainly allow us to doss down. So off we went in another rickshaw, weaving and honking and bouncing through the packed streets, back to the dak-bungalow suburb where the handsome, British-built college also stands, overlooking the sea.
The warden is away for the night, but his deputy received us most warmly – we might have been expected guests – and at once decided the luckless foreigners must have the warden's room. Within seconds of Rachel's lying on the narrow cot under the mosquito-net she was asleep and I then returned to the huge, high-ceilinged, almost unfurnished room where our host had been having his supper off a steel tray when we intruded. He ordered tea for me and we were joined by several of his staff, including three Tamils and a Madrasi Christian. All were dressed in _lunghis_ and loose shirts and each man carried with him his own light chair, though they might well have felt more relaxed sitting on the floor. Our host wears thick horn-rimmed spectacles, which suit his long, lean, very dark face, and he is obviously a man of outstanding ability. For hours we sat happily drinking tea and discussing South Indian languages, Bangladesh, Northern Ireland, the caste system, cow-worship, Watergate and Indian attitudes to birth control. I found these teachers excellent company. It is always the half-educated Indians who get one down. The educated and the uneducated each have their own style of charm and graciousness.
When the conversation turned to birth control I mentioned something that has been haunting me for the past few days – a colossal advertisement in Bombay's railway station proclaiming 'Sterilisation "The Best Method". Many Lucky Prizes Awards/Certificates to Promoters and Patients who Under Go Vasectomy from 20 Jan. '73 to 7 March '73.'
The deputy-warden and most of his staff agreed that, despite the inevitability of such a campaign, there is something disquieting – even sinister – about attempts to solve a population problem by depriving men and women, for ever, of their procreative powers. I asked their opinion of the sixty or so recanalisation centres, to which men who wish to replace dead children may apply; but it seems these operations carry no guarantee of success and the centres are little more than a propaganda device to reassure parents who fear sterilisation because of India's high infant mortality rates.
I have always been anti-sterilisation, perceiving behind the idea an insult and a threat to human dignity. Yet looking around any Indian railway station, or walking through any Indian bazaar, one realises there is now merely a choice of threats. And perhaps sterilisation is preferable to slaughtering or being slaughtered by one's neighbour.
The statistics are well known. An Indian is born every one and a half seconds, which means that more than 55,000 are born a day, which means that at present a country with 2.4 per cent of the world's land and 1.5 per cent of the world's income is supporting 14 per cent of the world's population. These are menacing figures, particularly when one has personally tasted the flavour of Indian urban life. Our struggle to get on a bus at Juhu beach was only slightly annoying; but for those who have no escape from the consequences of overpopulation, which in Indian cities constantly offend almost every sense, such experiences can be infuriating. During the hot weather, especially, they often provoke to uncontrollable violence people whose nerves are already frayed by hunger and money-worries.
A decade ago, when the world first heard of the Indian Government's sterilisation campaign, many people were deeply shocked; now one is half-inclined to wish it luck. And it is being moderately effective; the deputy-warden told me that well over two million men were sterilised during 1971–72. In 1965 India's Birth Control Programme was given 'top priority' and launched on a 'war footing' and in the fourth Five-Year Plan some Rs.3,000 million were to be set aside for its promotion: so no one can say the Indians have not been trying. Yet the population went up from 361 million in 1951 to 548 million in 1971. By now it must be nearly 600 million and if one dares to look ahead one can see the spectre of compulsory sterilisation on the horizon. My teacher friends emphasised that this would be repugnant to most Indians, but then we gloomily agreed that many ethical scruples may have had to be disregarded, all over the world, before the end of the twentieth century.
Now I am back in the warden's room, where I have had to close the window, because of weirdly zooming insects, and switch on the fan. Considering the status of its usual occupant, this apartment is very simple. The only furnishings are the cot, a long narrow table laden with books and papers, two camp-chairs and a steel filing-cabinet. Over a small shelf in one corner hangs a picture of a blue-bodied Shiva – representative of life-energy in all its manifestations – with a third eye in the middle of his forehead and wearing a necklace of serpents. On the shelf are the remains of a _puja_ offering, a safety razor and a small tin of Nescafé.
Some moments ago a kind student looked in to tell me our bus for Mundgod leaves at eight-thirty in the morning. When I first asked about this, nobody here had ever heard of Mundgod – a small town four miles from the Tibetan Refugee Settlement where we are going to spend the next few days. This settlement is run by an outstanding Tibetan refugee leader, T. C. Tethong, and his Canadian wife Judy, an old friend of mine. To get there it seems we must take one bus down the coast to Kumta, another to climb into the ghats and a third from Sirsi to Mundgod. My map tells me a more direct route would be through Kadra and Yellapur, but I suppose the local man knows best.
CHAPTER THREE
# _Tibetans in Mundgod_
## NOVEMBER 23RD. MUNDGOD TIBETAN SETTLEMENT
Four and a half months ago I stood in hot sunshine on a steep mountainside overlooking a deep green valley. Far above, long lines of freshly printed prayer-flags were suspended between pine trees and all round me hundreds of Tibetans were chattering, laughing and praying. The women looked gay in ankle-length _chubas_ and striped aprons; some of the older men had retained their pigtails, tied across the crown of the head, and a few wore turquoise and gold pendants on the left ear to mark their positions as lay state officials. Grey-haired peasants with calm, strong, wrinkled faces twirled prayer-wheels, wafts of incense came from the tall temple halfway down the slope and a four-man band was playing rousing Tibetan dance music. Occasionally lamas in orange and maroon robes passed through the crowd and were greeted reverently. Everyone looked happy and excited for we had gathered together to celebrate the thirty-eighth birthday of His Holiness the fourteenth Dalai Lama.
That was in Switzerland, well off the tourist track and three miles from the nearest village. Many of the more prosperous young Tibetans had come to the monastery by car from the nearby towns where they worked as watchmakers, carpenters or factory hands. They moved awkwardly in their long robes, now worn only on special occasions, and their wives fed babies from shining, sterilised bottles. The older children were drinking Coca-Cola through straws and exchanging remarks in Swiss German. Almost everyone was lavishly decked out in silver, jade and turquoise jewellery, but these ornaments were brand new. The old pieces had been sold in India for a few rupees when the refugees were starving.
Ten years ago I lived on another mountainside, also steep and pine-clad and criss-crossed with prayer-flags. That was at Dharamsala in the Himalayan foothills, where in those days most Tibetans wore lousy rags and the air reeked of makeshift latrines and so many orphaned children died every week – of dysentery, bronchitis, measles, scurvy and malnutrition – that one dared not allow oneself to feel for them.
Why, then, was I overcome by sadness as I looked around at the healthy, well-dressed, contented Tibetan community in Switzerland? United in loving families, secure in their well-paid jobs, accepted and admired by the Swiss, it seemed that for these seven hundred or eight hundred migrants, at least, the refugee story had had a happy ending. Yet to be among them oppressed me almost intolerably.
At eleven o'clock we moved into the temple and a long, long queue formed to lay ceremonial white muslin scarves before His Holiness's portrait. The altar was laden with butter lamps (an expensive expression of devotion in Switzerland), and with little mounds of rice and sacrificial cakes; and, watching the Tibetans ritualistically presenting their scarves, I wondered what – if anything – all this meant to youngsters who had lived most of their lives in Switzerland and would never live anywhere else. There was a striking contrast between the expressions and general demeanour of the young Tibetans, reared in Switzerland, and their elders, reared in Tibet. It sounds glib to say that the faces of the older Tibetans were marked by a serenity that passeth European understanding; yet this is the simple truth.
The scarf-bearing queue was still long when suddenly I knew I could take no more. The emotion I had been trying to suppress all morning had the strength and quality of one's feelings at the deathbed of a beloved friend. As we left the temple, Rachel asked, with the animal perception of a four-and-a-half-year-old, 'Why are you so sad today? This is a birthday party.' But of course I could not explain.
Remembering all that today, as we walked from Mundgod town, I half-dreaded arriving at this settlement. I am absurdly vulnerable about Tibetans. A sentimental fool, perhaps, but in good company; many distinguished scholars deplore the erosion of Tibet's traditional culture no less than I do.
We saw no motor traffic and few people on our narrow road. All around stretched miles of golden stubble, green pulses and dark ploughland, encircled in the distance by powder-blue mountains. The silence was broken only by the calls of jewelled birds, the occasional creaking of straw-laden ox-carts or the tinkling of cow-bells. The light had an exhilarating clarity, a cool breeze blew – we were at about 2,000 feet – and small cotton-wool clouds sailed high.
Suddenly I stopped and pointed into one of the wild mango trees that grow by the roadside. Rachel looked and went scarlet with excitement.
'Monkeys!' she whispered ecstatically. 'Millions and millions of monkeys!'
'About a dozen,' I corrected prosaically.
Half a mile farther on we turned a corner and far away in a stubble-field I saw what was unmistakably a group of Tibetans. Their physique and very way of moving is so utterly different from the Indians that they were at once identifiable and, as we drew nearer, I heard their familiar and beautiful harvest song: a most poignant sound. From the edge of the field we could see three elderly men and two young women threshing grain; they were dressed in rags and darkly sunburnt but their faces revealed what the Tibetans in Switzerland have lost. When they noticed us I waved and called ' _Tashi Dele!_ ' and they waved back and laughed and bowed and stuck out their tongues. (The origin of this custom had to be hastily explained to an appalled Rachel.) As we walked on my heart was full of hope; it seemed everything might be all right at Mundgod.
I found Judy astonishingly unchanged by marriage and the thirties. Tall and slender in her _chuba_ , she still looks like an eighteen-year-old and it is hard to believe she first came to India ten years ago, to work as a CUSO volunteer under the gruelling conditions I have described in another book.
Soon we were sitting drinking tea on the wide veranda of an attractive guest-bungalow vividly decorated in Tibetan style; this building is somewhat misleadingly known as 'The Palace' because it was built primarily for the Dalai Lama's use during his visits to South India. Judy and her husband, who is known as T. C., live in a tiny three-roomed bungalow, less than half the size of 'The Palace', on the same rise of land overlooking the administrative heart of the settlement – the office of His Holiness's representative (T. C.), the office of the Co-operative Society (of which T. C. is chairman) and a branch of the local bank. Nearby are the workshop, school, hospital, shop and old people's home for those who have no surviving relatives. And all around, replacing the dense forest that grew here only seven years ago, are the level, neat fields now owned by the refugees, not all of whose nine villages could be seen from our veranda.
As the sun was setting in glory we watched eighteen tractors being driven back to the workshop compound, while Tibetan songs and laughter rang faintly across ploughland and stubble; and I began to be aware that this settlement is successful beyond anything I had imagined possible. Then I felt more than ever curious to meet T. C., who is one of the few Tibetan aristocrats to have been influenced, as a refugee among refugees, by _noblesse oblige_. Since the first stampede into India fourteen years ago, after the tragic Lhasa uprising of March 1959, he has devoted his life to his compatriots – apart from three years spent in Germany, at the request of the Dalai Lama, acquiring a political science degree.
When we met at dinner I quickly came to understand why His Holiness regards Tsewang Choegral Tethong as one of his more dependable lieutenants. There is nothing facile about the leader of Mundgod – even his muscular, compact figure, which makes him look shorter than he is, has an uncompromising quality about it – yet he exercises that special brand of charm which is based on sincerity. Though never effusive, he is consistently kind; and after a few hours one has realised that he is also just, patient, obstinate when necessary and devout with that little-spoken-of yet deeply felt religious faith characteristic of educated lay Tibetans.
Now I long to explore Mundgod and examine in detail the Tethongs' achievement. T. C. confirmed my suspicion that we should have come today via Yellapur, but I am glad we did not miss that drive to Kumta through the high green spurs of the Western Ghats, where they slope steeply to meet mile after mile of lonely golden beaches, washed by a sapphire sea.
## NOVEMBER 24TH. MUNDGOD TIBETAN SETTLEMENT
In 1965, when the Indian Ministry of External Affairs offered the Tibetans 5,000 acres of virgin forest near Mundgod, T. C. came south with a small team to survey the possibilities; but for various reasons – mainly bureaucratic – reclamation work did not begin until December 1966. Four bulldozers were lent by Swiss Aid, the United Nations High Commission for Refugees and Oxfam, and for these the Government of India provided fuel, operators and mechanics. Of the three hundred Tibetans who came from the Himalayan road-camps in November 1966 some 75 per cent were farmers and 100 per cent were eager beavers. A government-sponsored transit-camp of tents was set up and the workers were paid Rs.1.25 a day plus their rations. Three years of bulldozing, clearing and building followed, and by the end of 1969 the reclamation had been completed and the fields were ready to be sown. (Though reclamation, one feels, is not quite the right word for subduing virgin forest.)
Meanwhile, at the end of 1967 sixteen British-made tractors had been presented by the World Council of Churches and three hundred farmers had come from the Kulu valley; and a few months later another three hundred or so arrived from the Kailasa region of West Tibet, via a detention camp in UP (The Indian fear of Chinese spies entering the country as Tibetan refugees has perhaps been allowed to become a phobia; yet such things have occasionally happened, and could happen again, and the Tibetans themselves are in favour of careful checking lest His Holiness might be assassinated when giving a mass-audience to newly arrived refugees.) In April 1968 another seven hundred men, women and children came from the road-camps around Simla, and in November 1968 over five hundred Ledakhi nomads arrived, including a few lazy trouble-makers who sound not unlike the difficult Dolpo nomads I was once up against in Nepal. Early in 1969 a second group of newly escaped West Tibetans arrived via the detention camps, and throughout that year other small groups came from Bhutan, Rajput and Delhi. By the end of 1970 the population of the settlement had been officially completed, with over 3,000 Tibetans living in nine villages; but a trickle of individual refugees still continues to flow southward and no one in real need is turned away.
The villages vary considerably in size but there are a total of 397 double houses for almost eight hundred families, and each family has one hundred and twenty feet by sixty feet of kitchen-garden where banana and papaya trees flourish – and vegetables and flowers, if the owners are energetic enough and the water-supply is adequate. Each village has its own water-storage tank, providing clean water from deep wells, but there is no sanitation – just the fields – and Judy is trying to introduce the sensible system of human manure conservation traditionally used in Tibet. (Though obviously it would have to be modified to suit a hot climate.)
At the time of land-distribution four acres were allocated to each five adults, plus half an acre for each child, so already economic inequality is apparent as the households with expanding families become poorer. For many years the more sophisticated Tibetans have been deliberately limiting their families and in Tibet some spontaneous form of birth control, possibly connected with the effect of high altitudes on hormones, seemed to keep the peasant birth rate down. Now, however, the ordinary refugee is very chary indeed of operations, pills, loops, caps or even the condom, which throughout India may be bought almost anywhere for the nominal sum of five paise and has recently become quite popular amongst Indian men. Unfortunately Tibetan peasants seem to think birth control in some way shameful or 'inauspicious' and, as they are particularly vigorous gossips, fear of what the neighbours might say is enough to keep them away from family-planning clinics. There is nothing in their religion to support this bias, so it is possible that they are now under the influence of some deep instinct of self-preservation. No one wants them to get caught up in the Indian vicious circle of malnutrition and stunted intelligence, but at this stage in their history is it, in fact, desirable to restrict the replacement of those uncounted tens of thousands 'eliminated' during the past fifteen years?
Before land distribution took place the acres already cleared were farmed collectively but – Tibetans not being natural collectivists – the output was low. However, by May 1971 each family had its own plot and production promptly soared. Ever since, the settlers' output per acre has been far above the local average, despite the poorish quality of the soil and a chronic shortage of fertilisers. In November 1967 the Co-operative Society was formed to handle crop selling, and seed and fertiliser buying. It flourishes, and very few members try to avoid paying their debts.
T. C. also runs a workshop where all the settlement's mechanical repairs are carried out, the necessary spare parts being made from scrap-iron. Despite their non-technological cultural background, most Tibetan youths have a marked flair for this sort of thing. The workshop serves, too, as a training centre for boys from both the Mundgod and Bylekuppa settlements, and T. C. would like to be able to employ all the surplus Mundgod school-leavers by making small spare parts on a contract basis. One hopes he will succeed. Unless their leaders take some such action – and training programme funds are readily available from Refugee Year donations – many of the younger refugees will soon have no alternative but to beg. True, they are free to set up as traders or craftsmen in Mundgod bazaar, or to seek labouring jobs outside the settlement: but such jobs for hundreds of school-leavers will not be easy to find, though the local people – to their credit – are very well disposed towards Tibetans. These Indians surely have legitimate grounds, if such can be said to exist, for envy and jealousy. Nobody has ever given them free land, the free means to reclaim and till it, free seeds, free fertilisers, free food and free housing. But, of course, it may be argued that neither has anybody ever deprived them of all they once possessed – the flaw in this argument being that so many Indians have never possessed anything.
After breakfast, we walked across to the gigantic, noisy workshop where several groups of alert young Tibetans in greasy overalls were manipulating complicated tools. They looked happy and absorbed, these members of the first generation of refugees to grow up with few, if any, memories of their homeland. Yet watching them I felt a pang, when I thought back to the simple way of life their own fathers still knew, scarcely twenty years ago, beyond the Himalayas. Even if political developments were to make a return to Tibet possible, neither the refugees nor their country can ever regain the Age of Freedom when most journeys meant riding contentedly for many days over the silent steppes. ('Freedom from what?' my more irritated progressive readers may enquire impatiently at this stage. And the short answer is, 'Freedom from the abominable effects of industrialisation, the consumer society and the internal combustion engine.')
Leaving T. C. in the workshop, the rest of us went on to the hospital, which is administered by Judy. These refugees have adjusted well to a climate which, though not hot by South Indian standards, is extremely hot by Tibetan standards; but tuberculosis remains a major problem. The most important members of the hospital staff are, of necessity, Indian, though the Tibetans would like to be able to supply their own doctors and nurses. Unfortunately, however, not all the young refugees trained abroad at vast expense are keen on returning to the relative hardships of life in India. The gadgets and glitter of the West have an almost hypnotic fascination for people in whose own country many peasants still use flint and steel to make fire; even His Holiness is not immune to this fascination, so it is absurd to expect adolescent refugees to withstand it.
I strolled through a few of the villages today and visited several homes. Although these three hundred and ninety-seven houses started out as identical bungalows, with red-tiled roofs, whitewashed walls and concrete floors, hardly any two are alike by now. Most families have added one or more rooms, using their own cash and labour and sometimes improvising rather impermanent walls of bamboo-matting plastered with cowdung. On the whole such building efforts add little to the beauty of a village, but they certainly preserve it from the drabness of uniformity. Each family has built its own mud stove but as usual there are no chimneys so every room is impregnated with wood smoke. Western-type furniture is rare, Tibetan couches and carpets being used instead. Every living-room has an altar in one corner, more or less elaborate but always with a decorated picture of His Holiness and a row of silver butter-lamps.
The two monasteries here are the pathetic remains of Drepung and Ganden, to which are attached small groups of Nyingmapa and Sakyapa lamas. In all, six hundred monks came to Mundgod from their notoriously unhealthy camp at Buxa and many of them are still plagued by lung diseases contracted there. The monks live in little houses like everyone else's but the temples are fine buildings, in the traditional Tibetan style, and there is also a Drepung debating hall. The villagers give just as many sons to the monasteries as they did in Tibet, so one sees dozens of little monks around the place; from The Palace we can hear their treble chanting carried on the breeze at prayer-times. Each monastery has three hundred adult monks who have been granted plots at the rate of two acres to three monks – a meagre ration indeed, when one thinks of the old days. The monks still farm collectively, but with them the system works well because of monastic discipline. Their relations with the lay-people are essentially as they were in Tibet and they perform the same ceremonies, in addition to cultivating their land. However, though time could be found for both ritual and agricultural activities it was soon realised the student monks could not also be expected to do the amount of intensive studying needed to keep their religious tradition alive. So His Holiness has just started a scheme whereby the twenty brightest students will be supported by their communities, by the settlement and by the Tibetan Government-in-Exile while completing their studies. Then they will take to the fields with the rest, leaving their juniors to concentrate on the awesome courses of philosophy and metaphysics which, after many years slogging, entitles a Tibetan monk to be called a 'lama', or teacher. This seems an excellent scheme and some people feel it may even herald a religious renaissance amongst the refugees. But this is perhaps being too optimistic.
## NOVEMBER 25TH. MUNDGOD TIBETAN SETTLEMENT
Yesterday Rachel several times begged to be taken to the nearby jungle to monkey-watch, so early this morning we set off, armed with 'rustling sticks' against the local cobras, kraits and vipers, all of which are said to be numerous. A brisk fifty-minute walk across pale gold stubble-fields, and up slopes entangled in green scrub and coarse reddish grass, took us to the settlement boundary. We crossed a narrow stream of cool, quick water, and then were in a green meadow that sloped slightly up to the edge of the trees. Against a clear sky the parakeets were emerald streaks, harshly warning the forest of our approach, and in the distance I could see the branches of a conspicuously tall banyan tree moving agitatedly as a troop of langurs heeded that warning.
Our monkey-watching was not nearly as successful on that isolated hillside as it had been on the road from Mundgod, where the monkeys are accustomed to human traffic. But during our wanderings through the thin forest, interspersed with grassy glades, I felt no less thrilled than Rachel to be surrounded by such a variety of exotic birds, butterflies, beetles, trees, vines, shrubs and flowering plants. According to T. C., the most troublesome local animal is the wild pig, which can wreck a whole maize crop in one night, and we saw much evidence of porcine rootings in the glades. (We have just had wild roast pork for supper – delicious.)
At last I suggested that if we wanted more than a glimpse of the langurs we had better sit very quietly behind a screen of shrubs and wait for them to reappear. Sitting quietly is altogether against Rachel's principles, but today the motive was strong enough and after not many minutes we saw a fine male langur loping across the grass, his silver coat gleaming where the sunlight fell through the trees. He was followed by two females, and then chatterings and screams made us both look up to see a whole gang of adolescents at play in that giant banyan. Forgetting herself, Rachel squealed with excitement and at once the tall male reappeared and raced across the grass not ten yards from us, swearing angrily, his white whiskers bristling against his black face. As he swept up the banyan the youngsters leaped on to another tree, and then another, and gradually the scoldings and rustlings died away. I looked at Rachel and quoted:
His hide was very mangy and his face was very red,
And ever and anon he scratched with energy his head.
His manners were not always nice, but how my spirit cried
To be an artless _Bandar_ loose upon the mountainside!
My literal-minded daughter frowned. 'Their hides weren't mangy,' she said. 'And their faces were black.'
On the way home I told her the story of Rama and his wife Sita, and Ravana and Hanuman, the monkey-king who was also a langur and probably the first detective in world literature. Then I told her that many Indians used to – and perhaps some still do – believe the English to be the descendants of Hanuman and a female servant of Ravana, the demon-king who held Sita a prisoner. This servant treated Sita so well that Rama promised her she should be the mother of a race who would one day rule India. And then Hanuman married her.
'But human beings and monkeys don't mate!' protested Rachel. 'Anyway, I think some of the _Indians_ look more like monkeys. The English look like us.'
'Ssh!' I said. 'You'll have the Race Relations Board after you.'
' _What_ is the Race Relations Board?' – and that kept us going until we got back to a late breakfast.
Mundgod's atmosphere is an excellent antidote to the affluent society; one sees many poor people, yet never a discontented face. I enjoy standing at the main settlement crossroads, just looking and listening. Usually a few figures are moving along the tracks: maybe an old man with braids across his head, twirling his prayer-wheel, on his way to gain merit by walking around the new _stupa_ near the hospital; or a young woman with baby on back going to the Tibetan-run store to buy material for a new _chuba_ and also twirling her prayer-wheel; or a group of children, clutching dog-eared copybooks, chasing each other home from school. Then a tractor will come busily bumping along to plough another field, or a Tibetan-owned truck, loaded with surplus rice for the market, will drive towards the public road, or one of the richer farmers may be seen manoeuvring his bullock-team with the assistance of a Harijan servant. The local Indians consider the Tibetans very good employers. And, judging by appearances, the local cattle find the Tibetans very good owners; all the settlement cattle are in markedly better condition than their Indian-owned brethren.
I do not find it easy to convey the elation I feel this evening. During previous visits to India I have known the Tibetans only as penniless, landless, homeless wanderers, often separated from their children through death or misfortune. Therefore to see them tilling their own fields, repairing their own machinery, sweeping their own floors, selling their own produce and – above all – playing with and loving their own children is an eminently heart-warming experience. It seems to me that here, miraculously, the authentic spirit of Tibet has been revived. All the qualities that made the Tibetans so admirable and lovable and enviable when first one knew them flourish throughout this settlement. The fact that most of the villagers have never been exposed to any but the most superficial non-Tibetan influence is no doubt partly responsible, and Mundgod's isolation must also help. The whole settlement is Tibetan-run – which of course means that it is, in a refugee context, artificial, and what I have called 'the authentic spirit of Tibet' may soon be quenched here as elsewhere. I remember Professor Tucci making the interesting point, in one of his tomes, that whereas Hinayana Buddhism can co-exist with the most advanced social theories, Mahayana Buddhism, of which Tibetan Lamaism is an eccentric offshoot, is virtually incapable of surviving in the modern world. He concluded that when its formalism broke up it would be hard to find a substitute, and I suppose one feels Mundgod to be such a special place because here this formalism has been successfully, if only temporarily, re-established.
## NOVEMBER 26TH. MUNDGOD TIBETAN SETTLEMENT
Today, while Rachel played with her Tibetan contemporaries, I spent hours in the villages listening to the grim recent histories of families and individuals; and yet again I marvelled at the fortitude of the ordinary Tibetan. In this oasis of calm and contentment Tibetan Buddhism emerges as a most powerful spiritual force, however much outsiders may scoff at its crude animist traits, exuberant demonology, comic superstitions and money-spinning lamas.
I feel the Tethongs do not realise how much they have achieved here. The factors that went to make Mundgod may be divided into four groups; one: practical help from the Government of India and the refugee charities; two: guidance and support from the Dalai Lama; three: the industry and discipline of the settlers themselves; and four – uniting all the rest – the dedication, energy, endurance and imagination of Judy and T. C.
Tibetan refugees, being exiles from a hierarchical, feudal society, need immensely strong leadership during a resettlement phase, and advice of one sort or another every hour of the day, and encouragement, understanding and unsentimental love. All this they got from the Tethongs in a way and to an extent that has enabled them to become what they now are – independent, happy, free and still unspoiled.
Being all the time on the spot (holidays are not part of the Tethong lifestyle), Judy and T. C. are perhaps more aware of the daily frustrations and the innumerable minor flaws of the settlement than of its remarkable atmosphere. Throughout a middle-aged lifetime I have felt for few people the wholehearted admiration and respect I feel for this couple. To administer funds wisely, to organise practical affairs efficiently, to treat people kindly – all that is accomplished often (though not often enough) in the refugee world. But to have resettled a group of people as culturally fragile as the Tibetans, without destroying their spiritual integrity, is a rare and very wonderful achievement.
From here we go to the Bylekuppa settlement, a few hundred miles farther south, not far from Mysore City, and it will be interesting to see how that earlier and bigger settlement compares with Mundgod.
CHAPTER FOUR
# _Discovering Coorg_
## NOVEMBER 27TH. UDIPI
This evening I feel lonely not only for the Tibetans but for the various livestock in our Palace suite: the two busy little lizards; the swarms of minute, industrious ants who were always dragging around the colossal (relatively) corpse of some beetle, moth or cockroach; and the pretty light-brown frog who lived in the loo and leaped out whenever the lid was lifted (how alliterative can I get!) to take refuge on the wall until the plug had been pulled and his home made habitable again. Sometimes he had a long wait since the water-supply was almost as erratic as the electricity, which went off at least three times a night for periods of anything from ten minutes to three hours.
During the four-hour journey down the Malabar Coast from Kumta to Udipi we crossed three rivers as they were about to enter the sea, and the fertile, vividly green, palmy landscape that Rachel calls 'fatly populated'. Near Udipi our road ran for a few miles close to the beach, where fine sand shone with a strange rosy patina while the setting sun laid a trembling, molten path across the water. Then we crossed the wide Kolluri estuary, and overlooking it stood a steep, solitary peak of the Western Ghats, those high, royal blue mountains that run from Gujerat to Cape Comorin, isolating the fertile coast from the harsher plains and hills and plateaux of South Central India.
I thought our Malabar travelling-companions exceptionally likeable, yet everywhere in India one is aware of being kept at arm's length – sometimes literally. This is partly a consequence of the caste laws, which still strongly influence many who have given up formally obeying them, and partly a result of my being a woman and therefore, according to traditional Hindu beliefs, an essentially inferior person.
Perhaps some outsiders are drawn to this opaque world of one of man's oldest societies – where foreigners are never fully accepted, and can never fully understand – simply because they intuitively recognise how good it is for the soul to be cut down to size. Jolting slowly along those lovely roads today, I briefly _felt_ unimportant and insignificant, in a way one couldn't possibly do at home. It was an odd but not unpleasing sensation: and there was a perceptible element of escapism in it. In Europe one knows one is unimportant and insignificant, but having been brought up in an ego-nurturing tradition one rarely or never feels it – and if somebody or something did make one feel it, that person, event or circumstance would almost certainly be resented.
This evening I think I can identify one of the things that went wrong during my first stay in India. After a slow journey through the Middle East, and through places as gloriously un-Westernised as Gilgit and the Hindu Kush, I found the degree of apparent Westernisation anti-climactic. Now, however, having flown direct from London – and perhaps having in the intervening decade become a little less obtuse – India's Westernisation seems to me very superficial: though that is another too sweeping generalisation, since even Hinduism has been modified by industrialisation. Yet only slightly, so far. On the whole, the British influence, like that of many earlier conquerors, is being inexorably assimilated into India's _dharma_ , which eventually will be a little changed by this contribution as by all the others – though the changes will not necessarily be those the British would have wished to effect.
At Bhatkal, a biggish port town halfway between Kumta and Udipi, Rachel was a little scared to see several groups of Moplak women in silken _burkhas_ on the streets and at the bus stand. One can understand how these completely shrouded figures, moving about so swiftly and silently in their dusty slippers – though apparently unable to see – could make a child feel faintly uneasy. Yet cheerful colours are fashionable in Bhatkal this winter. In one group I counted eight different shades: sky-blue, pale pink, turquoise, orange, mauve, green, pale yellow – and black. Very likely the lady in black was an elderly chaperone.
For over 2,000 years Arabs have been trading with the Malabar Coast and the present-day Moplahs (Muslim merchants) claim to be descended from ninth-century settlers. From what I have seen of the men, they must never have intermarried with Indians to any great extent for they remain perceptibly Semitic. Most of the native Muslims and many of the native Christians are the descendants of low-caste Hindus or outcastes who went over to Islam, or Christianity, hoping thereby to improve their social position – a move which was rarely successful. If the bonds of the caste system could be so easily broken Indian society would have evolved along very different lines.
It was after dark when we arrived here and having tried four full hotels I turned reluctantly towards the posh-looking tourist hotel, expecting to have to pay Lakshmi-knows-what; but as Udipi never has any tourists the charge for a single room, with a fan, is only Rs.5. Already the interior of this new building looks very shoddy and the latrines stink so frightfully that my fastidious daughter had to be taken out to the gutter.
Tomorrow I must buy some candles, before the feeble bulbs in these hotel rooms have ruined my eyes for ever.
## NOVEMBER 28TH. MERCARA
We left Udipi at ten-thirty this morning, after a fascinating three-hour 'explore' (Rachel's term). I am no lover of crowds, but Indian towns – when not poverty-dominated – vibrate with a contagious vitality and I thoroughly enjoyed Udipi's bazaar. The people seemed happy, healthy, relaxed, friendly; and during the busy early morning hours the streets were flooded with colour – brilliant saris, shimmering silk _burkhas_ , the vivid sweeping skirts of tribal women, the men's equally vivid ankle-length _lunghis_ (which a few swift tucking movements transform into knee-length kilts) and, contrasting with all the rest, the white robes of orthodox Brahmans or the white saris of Hindu widows.
The usual wide range of goods was being carried through the market on a wonderful diversity of heads from six-year-old girls with bundles of freshly cut grass to eighty-year-old men with rolls of bamboo matting twice the length of themselves. There were improbable loads of tin kitchen utensils tied up in old fishing-nets and balanced with circus-artiste skill; trays of coconuts, cauliflowers, cucumbers, tomatoes, radishes, aubergines, fresh sardines, salted sardines, oranges, limes, supportas, jack-fruit and plantains; bales of firewood and sisal and sugar-cane and bamboo rods; tremendous towers of wicker baskets, perilously balanced stacks of new-fired ochre pitchers, tins of kerosene, crates of hens, baskets of bricks, very long planks, bulging sacks, locked tin trunks and a newborn, orphaned calf in a round wicker basket on the head of a worried-looking young woman.
Throughout the bazaar cattle were being deferred to by all and Rachel is still an incredulous observer of the amiability of Indian bulls. Inevitably she finds the Hindu attitude to cows difficult to understand, though I notice she has not simply dismissed it as 'a silly custom'.
I cannot agree with Dr Johnson that, 'Pity is not natural to man. Children are always cruel. Savages are always cruel. Pity is acquired and improved by the cultivation of reason.' Like many small children, Rachel has had, for some time now, strong tendencies towards vegetarianism. By nature she is most sympathetic towards this aspect of Hinduism, though she relishes her meat course and realises that it is kinder painlessly to kill an animal, and eat it, than to allow it to die agonisingly of hunger and thirst.
We went to the bus stand at ten o'clock to secure a good seat on the ten-thirty Mangalore bus. The usual chaos prevailed, yet despite this chaos most Indian buses do depart and arrive on time. The Indian road transport system is, unexpectedly, a miracle of organisation and a credit to all concerned.
At its terminus a bus stands ready to leave for at least forty minutes before departure time, yet only when the engine has been switched on do the majority of passengers appear, sprinting from nowhere to hurl themselves aboard with shouts of alarm and indignation. Indians relish drama and obviously enjoy _almost_ missing the bus.
As we moved out of Udipi we were at last feeling the heat, though while the bus was moving – the windows were unglazed – we felt not too uncomfortable. As soon as it stopped, however – which it did six times during the forty-mile run – we both began to sweat spectacularly.
We were on the back seat among the Harijans and looking down that bus was like being at a flower show, so many young women had decorated their glossy black coiffures with exotic scented blossoms, fresh from the jungle. Those are the little touches that make India – for all its obtrusive squalor – seem so much more graceful than present-day Europe.
We arrived at Mangalore just as a crowded bus was about to leave for Mercara and leaped on board to find two front seats inexplicably empty; I can only suppose the watches of the passengers concerned were inaccurate beyond the Indian average. When I handed over our fares I was, for the first time, given tickets previously used. This meant the conductor was pocketing our fare, having got back the used tickets from accommodating passengers to whom he had no doubt paid a consideration. I hesitated. Should I demand a valid ticket, thereby upholding Western standards of morality? Or should I respect local customs, remembering that for Rs.2 the conductor – who probably has a wife and ten children at home – could buy himself a good square meal? I decided on the latter course and put my change and the dud tickets in my purse. Then I felt someone lightly touching my shoulder and looked around to see an elderly Brahman wearing a pained expression. 'You must ask for a good ticket,' he said reprovingly. 'Bus conductors are not poor. They have to pay a lot to get such a job. He should not be allowed to cheat. Please ask for a good ticket.'
'Very well,' I said, shamefacedly, at once seeing the Brahman's point of view. By contributing one's mite of acceptance to this sort of thing, one is simply perpetuating a tradition that India could well do without. And, of course, the conductor cheerfully gave me a valid ticket on request, with the air of a man who has played a good game and knows how to take a beating.
The eighty-five-mile drive into the province of Coorg took us back over the Western Ghats and as we climbed almost 4,000 feet from the coast the splendour of the landscape exceeded anything we had yet seen. Dense jungle, in which many of the trees were ablaze with blossom, covered the lower slopes. Next came a vast rubber plantation, where the tappers were at work, and then we were amongst a massive array of tumbled blue ridges and peaks. The air felt deliciously cool and on every side mountains rose steeply from deep, narrow, wild ravines, while occasionally one glimpsed, far below in a paddy-valley, the vivid green of a new crop or the gold of stubble. Over its final fifteen miles this road climbs 2,900 feet and at a certain point, where the gradient is one-in-twelve, our Brahman friend again tapped me on the shoulder. 'You must know,' he said, 'that the building of this road was begun in 1837 by a very brave young countryman of yours. You have heard of Lieutenant Fast?'
I shook my head, explaining, 'We come from Ireland, so I'm afraid Mr Fast was not our countryman.'
'Oh?' said the puzzled Brahman. 'Well, maybe Lieutenant Fast also came from Ireland. He was British, you see, and he died of jungle fever here, on the job. He was the engineer. We still call it Fast's Ghat. Not the younger people, of course. They call it Sampaje Ghat. But we old people don't mind remembering that the British built all our roads. There were not even cart-tracks when they came to Coorg. The Rajas never wanted roads built. They were afraid easy roads might mean easy invasions.'
'And weren't they right?' I said, drily.
The old Brahman looked at me with sudden quick suspicion. 'Are you anti-British? Anti-Imperialist? Do you have a war in Ireland? A civil war with Britain? Or am I becoming confused from the papers?'
'Not at all,' I said. 'That is an excellent description of what we have. But I'm not in the least anti-British – only anti-Imperialist.'
The Brahman gestured with his slim, wrinkled hands. 'Imperialism there has to be. It is part of the evolution of mankind. It is a necessary evil.'
It was my turn to look surprised, for such a historical approach is rather un-Indian. 'Are you a teacher?' I enquired.
The Brahman smiled. 'I was a Professor at Madras, but many years since I have retired. According to the _Laws of Manu_ I should now be a _Sannyasin_ , a holy beggar. But my wife might not like that. She might even join the Women's Lib!' He chuckled at my expression on hearing this allusion from Brahmanical lips. He was a charming old man and I was sorry to say goodbye at Mercara bus stand.
We soon found another Rs.5 hotel which is much more primitive than last night's, with no running water or anything fancy like that. However, we step out from our two-bedded cell on to a long balcony, level with the nearby mountain-tops and overlooking most of the red-tiled roofs of the town – a view which more than compensates for the state of the latrines. On the far side of the wide, shallow bowl containing Mercara's bazaar one can see the glint of two identical imposing gilded domes, which must be investigated tomorrow, and the steep green slopes that form the sides of this bowl are dotted with neat white bungalows. As for the glory of the surrounding mountains – when I look at them I guiltily wish that I were free to go trekking at my own pace. Why has nobody ever heard of Coorg? Or have I been alone in my ignorance of this most enchanting region? We shall certainly spend a few days here, though I had intended merely stopping overnight in Mercara and continuing to Bylekuppa tomorrow.
## NOVEMBER 29TH. MERCARA
After a seven o'clock breakfast of tea and potato-cakes we walked some way down Fast's Ghat to explore what we merely glimpsed yesterday, from the bus.
Mercara's average temperature is 66ºF and as we trotted downhill the sun was warm, the breeze fresh and the sky intensely blue – an almost incredible colour, to northern eyes. At intervals, in the cool depths of the forest, we saw sudden glorious flourishes of colour – tall trees laden with pink or cream or red flowers; and blue-jays, hoopoes, mynahs, weaver-birds and subaltern's pheasants were all busily breakfasting, and we chased gaudy butterflies as big as sparrows, and once Rachel came within inches of treading on a small snake. Probably it was harmless, but at the time my maternal blood ran cold. One is a much less light-hearted traveller with foal at foot.
We took short cuts at the hair-pin bends and whenever we wandered by mistake into a compound everyone was extraordinarily friendly. Even the wives or daughters of not very well-off farmers spoke intelligible English and were without that withdrawn, wary shyness which marks most Hindu women. Obviously the people of Coorg are no less exceptional than the landscape; both men and women make one feel welcome to a degree that is most uncommon in India. Also there is a splendid feeling of being isolated here, in a cosy sort of way – a quality in the atmosphere difficult to define but very attractive.
Across the street from our hotel, dominating Mercara and the southern and western approaches to it, stands a strongly fortified hilltop – the work of Mudduraja, a seventeenth-century Lingayat ruler. In the middle of the fort is that ruler's undistinguished palace, long since converted into the Commissioner's office, and on the way up from the road one passes the hall-door of Coorg's old-fashioned, no-nonsense gaol, where gaunt prisoners peer from tiny, heavily barred windows far above the ground, and armed guards look as though they would shoot first and ask questions afterwards should a helicopter chance to land in the courtyard.
Also inside the fort is a Mahatma Gandhi Memorial Library with a delightful notice in the entrance hall: 'Serene Silence, please! Have respect for thought!' – a typically Hindu sentiment. Several earnest-looking young men were sitting around large tables studying fat tomes, or consulting yellowed newspaper files, and in the large English language section (General) Patricia Lynch and Bertrand Russell stood shoulder to shoulder. But the selection of books in English on India was most impressive, though there were only two volumes on Coorg. A nice young librarian lent me the Coorg district volume of the Mysore State Gazetteer of India for 1965, very properly insisting on a Rs.15 deposit, and when he escorted us to the door I asked him the significance of the two realistic-looking grey stone elephants which stand at one end of the fortress compound and are marked 'Historic Monument. Do not touch.'
The young man smiled. 'British people always liked those monuments – so my father told me. They reminded the Coorgs how lucky they were to have British rulers. They were put up by the last Raja, who was very cruel and mad and enjoyed hurting people. Every morning he liked to be wakened by two special elephants trumpeting under his bedroom window over there' – he pointed across the compound. 'Then one night he sent a message to the mahouts that he didn't want to be wakened next morning, but they never got it. So in a temper when he was wakened too early he ordered the elephants and mahouts to be killed on the spot. But then he got his temper back and felt very sorry because they were such clever elephants. So he had those statues put up to honour them.'
'And what about the mahouts?' I asked.
The young man gestured vaguely. 'They were just riders,' he explained. 'Very clever and well-trained elephants are most valuable.'
From the fort we walked to the other side of Mercara to investigate those conspicuous gilded domes which mark the mausoleums of two Lingayat rulers of Coorg: Doddavirarajendra (died 1809) and his brother Lingarajendra (died 1820). On a high, grassy ridge, directly overlooking Mercara and that apparently infinite turmoil of blue mountains which is Coorg, some six or seven acres were levelled to build the twin tombs. Both are massive, square buildings in Islamic style, with minaret-like corner towers surmounted by statues of Nandi, the sacred Hindu bull, and on each dome is a gilded ball and weathercock. The windows have solid brass bars and the syenite blocks of the window frames are handsomely carved, as are the pillars (representing various manifestations of Shiva) which flank the stone steps leading up to locked doors. Obviously these memorials were devised by a somewhat eccentric family and what they may lack in formal beauty they make up for in individuality and sheer impressiveness. They are, in fact, admirably suited to rulers who were power-hungry, cunning, erratic, considerably talented and religiously eclectic – or perhaps 'omnivorous' would be a better word.
On the steep path up to the ridge we were overtaken by about twenty fascinated schoolchildren who soon swept Rachel off to play on the smooth green turf around the tombs. This gave me a chance to sit in the sun studying the _Coorg Gazetteer_ , which is quite informative about Doddavirarajendra and Lingarajendra. The former had no son and wanted his daughter Devammaji to succeed him, but she was only ten when her father died – having in his last years gone very mad and ordered the executions of many near relatives, principal officers of State and palace guards. Uncle Lingarajendra then usurped the throne and for nine years ruled energetically and efficiently, if unethically. He was succeeded by his dotty twenty-year-old son, Chickkavirarajendra, who felt so unsure of his position that he soon became even dottier and organised the killing of an inordinate number of his own relations. His subjects then complained about him to the British overlords of neighbouring Mysore, who presumably were not displeased to be regarded by the Coorgs as protectors.
Naturally, Vira Raja (as Chickkavirarajendra is usually called) was particularly anxious to kill his cousin Devammaji – the rightful heiress to the throne – and her husband Chennabasappa: so the young couple took refuge with the British Resident in Mysore, who refused to hand them back to an enraged Vira Raja. Vira Raja next wrote a series of rude letters to the Resident and, when these were ignored, begged several neighbouring rulers for military help against the foreign foe. If the British were looking for an excuse to annex Coorg this was it. Early in 1834 they accused Vira Raja of maladministration and made threatening noises. The Raja was then advised to surrender by his four Coorg dewans, who had long since come to despise the Lingayat dynasty and were openly pro-British – especially their leader, one Bopanna Apparanda.
I won't go into the earlier history of Coorg, which is bedevilled by gentlemen bearing such names as Satyavakya Kongunivarm-madharmma-maharajadhiraja and seems in any case rather obscure. But originally the Lingayat rulers were 'outsiders', so his subjects felt no obligation to remain loyal once Vira Raja had proved unworthy of respect. Moreover, the Coorgs had already, in the campaigns against Tippu Sultan, established a tradition of co-operation with the British and at the close of the eighteenth century a British Resident had been appointed to the Raja's Court. So it is not surprising that satisfaction was expressed when Lieutenant-Colonel J. S. Fraser, representing the Governor General of India, met the assembled leaders of Coorg at Kushalnagar in April 1834 and informed them that their ruler had been deposed.
Colonel Fraser then asked the leaders 'to express their wishes without apprehension or reserve, in regard to the form of government which they desired to be established for the future government of the country.' Without hesitation the Coorgs requested that their country be ruled by those laws and regulations already in force throughout the East India Company's dominions. Whereupon Colonel Fraser proclaimed Coorg annexed, because the people wished to be ruled by Britain, and on 6 April 1834 the Union Jack went up over Mercara Fort.
Thus did the British Lion acquire a valuable property without having to unsheathe his claws even once, the Coorgs being the only martial race on the subcontinent never to have taken up arms against the Raj. The Indian author of the _Mysore Gazetteer_ for 1965 gratefully points out that 'Coorg was under British rule from 1834 to 1947, over a century and a decade. The benefits conferred by the British rule were many and varied. The English built this state from a small loose-knit feudal principality into a prosperous and well-administered unit.' So here we have one imperialist story with a happy ending, and I suppose most people have never heard of Coorg simply because 'good news is no news'. While all sorts of gruesomely thrilling things were happening on The Frontier or in the Punjab, or in Lucknow or Calcutta or Sind or Maharashtra, the British and the Coorgs were being awfully nice to each other in Coorg.
There was, however, one person for whom this story did not have a happy ending – the 'Baddy', Vira Raja. On surrendering Coorg he expressed a wish to be retained as Raja, though he appreciated he could never again be more than a figurehead, and he was extremely annoyed when hustled off to Benares on a pension. Having brooded over this grievance for years he went to London in 1852, with two of his wives and his favourite daughter, to complain personally to the British Government. Nobody was interested, but Queen Victoria took pity on the first Indian prince to visit England and did a lot to help this forlorn little group of exiles. (Presumably she either did not know, or with regal tact pretended not to know, the status of the second lady in His Highness's entourage.) Eventually Gowramma, the favourite daughter, became a Christian and married an Englishman. Her father died in London in September 1859 and not long after she and her only son also died – both of consumption. And thus ended the Lingayat dynasty which had ruled Coorg for two hundred and thirty years.
Looking up from my _Gazetteer_ , I noticed that Rachel had her playmates – all of whom were eight or ten years old – completely under control. Everybody was doing exactly as she wanted them to do, and this is not the first time during the past fortnight that I have observed such a development. It worries me slightly that without one word of any common language a white child, who is being brought up in a totally unimperialistic environment of liberty, equality and fraternity, should unconsciously and effortlessly take up where the Raj left off.
On the way back to our hotel I suddenly remembered, as we passed the Rotary Club, that when last heard of an English friend of mine was running a stud-farm in Mysore State. So few British residents remain in South India that it seemed likely somebody at the club would have heard of the Fosters, and I soon discovered that their place is only forty miles north of Mercara, on the Coorg–Hassan border. Moreover, a helpful Rotarian said we could probably get a lift to Byerley Stud tomorrow with a local racehorse owner. A. C. Thimmiah – a cousin of the famous General – was then contacted by telephone and gladly agreed to meet us on the club veranda at nine-thirty a.m.
## NOVEMBER 30TH. BYERLEY STUD, NEAR BALLUPET
We woke to an Irish morning; thin, drifting cloud was draped over Mercara's mountains and the air felt cool and moist. 'A fine soft day, thank God!'
Punctually at nine-thirty Mr Thimmiah appeared, accompanied by his vivacious twenty-five-year-old daughter, Sita. A. C. Thimmiah – who prefers to be known as Tim – lives on an estate fifteen miles south of Mercara. He has a kindly, gentle glance and an interesting smile – half-sardonic, half-shy – and for all his patrician ways there is about him an immediately endearing air of simplicity, goodness and modesty. He is one of those rare people who inspire affection the moment one meets them, before a relationship can be said to exist at all; and his hobby is expatiating on Coorg, so he must have rejoiced to find himself in the back of the car with such a willing listener.
From Mercara our road descended gradually to Kushalnagar, winding through mile after dark green mile of coffee-estates, with Coorg's ever-present jumble of blue mountains lying beyond a series of deep, heavily forested valleys. Tim explained that the whole character of this region changed after coffee-planting was introduced – probably by Moplah traders from the coast – about the middle of the last century. Captain Le Hardy, the first British Superintendent of Coorg, encouraged the pioneer planters and Europeans soon made it the area's main cash crop. Finding the people and climate extraordinarily agreeable, many Europeans settled here, as owners or managers of plantations, and employed thousands of former slaves – freed when the British annexed Coorg – and further thousands of landless peasants from Mysore, Cochin, Hassan and South Kanara. Coffee-taxes provided the government with much revenue and soon cardamom jungles were being leased to the highest bidder, which meant even more revenue. New towns were built, old towns flourished and trade increased as imported articles became popular. Yet Coorgs remained the principal landowners, despite the influx of foreigners, and the whole Coorg community benefited enormously from the coffee-trade. However, there has to be a snag. By 1870 much of the forest had been converted to estates and now the annual rainfall is decreasing; even in the remaining forests the once-famous Coorg bamboo-thickets have declined. From time immemorial this region has regularly produced an abundance of rice for export to Malabar, but if the rainfall continues to decrease the paddy-crop must eventually suffer.
Kushalnagar is a straggling, dusty little town some 2,000 feet lower than Mercara and only a few miles from the old Mysore–Coorg border. During British days it was called Fraserpet, in honour of that Colonel Fraser already mentioned, and Tim still uses this name. As we drove slowly through the crowded bazaar he told me that one of his great-grandfathers was Bopanna Apparanda – usually known as Dewan Bopu – who, as Vira Raja's Chief Minister, was mainly responsible for persuading the last ruler of Coorg to surrender to the British. At Kushalnagar Dewan Bopu officially welcomed Colonel Fraser to Coorg, and soon afterwards became Captain Le Hardy's right-hand man. During the Kanara rebellion of 1836–37 he led his own private army to fight at Sulya and Puttur, and then led a separate thousand-man expedition to put down 'impostors' in another direction. Afterwards, the British offered generous rewards to their allies. But Dewan Bopu, like every other Coorg leader, declined with thanks, pointing out that 'We Kodavas do not require pay because to fight is our duty which we owe to our country to secure our tranquillity'. Later, during the Mutiny, Coorg volunteers stood guard at the Mysore, Malabar and Mangalore boundary posts and were rewarded for this spontaneous display of loyalty by being exempted from the 1861 Indian Arms Act, which made it an offence for all other 'natives' to carry arms.
As we drove into north Coorg, Tim explained that amidst the darkly tangled jungle on the steep mountains grew millions of rupees' worth of teak, ebony, eucalyptus, rosewood, sandalwood and _ood_ – a sweet-smelling wood of which I had never heard before. One rosewood tree, which will have taken sixty or seventy years to mature, is at present worth about £10,000. Pepper-vines, cardamom and various spices also grow wild in these forests, and a few timid aboriginal tribes survive in the remotest corners, only rarely emerging; but their numbers, sadly, are dwindling.
Beyond the small town of Kodlipet the landscape changed to sweeping uplands of golden grass and low green scrub. Then, near the Coorg border, we exchanged the narrow main road for a bumpy dirt track and soon – for no particular reason, as it seemed – we had bounced off the track to drive for a few miles over open scrubland, leading apparently nowhere. When suddenly we were amidst trim paddocks, full of glossy mares and lively foals, I had the impression of a conjuring trick.
This eighty-acre stud-farm employs twenty-eight locals – mostly syces – for whom solidly built little houses are provided nearby. According to Tim, the place was a wilderness when the Fosters took over; now it is a thriving example of what can be done in India with not much money but a great deal of thought and hard work. Apart from their bloodstock interests, Fred and Shelagh are keen to improve the local cattle and their approach to this problem is immeasurably more sensible than that of most international aid organisations. Like many Indian problems, this one seems insoluble at village level. Planters, landowners and state-run experimental farms can all afford to improve their stock, but what does this profit the half-starved villager and his family? Of what use is a fine sturdy heifer from an Ayrshire or Charollais bull if she cannot get the feed she needs to keep her big frame fit? Before you improve village cattle you must improve the available fodder and Fred is now experimenting to find out which of the various new strains of grass is best suited to this area.
There is a nice sense of historical continuity about the Fosters' present way of life. Their ancestors were pioneers in New Zealand and India and they are still carrying on the tradition in this remote corner of Mysore, much of which was originally opened up by Fred's father. Their little bungalow is emphatically a Pioneers' home, rather than an Exploiters', and to our great delight the 'guest room' is an ancient and honourable horse-box called Genghis Khan, which has several times done the India-Britain-India round trip behind an even more ancient and honourable Land Rover.
Also staying here for the weekend are the Fosters' only remaining European neighbours, David and Jane Hughes, who manage a company plantation eighty miles away, at the far end of Coorg. For the few Europeans who have not yet uprooted from rural India loneliness is obviously something of a problem, though they may have adjusted gracefully to an independent India and acquired many Indian friends. However, it is hard to imagine such people, whose families have usually been India-based for generations, at ease against any other background. They still need India: and I strongly suspect that India, though she would never admit it, still needs them.
After lunch we strolled around the farm, which on all sides overlooks silent miles of untouched country, stretching away in green-brown-gold undulations to the lavender shadows of distant mountains. In every sense, the atmosphere here is totally unpolluted. Indian atmospheres tend to be very strong, whatever their quality. On that evening last week when we entered Mysore State from Goa, our bus passed through a village on the edge of the forest where I was quite overcome by an awareness of evil – a feeling altogether unexpected and inexplicable, but none the less definite for that. (I omitted it from my diary that night because I was still trying to shake off the unpleasant after-effects.) Similarly, amidst this tranquil isolation one is very aware of Good being in the ascendancy: perhaps Varuna dwells here.
## DECEMBER 1ST. BYERLEY STUD
We breakfasted on the veranda (bacon and eggs, naturally) while files of almost black-skinned men and women servants passed to and fro, their bare feet noiseless on the dewy grass, their ornaments tinkling and flashing, their eyes respectfully averted from the sahibs and mem-sahibs, who were putting away more good food in fifteen minutes than the average Indian can lay hands on in a month.
One of the stable girls is particularly striking: tall, lithe and elegant in an emerald-green sari, with ebony hair tied in a glossy, waist-length tress. Her regular, fine-boned features wear a permanent expression of faintly amused disdain and she is unmistakably a personality. However, as a guest I would be wasting my time trying to establish contact; in India, any attempt to run with the hare and the hounds inevitably leaves all concerned feeling thoroughly embarrassed. But I can't help wondering what she and her contemporaries make of European employers: certain subtle changes of attitude must surely have taken place during the past quarter-century. A whole generation has grown up that was born free – if 'free' is an allowable adjective for India's poverty-bound millions – and even in a backwater like this the no-longer-ruling sahibs and mem-sahibs must be suffering from some loss of status. And yet – while writing these words I have remembered Rachel's bossing of her Indian playmates, who seem never to resent the domineering white child. Plainly the British control of their Indian Empire was based on something more than Might, though I honestly do not know whether I believe that 'something' to have been a defect in the Indian character, or a virtue in the British, or a combination of virtues and vices on both sides that just happened to make possible the domination of millions by thousands.
Throughout today I have felt as though I had slipped back fifty or a hundred years in time, not because there is anything imperialistic about the way of life at Byerley Stud but because much of our conversation could have been lifted straight from an Edmund Candler novel, with occasional lapses into Flora Annie Steel. And of course having servants of any kind about the place does strike the visitor fresh from Europe as too quaint for words. Their presence gives an entirely different flavour to life, which is nice for a change, though personally I should not care for it permanently. However, the villagers working here undoubtedly appreciate being well paid, housed, fed and clothed; they would never be able to comprehend my democratic distaste for the sort of relationship that is traditional in India between masters and servants and that appears to them as a right and proper extension of the caste system.
Before the Thimmiahs left yesterday it was arranged that we should go to stay with them on December 9th, for _Huthri_. This is the most important of all Coorg's religious festivals and the occasion when every family member returns to the ancestral home. Meanwhile, we should have time to visit (at last!) Bylekuppa Tibetan Camp, and to spend a day or two in Mysore City looking up Kay Webb – a medical missionary with whom I worked in Nepal. I feel tonight that Fate has taken over the organising of this journey and is making a pretty good job of it.
CHAPTER FIVE
# _Musings in Mysore_
## DECEMBER 2ND. KUSHALNAGAR
Having said our goodbyes to the Fosters, Rachel and I strolled for a couple of hours along a narrow, pot-holed, tree-lined road. The only traffic was an occasional herd of cattle being driven by ragged, grim-faced men, none of whom returned our greetings. We passed a few huts with shaggy straw thatches and glimpsed a few toddlers who fled from our strange white faces, howling with terror. Perhaps their mothers use Europeans as bogeymen.
At noon the remains of a bus picked us up. Its seats were torn, its glazed windows broken, its floorboards sagging in the middle and its brakes so imperfect that at every stop wooden blocks had to be thrust under the back wheels by a small boy specially employed for the purpose. As long as the road remained level we crawled along at ten or twelve miles per hour, the engine sounding like a concrete-mixer, but at the foot of the first slope we stopped dead where we would have seriously impeded any other traffic had it existed. I soon realised that this was no crisis, but common form. All the standing passengers scrambled out without comment and proceeded to walk up the hill, followed by the bus containing its legal load (according to the notice over the engine) of thirty-eight seated passengers. In due course I counted forty-three illegal passengers re-entering through the back door and several others squeezed into the cab. We then went careering down a steep mountain at hair-whitening speed and I began to understand India's bus-disaster statistics; had we gone over that parapet none of us could possibly have survived. In reports of bus crashes one usually reads that the driver and conductor, if amongst the survivors, have 'absconded' (a favourite word of Indian journalists). But those drivers and conductors who escape both death and imprisonment must be rich men, since for them the fares of the illegal passengers are clear profit.
On buses one often observes sex discrimination in action. At Kodlipet, where we changed into a marginally less decrepit bus, a poorly dressed young couple came aboard when there was only one seat vacant – in the 'Ladies' section. The obviously pregnant wife was holding a baby boy, but it was the husband who sat down and took the baby on his knee. His woman was to be left strap-hanging for two hours and she had to refuse my seat because I was in the 'Men's' section. I then offered it to her husband, so that she could have his; but though he had no right to be in the Ladies' section he simply gave me a stony stare, knowing that in any dispute public sympathy would be on his side.
It was five-thirty when we arrived here so for Rachel's sake I decided to stay in a hotel – Rs.3 for a twin-bedded room! – though we are only seven or eight miles from Bylekuppa.
## DECEMBER 3RD. BYLEKUPPA TIBETAN SETTLEMENT
Last night my sleep was disturbed every few minutes by fleas, mosquitoes, pi-dogs fighting under our ground-floor window, jackals howling in the compound and strident Indian jazz being played over a public amplifier from ten past four onwards.
As we walked out of Kushalnagar at seven-thirty we saw many prosperous-looking Tibetans coming into the town on their own bicycles or scooters or bullock-carts, or in settlement jeeps or trucks. At the Bylekuppa police-checkpost I had to produce a letter of introduction from T. C. and the security precautions here underline the essential difference between this settlement and Mundgod. Bylekuppa was started in 1963, amidst considerable controversy and publicity, and it has always been under Indian supervision and influence. Also, being on the main Mangalore–Mysore road it is over-exposed to Western curiosity and interference. But one must not expect perfection everywhere and, as T. C. readily admits, Mundgod has benefited through avoiding the mistakes made here during the first experimental resettling of large numbers of Tibetans in South India.
Despite these mistakes, most of Bylekuppa's 8,000 Tibetans are now prospering. Some have built, independently, little houses for married children on their own fields, and the majority are probably better off, materially, than they could ever have been in Tibet. Whether they are as well off in other respects is a matter of opinion.
As I write – in the settlement guest-bungalow, drinking the settlement beer – I find myself rapidly becoming incompetent to comment further. This beer is a Sikkimese variation on the _chang_ theme and is made here from _ragi_ , a highly nutritious grain known as 'the national millet of Mysore'. It is served in a huge glass jar placed in a shallow dish and filled to the brim with fermenting _ragi_ , from which protrudes a bamboo 'straw'. To mix one's drink one slowly pours hot water from a half-gallon kettle on to the grain. After a few minutes the brew is ready to be imbibed through the 'straw' and one thinks how pleasant and innocent it is. One adds some more water, and imbibes again, and after repeating this ritual a few times one begins to spill a little of the water as one adds it...
## DECEMBER 4TH. MYSORE CITY
On the Mysore Plateau many solitary, spreading trees grow in the wide, red-brown fields, giving the landscape a slightly English look – accentuated today by a scatter of bulky white clouds drifting across the deep blue sky. It could have been a perfect June day at home, and as Mysore is almost 2,500 feet above sea-level it was not too hot even when we arrived in the city centre at one o'clock.
A helpful receptionist at the Holdsworth Memorial Hospital told us that Kay will be back from her village leper-clinics tomorrow afternoon and we then rambled off in search of suitable accommodation. In this 'Palas Hotel' our Rs.3 room has no window, scarcely enough space for me to turn around when wearing a rucksack and so much wildlife on the floor (already I have counted six species of insect) that I shall have to sleep beside Rachel on the narrow plank bed. Judging by the goings-on in the corridors, the place is an ill-disguised brothel; but since I am above the age of provoking sexual assault, and Rachel below it, this detail is of no practical consequence. More disquieting is the fact that the restaurant washing-up is done on the floor of the filthy latrine just outside our bedroom door – something I did not observe until after we had enjoyed an excellent lunch.
Mysore City is said to have deteriorated since the British left but I find it most attractive. It is small enough to be tackled on foot and there are few motor vehicles on the wide, straight, tree-lined streets, most of which run between solid, well-kept, cream-washed buildings with terraced roofs and spacious gardens. The traffic consists mainly of horse-gharries, pedal-cycles, bullock-carts and multitudes of wandering cattle, many of whom lie complacently in the middle of main roads chewing the cud as though the internal combustion engine had never been invented. One has to like a city in which the cow still takes precedence over the car.
The people, too, are congenial – except in the State-run tourist bureau, where I found the staff most unhelpful. In a desperate effort to arouse their sense of duty I murmured something about collecting material for a travel-book, but this merely prompted them to exchange smiles. Plainly they found it impossible to believe that anyone so poorly clad and generally unimpressive could sign her name, never mind write a book. Indians tend to rely heavily on outward appearances when judging foreigners, which is natural enough. Occasionally, however, the use of this criterion, unaided by any other, leads to regrettable _contretemps_ with sartorially eccentric visitors who are really quite respectable.
## DECEMBER 5TH. MYSORE CITY
I notice, with some unease, that the older I get the more sentimental I feel about kings and queens, emperors and emirs, the Nizam and the Wali and suchlike personages. But perhaps this is less a symptom of senile decay than an emotional retreat from a world which daily becomes more anarchic, ugly and false. In Europe the lot of the average man has in some ways been greatly improved over the past half-century, but in India technology seems only strong enough to erode valuable traditions, without providing even the limited amount of good we have derived from it. Hence modern India encourages one to look back, even more wistfully than usual, to an age when life was slower, more rhythmic and more dignified – and yet in many ways gayer, freer, more colourful and more spontaneous.
So wandered my thoughts early this morning, as we strolled along neat gravel paths between neat lawns in the vast compound of Mysore City's famous fort. All around us stretched handsome red-brown fortifications, ahead rose soaring twin temples – the 'private chapels' of the ex-rulers – and dominating all else was the Maharaja's Palace, built in 1897 and extravagantly though not displeasingly ornate. Indeed, from the romantic tourist's point of view it is eminently satisfactory, being just the sort of edifice in which an Eastern potentate might be expected to reside.
The feudal past looks good in Mysore. By the end of the eighteenth century the British had defeated the Muslim interloper, Tippu Sultan, and restored to the throne an old and much-loved Hindu dynasty. This restoration was not, however, immediately successful on the practical level, and British administrators were appointed in 1831. A succession of dedicated Englishmen ran the State efficiently for the next half-century, until the Wadeyars again took over, this time proving not merely competent but brilliant rulers. During the 1930s Gandhi described Mysore as 'a model state'. More than any of their princely rivals, the Wadeyar Maharajas fulfilled the immemorial Hindu ideal of kingship – which was fitting, since the history of Mysore is inextricably interwoven with the legends of the Ramayana and Mahabharata.
In the business of government the Maharajas were assisted not only by British political agents but by a number of distinguished dewans, many of whom were Muslims – though none the less loved and trusted by their Hindu masters on that account. Yet the man now generally regarded as 'the maker of modern Mysore' started off as a poor Hindu village lad. His name was Dr M. Visvesvaraya and he is known as 'the Engineer-Statesman' because he organised the building of an astonishing number of dams, canals, factories, hospitals, schools and colleges – including India's first polytechnic. Already I have several times been told the story of his two fountain-pens. So determined was he to give a good example that he used separate pens for personal and official work and bought the personal one, and the ink to fill it, out of his own pocket. To such obsessional behaviour does India reduce honest men.
During its final princely period, Mysore attracted many scientists, artists and musicians. The Maharajas – fine scholars themselves – were generous and perceptive patrons of every form of creative endeavour and Jayachamaraja Wadeyar, the last Maharaja, is a composer of distinction. But now he can no longer afford to subsidise young musicians and I find this very sad.
However, one must not wax too sentimental/romantic/monarchist. Of the five hundred and sixty-two 'native princes' left theoretically in control of two-fifths of India in the autumn of 1858, hundreds were ineffectual and dozens were downright nasty. When Queen Victoria made further annexations of territory impossible, by announcing that the Raj was to replace John Company, most old Company hands were outraged and Lord Elphinstone – a nephew of the incomparable Mountstuart Elphinstone – foretold that the princely states could be useful only as 'sinks to receive all the corrupt matter that abounds in India'. The following century justified his cynicism, in many cases, though it is wildly misleading to generalise thus about 'princely states' when some consisted of only a few acres and others of more than 80,000 square miles.
Had the mutiny been delayed for a decade, John Company might well have secured that remaining two-fifths of the subcontinent – or most of it – and thus the government of a new Indian democratic Republic would have been spared the embarrassment of coping with old Indian undemocratic princes. For their own reasons, the princes had consistently opposed the idea of an independent India, in which they would no longer enjoy British protection. However, thanks to the combined efforts of S. V. Patel, Lord Mountbatten and Pandit Nehru, they proved less intractable than had been expected. Most were concerned with the trappings rather than the realities of power and so were easily enough brought to heel when Mr Nehru – temporarily, and not for the last time, neglecting his pacific image – brusquely declared that any princely state which chose to stay out of the new India would be treated as 'hostile'. Two years later the states had all been absorbed into the Republic and their rulers soothed with promises that they and their heirs forever would receive annual pensions ('Privy Purses'), and be allowed to retain their private property, honorary titles, personal flags and the various other princely perks to which so many of them attached such importance.
Unfortunately, however, that is not – could not be, in modern India – the end of the story. Anti-Congress politicians saw the concessions granted to the princes as useful ammunition since public opinion, throughout what had been British India, was in an understandably anti-prince mood. Typical of the criticisms made by secularised agitators was the accusation that the princes had insensitively flaunted loads of precious stones in public while their people starved around them. This taunt ignored the fact that the wearing of as many jewels as could possibly be fitted on to one man's person was often part of a Hindu ruler's duty. In Mysore, most of the Maharaja's subjects believed jewels to have magic properties capable of spreading beauty, abundance and security throughout the land if – but only if – the jewels were worn by him whose body symbolised the people of the state.
After years of wrangling the government gave way to the agitators in 1971 and withdrew the princes' pensions and privileges – though the saving was negligible in an all-India context. At least where Mysore was concerned, this seems to have been a blatant example of 'democracy' enforcing the will of an articulate minority at the expense of an inarticulate majority, who even today remain deeply attached to their ex-ruler.
In 1956, when many of India's state boundaries were redrawn – generally on a linguistic basis – Mysore was doubled in area and almost doubled in population by the inclusion of much of the old states of Bombay and Hyderabad, and what had been the separate province of Coorg. This new geographical entity – last month renamed Karnataka – has an area of 74,000 square miles and a population of 30 million, out of whom some 17 million speak Kannada, Karnataka's official language. Other languages spoken by significant numbers are Telugu, Urdu, Marathi, Tamil, Tulu, Konkani, Malayalam, Banjari, Hindi and – in Coorg – Kodagu. Kodagu and Tulu – the language of South Kanara – both use the Kannada script but each of the other languages has its own script though Old Kannada and Tamil are so alike they were once thought to be dialects of the same language.
The ancient Karnataka–Vijayanagar kingdom, of which the state of Mysore was the residue, lost its identity in the mid-seventeenth century during the Muslim conquest of the Karnatic. Previously, it had stretched from the sacred River Godavari to the even more sacred River Cauvery and for three centuries its rulers had dedicated themselves to preserving their ancient Hindu society from destruction by Islam. Frequently their armies were beaten but the fact that one now finds South India so different from North India is a measure of their success on other and ultimately more important battlefields.
Although Karnataka has been designed to approximate in area and ethnic content to the old Vijayanagar kingdom, the majority of modern Kannadigas naturally cannot feel towards their new state as they did towards Mysore under the Wadeyars. For almost 3,000 years, while empires waxed and waned, the small Hindu kingdom remained a constant feature of Indian life, especially in the south, and from the peasants' point of view a secular democratic state is a poor substitute. Despite long periods spent under the suzerainty of various imperial powers the rulers of South Indian kingdoms usually retained considerable local control and their mere presence gave emotional stability to the social structure, however inept or corrupt individual rulers might be. In theory, Indians should feel much more secure these days, when they can choose at the polls the sort of rulers they want, but for the people of a caste-dominated society a feudal overlordship of some kind is more psychologically comfortable than parliamentary democracy. Several years ago Dr Radhakrishnan wrote, '... caste... today has become a political evil; it has become an administrative evil. We are utilising caste loyalties for the purpose of winning our elections or getting people into jobs, exercising some form of favouritism or nepotism.' The recent abrupt political Westernisation of India has probably been the most traumatic single event in the whole history of the subcontinent and a growing number of Indians believe the process should somehow have been accomplished more gradually.
I felt acutely aware of the past as we entered the sumptuous though now desolate-feeling Sajje Hall, where the Maharaja used to give audience to his people every September, during the Navaratri festival. Rachel was greatly taken by the throne, which is made of fig-wood overlaid with ivory, plated with gold and silver and carved with innumerable figures from Hindu mythology.
On our way out of the fort, when I turned aside for a moment to try to get a photograph of the zenana wing, a poorly dressed elderly man emerged from a distant doorway and came running towards us, angrily shouting and gesticulating. At first I, too, felt angry, for we had been much plagued, in and around the palace, by aggressive pseudo-guides demanding rupees. But then I noticed something different about this shabby little man who was pointing to the ornate zenana windows while vigorously shaking his head and trying to talk English. He did not want rupees: he simply wanted us to go away.
At last I got the message – 'Maharana still here! No allowed visitors to this side! Away with quickness!' He paused, and suddenly the right word came. ' _Private_ here!' he exclaimed triumphantly. 'Away! Private! No looking! This _only_ for Maharana!'
I apologised profusely, and asked why there was no warning notice. But the guardian of the zenana merely repeated, 'Away with quickness! Private! Here lives our Maharana!'
We went away then, 'with quickness', and I was sadly aware of having seen, in the eyes of this scruffy retainer, the last glowing embers of a reverence and loyalty such as 'the elected representatives of the people' rarely inspire in any country.
Outside the gateway by which we left the fort several men were saying their morning prayers in a small public temple. Rachel wanted to ring the temple bell but I explained that not even Hindu women – never mind _mleccha_ girls – are allowed to do this. However, consolation was at hand. On the little temple veranda sat two tame rhesus monkeys, tied to the wall by long chains and still wrapped in their night attire – a communal piece of cotton. They hailed Rachel's appearance with jibber-jabbers of joy and she spent half an hour playing with her cousins, after I had prudently removed her spectacles and hair-band. Every few moments they reduced her to paroxysms of laughter, and she and they combined had the same effect on many of the passers-by while I sat enjoying the morning sun, and admiring the massive lines of the fortifications, and appreciating the friendliness of the atmosphere.
As we approached Mysore yesterday my eye was drawn across the level plateau to a conspicuous, isolated mountain not far from the city's outskirts. This is Chamundi Hill (3,489 feet), on which stands a much-visited temple dedicated to Chamundi – the family goddess of the Wadeyars – who once upon a time killed two demons, named Chanda and Mundi, on the site of the temple. In fact Chamundi is just another of the goddess Kali's many names; my only complaint against Hinduism is that, not content with having tens of thousands of gods and goddesses, many of these deities confront the bewildered _mleccha_ with a memory-defeating multiplicity of names. But the important thing is not to be misled by all this into regarding Hinduism as an essentially polytheistic religion. The late K. M. Sen explained the situation with his customary succinctness: 'Depending on the social traditions of particular sections of the people, Hindus show a particular attachment to a particular figure in Hindu mythology and worship God in that form. The Nameless and the Formless is called by different names, and the different forms are attributed to Him, but it is not forgotten that He is One.' Incidentally, travellers in India should keep K. M. Sen's _Hinduism_ permanently within reach. A Pelican book – published in 1961 – it weighs only a few ounces, and to the outsider who is trying to look sympathetically in, but is not a trained philosopher, it is more valuable than a dozen weightier tomes I could mention.
Kali is of course Siva's wife and she is also known as Sati, Gauri, Annapurna, Parvati, Durga, Bhawani and Devi. As Kali she requires to be frequently mollified by sacrifices of a bloody nature and recently, in some remote Maharashtrian village, a six-year-old boy was killed to placate her. Nowadays human sacrifices are made only by those generally regarded as insane, but it is not surprising that most foreigners despair of ever understanding a religion which can directly inspire one sort of devotee to murder a child and another to refrain from killing a gnat. E. M. Forster perfectly describes the _mleccha_ 's difficulty in _A Passage to India_ : 'The fissures in the Indian soil are infinite: Hinduism, so solid from a distance, is riven into sects and clans, which radiate and join and change their names according to the aspect from which they are approached.'
Buses frequently leave Mysore's bus stand for the top of Chamundi Hill, but because of the temple's popularity as a place of pilgrimage it is extremely difficult to board one. Twice this morning we were left behind, having been at the head of the queue, and for this I blame my own absurd European reaction to people in a hurry. Instinctively one moves aside to let them pass and today I had to make a real effort of will to overcome this automatic reaction. I also had to make an effort of muscle to push, pull or slap people out of the way as we boarded the third bus. Rachel was nearly trampled underfoot and became momentarily panic-stricken, yet this was a bus with separate entrances for men and women, so I only had to deal with the weaker sex. The strength of some of those wiry little peasant women, who could curl up in my rucksack, is quite extraordinary.
Here I again noticed a bus conductor treating women and low-caste men as though they were draught-animals, shouting at them abusively and occasionally even striking them. For a people who are widely believed to profess a philosophy of _ahimsa_ , or non-violence, the Indians seem inordinately aggressive in their daily lives. It was Gandhi who created, almost single-handed, the false impression that they are gentle and peaceful. All the still influential kings and heroes of Sanskrit literature were expected to be ferocious slayers of men and, apart from the Mahatma's not entirely successful _ahimsa_ campaign, there is nothing whatever in the past 2,000 years of Indian history to support the view that Hindus are basically pacifist. Their violence, indeed, is part of the mystery of India, for it always seems to have causes and cures unknown to us.
This morning's pandemonium, for instance, seemed almost a mini-civil war. First men, women and children fought tooth (literally: I was bitten on the forearm) and nail to board that bus, and then the seething mob of women was set upon by the conductor and clouted and shouted at to get it so arranged that another dozen could be fitted in. Yet ten minutes later the conductor and his women victims were laughing and joking together, like old friends, and men who had recently been doing each other grievous bodily harm were cordially exchanging newspapers. At which point I remembered N. C. Chaudhuri's remark that 'Somehow an alkali is always present with the acid of Hindu life: it is a marvellous and boundless tolerance of bad language and blows, which is some sort of a conditioned reflex of forgiveness. The Hindu possesses a faculty of callous charity.' He needs it, too.
Chamundi Hill is so precipitous that Mysore quickly shrinks to toytown proportions and on clear days the surrounding country can be overlooked in every direction for at least one hundred miles. Two-thirds of the way up we stopped for everyone to unwedge themselves and pay homage to a sixteen-foot statue of Nandi, hewn out of solid rock in 1659. Despite the early hour he was wearing fresh garlands on his forehead and the bell of his gigantic necklace was draped with marigolds. Our fellow-passengers produced further garlands and Rachel asked in a penetrating whisper, 'Do they believe bulls are gods? Is that a statue of a _real_ bull? Why is he so big? Is he prehistoric?'
'No,' I said, 'he's not prehistoric and he's not real and Hindus don't think bulls are gods. But some of them worship Nandi as a symbol of the god Shiva, and he is generally regarded as a sort of chamberlain, or guardian, of all Shiva's temples. And he represents, and protects, all four-footed animals.'
'I see,' said Rachel, untruthfully.
As Chamundi Temple is now being turned into a tourist attraction its environs are becoming unattractive. When we arrived a canopied figure of Chamundi, which normally resides in the innermost sanctum, was being carried round a courtyard on a palanquin and perfunctorily whisked with yak-tails. In attendance were four grossly fat priests covered in sandalwood ash and red powder – the first fat Indians I have seen since leaving Bombay. The contrast was most striking between those pot-bellied parasites, with greed ever shining in their eyes, and the throngs of simple, prayerful, underfed worshippers devoutly doing their _pujas_ and repeatedly handing coins to the priests or their attendants. As soon as we appeared, two of these minions were deputed to harass us, which they did with considerable verve but no success.
Although Hindu priests are not supposed to minister to a temple for more than three years few have ever been willing to retire from working this particular gold mine and by now there are separate priestly sub-castes whose ill-educated members do not intermarry with other Brahmans. These men are mildly derided by most people, yet nobody can worship in the temples without their expensive professional aid. It is never easy to trace Indian beliefs, customs or laws back to source, but one cannot help suspecting a link between the intricate refinements of Hindu ritualism and priestly greed. Although the person who brings the offering must perform his own _puja_ he cannot do so – even if himself a Brahman – without professional help, and only by paying for this can he retain the merit of his _puja_. The ritual fee has thus become an indispensable part of the rite, just as in Ireland no Catholic would go empty-handed to his parish priest to request the celebration of a mass for his 'special intention'. Indeed, the French writer Madeleine Biardeau – perhaps the most perceptive contemporary student of India – remarks that 'it is tempting to compare what has remained of ancient Vedic ritual, which prescribes this or that _puja_ to obtain this or that result – and quite often an entirely profane result – with what one knows of the Roman Catholic religion'. However that may be, the fact remains that many visitors leave India convinced that Brahmans are a bad lot, though in fact the temple-priests form only a tiny part of the Brahman population. Many Brahmans are true ascetics; many others – like our friend on the bus to Mercara – are charming and cultivated gentlemen; and a high-powered minority are scholars who regard it as their duty to hand on the torch of Hindu culture – free of charge – to the next generation.
Quite close to Chamundi temple is a garishly painted little bungalow with a large notice over the entrance proclaiming it to be 'The Godly Museum'. It belongs to a new sect called the Prajapita Brahma Kumaris which has its headquarters at the Godly University on Mount Abu, a place better known as the site of the Dilwara temples. From a half-demented-looking young woman at the desk inside the door I bought for ten paise a booklet which informed me that
in 1937, Incorporeal God Almighty whom we know as 'Shiva' (World Benefactor) descended in the corporeal body of a jewel merchant, and blessing him with numerous meaningful divine visions revealed to him that a world war would soon be coming, in which nuclear weapons would be used and the present vicious Iron-aged world would meet its tragic end by means of that war, natural calamities and civil wars. On the other hand, he saw the visions of the forthcoming Golden-aged Deity World... He got the most blissful vision of God also and His Divine voice called him up to become instrumental for the re-establishment of the ensuing Golden-aged viceless and peaceful Deity World... He became a medium to God Shiva whom some people also call 'Jehovah'... This Institution is now teaching God's knowledge and Easy Raj Yoga through 250 Godly Service Centres in various towns and villages of India... Scientists only recently landed on the moon but this Institution knew beforehand that there was no life on the moon. Divine Insight also reveals to you regions beyond the sun, the moon and the stars without any expense or difficulty... Several persons have given up easily such sticky habits as drinking, smoking, etc., because as a result of having acquired Godly Knowledge, they no longer feel any necessity for them... They are now delighted to have purity, mental health and happiness as a routine, through the Easy Raj Yoga taught by this Godly University.
Godly Museums try to explain the Easy Raj Yoga principles and methods through pictures and wallcharts which – to judge by the Mysore examples – are the work of a mentally retarded religious maniac. Various motifs from European popular religious 'art' are incorporated, including the Sacred Heart and the Blessed Virgin (looking slightly dazed, as well she might in these surroundings). Abraham and Mohammad also feature in a bizarre representation of the Kalpa Tree, and Rachel particularly liked the chart inscribed 'Skeliton of Bones and Flesh', which taught that we have a 'Mind to Think' and an 'Intelect to Decide'. Another chart taught that 'World History and Geography Repeat Dramatically Every 5,000 years' – at which point I felt I had had enough. As we withdrew, the receptionist presented me with another booklet and said she hoped I would soon attain Self-realisation, Bliss, Liberation, Fruition and Purity.
In India people will eagerly experiment with any spiritual novelty that comes their way; nor have we any right to assume that those experiments must always be unsuccessful just because they seem totally haywire to us. At least experimenting Hindus are spared the conflicts and punishments that once were endured by experimenting Christians. Despite the rigidity of many of its taboos, Hinduism has no central authority to forbid or discourage unorthodoxy. Indeed, to the Indian mind there is no such thing as 'Hinduism'; the term was coined by foreigners to describe that complex of distinctively Indian yet often dissimilar faiths which they encountered on the subcontinent. The Indians themselves, when referring to what we call Hinduism, use the ancient and very satisfying word _dharma. Dharma_ means a whole way of life and thought and feeling, and therefore not only covers religious beliefs and practices but includes the processes by which these have formed the Indian peoples' characters, and influenced the development of their society, over the past three or four thousand years.
The Indian _dharma_ is so peculiarly flexible that it can take even the Prajapita Brahma Kumaris in its stride. At first I was a little startled to read that this network of oddly godly museums has been commended by the President of India, State governors, cabinet ministers, judges of the supreme court and so forth; but then I saw how natural it was, in India, that the highest in the land should approve of any sincere spiritual movement, however apparently crazy.
By two o'clock we had collected our kit from the hotel and were on the way to meet Kay. Then suddenly Rachel said, 'Stop! I hear a band!' (She has become passionately addicted to every form of Indian music.) Obeying, I too could hear gay, martial airs and then, in the near distance, we saw half a dozen drummers and pipers crossing the road at an intersection. They were following a palanquin clumsily decorated with plantain leaves, coconuts, papayas, bunches of bananas and branches of bougainvillaea, and behind them trailed a procession of a hundred or so shabbily dressed men and women. The palanquin was preceded by a boy of about twelve, carrying a smouldering length of sandalwood, so I knew that despite the gay music a corpse was on its way to the burning ghats. When I had explained the situation Rachel exclaimed, 'Let's follow and see what happens!' Which we did – this being a traveller's attitude of which I thoroughly approve – though the procession led us away from the hospital.
Rachel seemed a little disappointed by her first corpse. 'He doesn't _look_ very dead,' she observed. Nor did he, poor chap, as he sat cross-legged amidst the bougainvillaea, wearing a grey woollen turban, red _lunghi_ and brown sports jacket. His brow was streaked with ash and saffron and a support had been tied beneath his chin. He may not have been very dearly beloved, since even the chief mourners looked bored rather than distressed. Everyone seemed to welcome our attendance, as a form of light relief, but the burning ghats were miles away and we had to turn back at three o'clock, lest we might miss Kay.
On the hospital veranda we were joined by the first white person we had seen in Mysore City – an elderly Englishwoman, kindly looking and frail, with 'missionary' stamped all over her. When we had chatted amiably for some moments, about nothing in particular, she suddenly turned to Rachel and asked, 'Do you love Jesus?'
I held my breath, foreseeing some artless regurgitation of K. M. Sen.
'Yes,' said Rachel, 'and I love Ganesh and Hanuman. Especially Ganesh. He has such a nice fat tummy. He's Shiva's son,' she added helpfully.
The missionary's reaction was even worse than I had expected. She looked so hurt – as though personally insulted – that I truly felt sorry for her. Avoiding my gaze, she asked in a taut sort of voice – 'Does the child not know there is only one God?'
'Of course I know!' said Rachel quickly and rather huffily, resenting the slight on her theology. 'But he has lots of different names.'
There seemed no point in my adding anything to that stark statement, which brought a flush of outrage to the unfortunate missionary's cheeks. As I made some inane remark about the Mysore climate our companion stood up, stiffly said goodbye and walked away. Watching her go, I wondered how many years she has devoted to her Christianising campaign. Probably forty or fifty – a lifetime – only to see, at the end of it, not Hindus coming increasingly to appreciate Christianity but Christians coming increasingly to appreciate Hinduism.
Yet it is perhaps foolish to waste sympathy on the remnants of a class well described by J. R. Ackerley, to whom a typical 1930s memsahib said, 'You'll never understand the dark and tortuous minds of the natives... and if you do I shan't like you – you won't be healthy.' Granted, few _mlecchas_ can understand the Hindu mind, however hard they try, but it now seems exceedingly strange that so many Europeans spent most of their lives in India without even wanting to know what makes the 'natives' tick. Probably this intellectual aloofness was partly based on a fear of Hinduism's pervasive eroticism. We find India's alleged obscenities innocent indeed, beside our own home-grown pornography, but in many books by what were then known as Anglo-Indians one perceives revulsion overlaying fascination whenever Hindu sexuality is hinted at. This is a very unpleasant aspect of the British–Indian relationship and it persisted until the Empire expired.
In retrospect, one can see that British arrogance in India was not always as simple as it looked. But whether it sprang from a genuine, uncomplicated racial superiority-complex, or was a cover for fundamental uncertainties, it alienated countless thoughtful Indians who might otherwise have taken a friendly interest in Western spirituality. Many British missionaries gave the impression that for them Christianity was the one true faith less because Christ had founded it than because Englishmen practised it – and look how civilised, clever, well-organised and advanced _they_ were!
Of course there was the occasional realist, like Thomas Edwardes, who in 1880 observed that
Neither Buddhism, Hinduism nor Mohammedanism... can be expected to fall asunder and evaporate at the touch of the Ithuriel spear of Christianity. These religions are part of the race characteristics of the peoples who possess them, and are worked into the very tissue of their lives... and, until events arise that shall materially alter the conditions of their existence, these historic faiths will retain their supremacy... in the lives of their adherents.
Educated Hindus have always distinguished between conversion in response to outside pressure and conversion as a result of some personal inner change. The first, which in their experience has usually had political overtones, they see as a threat to social and national order: the second they can and do sympathise with. However, despite Hinduism's traditional tolerance there has been a strong post-Independence move to make 'conversions' illegal and, though unlikely to succeed, this is a significant symptom of India's new nationalism. The extremist Hindus, such as the Rashtriya Swayamasevak Sangh – one of whose members assassinated Gandhi – interpret missionary efforts as 'an integral part of the domination of white races over Asia'. And basically they are right, though few of the men who ruled India were themselves pro-missionary.
More important than the extremists' attitude is the resentment felt by politicians and industrialists because some aboriginal tribes are being encouraged by their Roman Catholic and Lutheran friends to fight for various forms of national autonomy. This could cause endless trouble, as much of India's unexploited mineral wealth is in aboriginal territory. Already missionary and industrial activities have undermined the tribal way of life and it is certain that these primitive hunting peoples, who have survived for so long amidst India's jungly mountains, are now doomed.
Yet one cannot ignore the immense amount of good that has been done all over India by medical missionaries. Kay is a typical example, as selflessly dedicated to 'the cause' as anyone could be. By worldly standards there is nothing in it for her – no money, fame, glamour, adventure – nothing but hard work and discomfort and worry and frustration and the consoling conviction that she is doing God's will. At four-thirty she returned from three days of camping out near her jungle leper-clinics and swept us off to spend the night on her bedroom floor. Since our Nepalese days she seems to have become a shade more paternalistic (sorry: maternalistic) in her approach to 'heathens', but otherwise she is splendidly unchanged. And, despite certain radical differences in our outlooks, it has done me good to see her again.
CHAPTER SIX
# _Andanipura Farm_
## DECEMBER 6TH. ANDANIPURA FARM, NEAR KUDIGE
Last week, on the way to Byerley Stud, Tim pointed out an estate near the village of Kudige which belongs to his wife's brother, K. C. Appayya, who is one of Coorg's few experimental farmers. I expressed an interest in Mr Appayya's agricultural theories – and at once, with characteristic impulsive kindness, Tim announced that he would arrange for us to spend a couple of nights at Andanipura before we moved down to South Coorg for _Huthri_. At the time I felt ungratefully lukewarm about this plan, since a tour of the stately homes of Coorg was not really the object of our journey, but the Appayyas are such a warm-hearted and fascinating couple that I am now blessing Tim for having introduced us.
This morning we got a bus from Mysore to Kushalnagar, and from there to Kudige we shared a ramshackle five-seater car with fourteen other passengers – which meant paying only fifty paise for the four-mile journey. Rachel went free, though she must have added considerably to the already acute discomfort of the pyramid of men on whom she sat.
Our taxi put us down where the Andanipura track meets the motor road and we walked for half a mile between acres of wild heliotrope until suddenly this house came into view – a new, crescent-shaped bungalow, surrounded by banks of white and scarlet flowers. As we aproached the vine-draped veranda 'Casey' – his Cambridge nickname – came hopping down the steps to meet us. A rotund, bright-eyed little man, with the air of one who cannot help enjoying life, he irresistibly reminded me of a cock-robin – an impression reinforced by his quick, darting movements while he poured drinks, and said how happy he was to meet us, all the while making rapid, pecking movements of the head as though each word had to be captured before being articulated.
Then his wife appeared, in a turquoise Coorg sari spangled with tiny golden stars and tied on the left shoulder with a golden brooch. As we stood up to greet her I was reminded of a Botticelli Madonna. In India womanly beauty often has an ethereal quality and even Rachel was overcome by Shanti's loveliness. When we went to our room she said – 'I think our hostess would look like a queen if she wore a crown.'
Within moments the Appayyas had made us feel like dear friends instead of total strangers, and before sitting down to a superbly cooked lunch I had my first bath for a week and massacred the numerous fleas which had been my constant companions since that night we spent in Kushalnagar's Hilton. So this afternoon all is right with my world.
The siesta-habit is a great boon to writers; while everyone else snoozes I can get on with my diary. I am now sitting on the veranda, facing a semicircle of mountains and overlooking the Appayyas' farmlands. There are gay expanses of sunflowers in full bloom, and guava orchards, and glowing acres of paddy, and across wide fields from which a tobacco crop has just been harvested pairs of small black oxen are drawing simple wooden ploughs. Casey uses tractors sparingly; with the oil-crisis gathering momentum oxen make more sense. Of course most South Indian farmers will scarcely notice this crisis, since they are still using 'agricultural machinery' first invented 5,000 years ago.
Casey hopes to be able to improve production in the less fertile parts of Coorg and here he has demonstrably made a good start. However, he is worried by recent rumours about State government plans to confiscate big estates and divide them among the villagers, paying the owners Rs.60 (£3) per acre as compensation. Even to my politically naïve ears, this sounds more like a vote-catching device than a genuine programme. But what disturbs Casey is that such threats could so easily be carried out, without anyone paying the slightest attention to the landowners' pleas. Power has very definitely shifted, in modern India, to the hands of the career politicians.
I know too little about the intricacies of this problem to have strong views on it, though I cannot but sympathise with men like Tim and Casey, who clearly do not abuse their privileges. According to the _Gazetteer_ , Coorg, fifteen years ago, had some 60,000 agricultural holdings, of which 42,000 were under five acres, 6,700 between five and ten acres, 10,040 between ten and fifteen acres, 880 between fifteen and thirty acres and 806 above thirty acres. The _Gazetteer_ gave no indication of the average size of the 'above thirty acres' estates, but I am told that Tim – admittedly one of Coorg's chief landowners – holds some five hundred acres of coffee, apart from his paddy, grazing and forest. So on the one hand it does seem an excellent idea to give the peasants more land, though the estates of the rich 806 might not go very far amongst the poor 42,000. On the other hand, any drastic land redistribution would inevitably lead to a perilous drop in food production at a time when India desperately needs more and more food for those 55,000 additional citizens born every day. But if the _status quo_ is maintained, how are the peasants to gain the funds and experience needed to cultivate larger holdings efficiently?
I always seem to end my digressions on Indian problems with a question mark.
## DECEMBER 7TH. ANDANIPURA FARM
The hospitality here is so generous that by bedtime last night I was in no fit state to do my usual late writing stint. We had a memorable evening, during which – while still able to focus – I got out my map and with Casey's aid established the boundaries of Coorg. It is a small district, by Indian standards – only about 1,585 square miles. Its greatest length is just over sixty miles, its greatest width scarcely forty. To the east it merges into the high Mysore Plateau, to the west its mountainous frontier is twenty to thirty miles from the Malabar Coast. Most of its rivers flow east and are too shallow to be navigable.
The Appayyas, like Tim, enjoy nothing better than explaining and speculating about their own distinctive culture. The speculation centres on the origin of the Coorg race, a puzzle which greatly intrigues those Coorgs who have read the informed guesses made by foreign experts about their forebears. Yesterday, for example, on the Mysore bus, a charming old gentleman from Mercara enthusiastically presented me with his own personal theories, but unfortunately I could only catch one word in ten above the roar of the engine. When the bus stopped at Hunsur, and we got out to drink tea together, I gathered that 'a singular tendency towards brachycephalism distinguishes Coorgs from other South Indian races'. This might have enlightened me had I known what the 'ism' in question means. But I do not, and as I was about to request a translation we saw the driver rinsing out his mouth and had to hurry back to our seats.
From the start of their association with this region, the British were impressed by the Coorgs' comparative indifference to the taboos of the caste-system and by their marked independence of Brahmanism. These traits set them decisively apart from other South Indians, as do their traditional costumes and fair skins. Yet the Coorg language is purely Dravidian and more closely allied to Tamil and Malayalam than to Kannada. This is the sort of contradiction that makes the 'Coorg origins' problem seem insoluble.
The _Puranas_ prove Coorg to have been long recognised as a region with a separate identity (The _Puranas_ – 'Ancient Stories' – are a vast collection of myth and folklore accumulated during the first millennium AD.) According to the Cauvery _Purana_ , the Coorgs are descended from a _Kshatria_ (Aryan warrior) father and _sudra_ (non-Aryan slave) mother and so are called _Ugras_ , a word meaning fierce, formidable and powerful, and also used to describe a tribe of mixed caste origins. This ties in very nicely with the Coorgs' attitude to caste taboos; and they have had the best of both worlds, being traditionally regarded as equal to the _Kshatrias_ , except in the possession of the four Vedas and six Angas.
Casey quoted Fr Henry Heras of the St Xavier's Historical Society, who believed the Coorgs to have been mentioned in Mohenjodaro inscriptions; but this left me unimpressed, since the Indus Valley script has not yet been 'cracked'. He also quoted Professor Ghurye of Bombay, who believes they belong to the Indo-Scythian race. Another pleasing and not impossible theory is that they have some Roman blood. This could be a result of intermarriage either with the numerous Roman traders who appear to have settled in South India during the reigns of Augustus and Tiberius, or with the Roman mercenaries employed by early Pandyan rulers, if these fled to the safety of mountainous Coorg when the Pandyan Kingdom collapsed in the eighth century.
Everyone in Coorg must have their own favourite answer to this ethnological riddle, so I decided last evening to sponsor the delightful though highly improbable theory that the Coorgs are descended from yet another group of Alexander's ubiquitous soldiers.
The Appayyas have two children, and though Shanti is thirty-six years old and her daughter Kalpana sixteen years old they look like sisters – as do many Indian mothers and daughters of the privileged classes. Obviously being a Repressed Indian wife and mother is a much less ageing occupation than being a Liberated Western wife and mother.
The twelve-year-old son of the house, just home from school for the short winter holidays, promises to be as handsome as his parents. I cannot even attempt to spell him since the use of traditional Hindu names has very properly been resumed, after a period during which it was fashionable in Coorg to call one's children Bobby, Tommy, Mickey, Kitty, Pam, Betty and so on. Many Coorg children are sent away to school at the age of four; but judging by the affectionate Appayya family atmosphere, this does nothing to alienate them from their parents.
Kalpana expects to begin her university career in six months' time, at either Bangalore or Madras, but the present student unrest in India is so extreme that her parents naturally feel uneasy about the prospect of their ewe lamb falling among rioters. Yet they are as determined as she that she shall get a degree. This surprised me at first, since Karnataka's sixteen engineering colleges, nine medical colleges and four universities annually produce many thousands of graduates who cannot hope for appropriate jobs unless they know how to manipulate the relevant set of strings. However, when Kalpana graduates she will be looking for a husband rather than a job and I soon realised that in her circle 'attending college' is regarded much as 'finishing abroad' once was in Britain. Neither Shanti nor Casey seemed to see my point when I hinted last night – after their daughter had gone to bed – that for a girl of her personality, intelligence and beauty a university degree was surely superfluous, unless she proposed to use it. Since formal education first came within their reach, in the 1830s, the Coorgs – both men and women, of all classes – have been avid for it, and they remain reluctant to admit that nowadays the intelligent daughter of intelligent parents can complete her education more effectively at home than at a grossly overcrowded and understaffed college.
At the moment utter chaos prevails in Bangalore University, and conditions seem not much better in Madras. I have been following a curious drama in the newspapers, to do with a recent speech made by Mr Basavalingappa, one of the Karnataka State Ministers, who innocently deplored the numbers of trashy novelettes now being written in Kannada. South Indians have become so touchy about language issues that the poor man was immediately accused of being anti-Kannada – the worst imaginable crime in Karnataka. After days of serious student rioting all but two of Karnataka's eleven cabinet ministers resigned yesterday in protest against their colleague's remark and the chief minister begged everyone – but particularly the students – to 'put an end to this pointless controversy'. Of course there must be more involved than appears in the papers: Mr Basavalingappa has recently been at the centre of other rows. Moreover, he is a Harijan, and so cannot afford to be too controversial lest he might provoke inter-caste friction. The powerful conservative element in rural India strongly resents the fact that Harijans can now become high government officials.
I am beginning to feel vaguely guilty about having fallen so deeply in love with Coorg. I set out, after all, to tour South India, and my lingering here seems suspiciously like escapism. Undeniably, Coorg is a place apart – clean, quiet, uncrowded, unmodernised, not impoverished at any level of society, never too hot or too cold at any time of the day or night and populated by exceptionally congenial people. Add a truly magnificent landscape to all this and you have Paradise. No wonder the Coorgs are so proud of their country, with something more than the normal regional pride of Indians.
Atmosphere is such a mysterious thing. Why or how could I feel so sure, on our first evening in Mercara, that for me Coorg was somewhere special? I then knew nothing whatever about the place, so no part of my initial reaction can be attributed to preconceived ideas; yet my antennae were functioning with flawless precision – as most people's do, if their owners are willing to rely on them.
_Later_. This afternoon, when I mentioned that I would like to live for a couple of months in Coorg, Casey said it would be impossible to rent accommodation since letting rooms or houses is not part of the local way of life. But then he added, reassuringly, that Tim would solve my problem; and I fancy there are few Coorg problems beyond the ingenuity of that descendant of dewans.
Until Casey explained, I had not realised that there are no Coorg villages, as we understand the term. Instead, the Coorgs live either in large, isolated houses on their estates, or in groups of several smaller houses occupied by members of a joint family and surrounded by the family lands. A scattering of such homesteads is known as a _grama_ and corresponds to what we in Ireland call a 'townland'. A group of _gramas_ forms a _nad_ and in Coorg today there are six _taluks_ , divided into twenty-four _nads_. Such real villages as exist are occupied by Moplah traders or non-Coorg Hindu merchants and craftsmen.
After tea we all strolled down to the farm buildings, accompanied by two sloppy Labradors. Casey employs about ninety farm workers – men and women – and his openly feudal relationship with them seems to suit everybody. He told me that the 80,000 true Coorgs now form only about one-sixth of the population of Coorg, but are so dominant a minority that their culture has powerfully influenced most of their neighbours. Coorg customs have been adopted by thousands whose forefathers were freed slaves, or plantation workers imported from nearby states a century ago, or tribesmen forced by the reduction of the forests to become part of the farming community. As a pleasing result of this, the graceful traditional Coorg women's costume may even now be seen all over the countryside, worn by the peasantry, though the majority of the younger 'genuine' Coorg women have foolishly abandoned it.
Shanti and I went back to the house together, leaving the rest pottering about the farmyard, and as we walked through gay acres of sunflowers the conversation turned to recent pro-women changes in the laws of India.
According to Coorg Civil Law, which in this respect follows the general Hindu law, a daughter only has the right of maintenance from her father's family property until marriage, and after marriage no right either of share or inheritance. In theory, however, all ancient tribal, regional or religious laws have been superseded since Independence by new laws giving women full equality with men, so that they may now own property and insist on full and equal shares in any family inheritance. But most villagers, of both sexes, disapprove of this violent tampering with the fundamentals of Hindu society. They do not want their country reduced to the level of that pernicious, permissive Western world of which, through their transistors, they from time to time hear faint and disquieting rumours; and they cannot conceive of a moral world in which men and women are treated as equals. It is one of history's minor ironies that these particular changes should have been enforced immediately an Indian government came to power, when for so long the Raj had scrupulously avoided offending Hindu susceptibilities.
Yet the influence of the Raj did appreciably improve the position of many urban women and this new legislation must eventually bring about a change in rural India. Listening to Shanti, I got the impression she would prefer not to see an abrupt change, even if such a thing were possible; and on such a basic point as arranged marriages few mature Indians – outside of a tiny cosmopolitan 'sub-caste' which is no longer truly Indian – are prepared to advocate any change, ever. Even a couple as liberal as the Appayyas would feel deeply distressed should their daughter set out on a personal husband-hunt instead of depending on her parents' judgement.
I asked Shanti what the average parents' priorities are as they cast about for suitable mates for their young, and she replied without hesitation that all Coorgs consider 'blood' the most important qualification – by which I assume she meant caste and sub-caste. Next comes 'honour' (that is, moral character), and then property, health, looks and accomplishments. On the question of honour a boy's parents pay special attention to the character of a girl's mother and Shanti quoted a Coorg proverb – 'If the mother has a white tail the daughter will at least have a white spot.' So if a girl can produce a mother with an unblemished reputation it does not much matter what unsavoury predilections she may have inherited from her father.
Shanti also remarked on a change I have recently heard mentioned by several other Indians – the tendency amongst today's youngsters to abandon that love-match ideal which twenty or twenty-five years ago was the dream of every progressive young Indian. Some of those youngsters are themselves the victims of love-matches gone wrong, and many others know that a high percentage of such marriages failed. This failure rate is hardly surprising since there is little in the Indians' cultural background to help them to create the sort of relationship that should develop out of a love-match.
According to Casey, the Coorg Civil Law is still widely respected and Coorgs have only recently been permitted to own private property. Until the joint-family system was weakened by migration, no individual could acquire or inherit property that was separate from the family possessions. Now, however, men are allowed to leave to their children – without having first to seek permission from the _Koravakara_ (Head of the House) – all property acquired through their personal effort. But the Coorg who has prospered in some faraway city is still criticised if he does not annually donate a generous portion of his wealth to the family pool. And nothing is allowed to interfere with the cultivation of the joint-family lands by the joint-family for the benefit of the joint-family.
It seemed to me, listening to Casey's explanations, that the _Koravakara_ is not to be envied. As the eldest son, he has all the worry and responsibility, when he succeeds his father, of managing the entire estate, yet he is not entitled to an even fractionally larger share of anything than his brothers – or his widowed sisters-in-law, on behalf of their sons, should his brothers predecease him.
The adoption laws are interesting. A childless Coorg widow may adopt a son to inherit her husband's share of property, and so may a Coorg male who is himself disqualified from inheriting through disease or blindness, or an unmarried Coorg female who has no brothers. (Spinsters are very rare in India but they can happen, usually because of some physiological defect.) An illegitimate son or daughter may not, however, be adopted, nor can a boy be purchased. Most people prefer to adopt a spare son of a daughter of their own household, if such is available. Adoptions are not recorded in writing, but a little ceremony takes place in the presence of relatives and friends; and, if adoptive parents subsequently produce a son of their own, he and the adopted boy have equal rights and the latter, being the elder, will eventually become the _Koravakara_. Many childless Hindu men adopt because they fear _Putt_ , a place of torment reserved by some unspecified but obviously unreasonable god for those who have no son to perform the last rites over their corpse. But Coorgs are made of sterner stuff. They don't believe in _Putt_ and their motives for adoption are always strictly practical.
CHAPTER SEVEN
# _The Huthri Festival_
## DECEMBER 8TH. GREEN HILLS, NEAR VIRAJPET
This address – sounding so like a stockbroker's fine detached residence in darkest Surrey – is a typical period aberration on the part of a wealthy Coorg landowner and Cambridge graduate of the early twentieth century.
For some odd reason, now quite forgotten, a Swiss architect designed Green Hills in about 1910, when Tim's father moved out of the ancestral home. By my humble standards – or, indeed, by normal Coorg standards – it is an imposing mini-palace, full of ebony and teak and rosewood, and silver and ivory and brass, and ancient armour, and swords that were wielded in famous battles, and of course the inevitable, magnificent shikar trophies which Rachel and I find so very off-putting. However, though Tim was one of the most celebrated hunters of his generation, and prided himself on always going into the forests on foot, even he has at last been bitten by the conservation bug. But it may already be too late to save the Coorg tiger.
This morning the Appayyas insisted on providing us with an ancient retainer as escort, which I felt was taking concern for one's guests a bit far. Obviously none of them could imagine a foreign woman, who spoke only English, being able to find her way unaided from Andanipura to Green Hills – a distance of some thirty miles.
When we changed buses at Mercara I bought today's _Deccan Herald_ and read: 'Three Killed in Bus Capsize: A bus proceeding from Coimbatore to Velanthavalam village had more than one hundred passengers at the time of the accident... The driver was reported to have absconded, while the conductor surrendered at the Madukkarai police station.' Folding up the newspaper I looked around and estimated there were no more than sixty-five people in our forty-four-seater bus, so we seemed likely enough to survive.
The road from Mercara to Green Hills – which is five miles north of the market town of Virajpet – winds through South Coorg, where the landscape is less rugged than in the north but even more beautiful. This whole area – Yedenal Kanad Taluk – is extraordinarily fertile and generally considered the centre of Coorg life. Many leading families live here and Virajpet, though a smaller town than Mercara, is the province's most important commercial centre.
I find myself automatically using the word 'province' when writing of Coorg, though the term is no longer technically correct. Under the British, Coorg was a province – the smallest in India, administered by a commissioner – but now it is merely one of Karnataka's many districts. However, I may perhaps be allowed this inaccuracy, in view of Coorg's 'natural' – as distinct from political – independence.
The bus put us down at the freshly painted white wooden gates of the Green Hills estate and as we walked up a long drive I could for a moment have believed myself in some quiet corner of England. On either side, green parkland was dotted with handsome trees; nearby grazed a few fine horses and a herd of even finer cows, and in the distance, beyond the big house amidst its brilliant abundance of flowers and shrubs, lay the long, uneven line of the ghats. Their gentle blue contrasted with the vivid, sharp, almost incredible blue of this Coorg sky – a sky such as one would never, it must be admitted, see in England. Nor would one pass there a nursery of orange-tree saplings and baby coffee-bushes, each infant protected by a wicker shield; and the bull would not be a glossy red Sindhi with a splendid hump, nor would the house be surrounded by graceful groves of immensely tall areca-nut and coconut-palms.
We arrived just as lunch was being served on the veranda and Sita introduced us to her mother, her two brothers, various visiting relatives and five dogs including a Great Dane the size of a pony. More relatives will arrive this evening for the _Huthri_ Festival tomorrow.
One has to admire the Coorgs' devotion to their own customs. Observing the Thimmiah family today, I noticed that when junior members meet their elders they bow respectfully to touch the older person's knees with the fingertips, which are then pressed to their own forehead and, finally, to their superior's feet. This form of obeisance takes longer to describe than to carry out: the whole series of gestures is somehow swiftly accomplished in one graceful movement. And it pleases me to see such a tradition maintained, even in the most sophisticated circles.
_Huthri_ literally means 'new rice crop' and the festivities go on for about a week. These celebrations are simple – mainly dancing, singing, eating and drinking – but _Huthri_ is greatly looked forward to as the one occasion when nothing short of serious illness prevents every family member from returning to the ancestral home. The central event is the solemn cutting of the first sheaf of paddy by the head of the family. This must be done on the night of a full moon, in either November or December, at a precise moment which has been declared auspicious by the _Kanias_ (astrologers). No one yet knows when the 1973 auspicious moment will be, but tomorrow's newspapers are expected to publish it. I felt slightly cheated on being told this; an announcement about a ceremony that may well antedate the written word – never mind the printed word – by thousands of years should surely be publicised in some more romantic way than through the newspapers.
A thorough spring-cleaning of every house, outbuilding, yard and garden precedes _Huthri_ , and today all doorways and windows were decorated with festoons of mango and peepul branches and garlands of flowers. The pathways and gateways from the fields to the house must also be decorated with elaborate floral arches, and this afternoon Rachel and I went for a long walk so that none of the busy household would feel it necessary to entertain us.
On our way we explored one of Tim's big plantations where the coffee-berries were swelling and ripening beneath towering, ancient shade-trees. As coffee-bushes need shade the forests never had to be completely cleared to make way for the plantations and walking through coffee is always a delight; enough trees remain for the insect and bird life to flourish and this afternoon we saw three sensationally large butterflies and several jewel-like birds.
As we were leaving the plantation I happened to notice, in an uncleared patch of forest near the road, one of those primitive non-shrines which seem much more relevant to the religious life of Indian peasants than the ornate, Brahman-dominated temples. A long, flat stone (not a _lingam_ ) lay on the ground amidst the tangled roots of a gigantic tree that seemed as old as the earth itself. No attempt had been made to erect even the crudest shelter over this altar-like boulder but many small objects were piled nearby and, when my eyes had got used to the perpetual twilight beneath that dense canopy of leaves, I saw the simple pottery votive offerings of people whose ancestors were worshipping thus before ever Brahmanistic Hinduism was heard of. These clumsily made little figures represented elephants, cattle, goats, dogs or pigs and some looked fresh from the fire. We circled the colossal tree under which the stone lay, following a path trodden by countless generations, and I noticed that piles of broken pottery almost covered the complex roots. I wondered then if human sacrifices had ever been made in this appropriate setting. But if once upon a time such rites did take place the victims must have been as happy to die as Christian martyrs, for there is now no stain of terror or brutality on the atmosphere. (In letting my mind run on these morbid lines, I was not being unduly fanciful. Up to the middle of the last century, at Kirindadu and Konincheri villages in nearby Katiednad, a human sacrifice was offered to Bhadra Kali in the June and December of every third year. Then gradually, as the British influence spread, human victims were replaced by animals.)
When I asked Tim about the stone slab in the sacred grove he said – rather surprisingly – that he had never heard of it, but that it could be one of those altars dedicated to the local god Bete-Ayyappa – Lord-father of hunting expeditions – which are found all over Coorg in forests and fields. He added that in honour of this god the Coorgs have reserved a certain tract of forest in each _nad_ which is considered sacred and where no trees may be cut. Despite Coorg's abundant forest wealth, the indiscriminate felling of trees has always been discouraged and very ancient customs – which have the force of laws – specify which trees should be used for fuel, which for building, which for furniture and so on. It is laid down that only the branches should be cut; nobody has the right to fell a tree unless he has already planted two.
## DECEMBER 9TH
By dinner-time last night all the family had assembled for today's _Huthri_ ceremonies and a more congenial gathering it would be hard to imagine. I am still searching for words to convey exactly what it is that makes the Coorgs seem so endearing. Perhaps I came across a clue to it this morning, when reading an early book on Coorg borrowed from Tim's library. Some one hundred and twenty years ago a Swiss missionary – Dr Moegling – wrote of the Coorgs that 'strangers are received among them and naturalised without difficulty.' And for the ordinary traveller it is not only heart-warming but flattering to be made to feel immediately at home by people who, though Westernised in many superficial ways, have so far remained emphatically a race apart.
This evening's ceremonies began at seven-thirty when we were sitting on the veranda sipping our gins or whiskies. Suddenly Sita said, 'Listen!' – and we heard the distant beating of drums and clashing of cymbals and the occasional long, solemn note of a horn. As the music drew nearer I moved to sit on the broad wooden parapet at the edge of the veranda, overlooking a level stretch of freshly swept beaten earth – some fifty yards by twenty – on which the _Holeyas_ would dance. These are the labourers who work in the paddy-valleys and many of whose ancestors have been the _Holeyas_ of Tim's ancestors for centuries.
There was nothing outwardly remarkable about the forty or so men and boys who soon appeared, dressed in everyday clothes and led by a five-man band. At first they seemed rather self-conscious but then something took hold of them – the music? the home-distilled Arak they had been drinking? or simply the _Huthri_ spirit? – and for two hours they danced and chanted like beings possessed by some happy demon. This was a glorious scene, lit by the full moon – slim, agile figures leaping and crouching, and twisting and wriggling, and bounding and swaying in their improvised dances. It was every man for himself, from a turbanned greybeard who must have been well over seventy years old to a chubby, vigorously pirouetting four-year-old. And overhead the leaves of the tall palms stirred and glinted against a blue velvet sky, while fireworks of every conceivable sort were being let off at frequent intervals by the small boys of the family.
Meanwhile, the menfolk had been taking a purifying bath and dressing in their traditional costume, which is so dignified, attractive and practical that I cannot imagine why they ever abandoned it in favour of Western clothes. The coat – called a _kupya_ , and usually made of thick black cloth – reaches a little below the knees and has a vee-neck, elbow-length sleeves and a scarlet and gold silken tasselled sash. Under it is worn a white shirt and into the sash is tucked a _peechekathi_ or an _odikathi_ , or both. The former is a short, sharp dagger with an ivory handle and a silver and gold ornamental scabbard; the latter is a heavy, curved knife very like the Gurkha _kukri_. On ceremonial occasions the male Coorg costume must include a _peechekathi_ , attached to the silken sash by a long silver chain decorated with exquisite silver miniatures of all the traditional Coorg weapons. The unique, flat-topped Coorg turban completes this striking outfit and the legs and feet should be left bare; but nowadays almost everybody is hookworm-conscious and wears light sandals. A strong streak of egalitarianism runs through Coorg society and at ceremonial gatherings it is impossible to tell the difference, by their attire, between the poorest farmer and the richest coffee planter.
For _Huthri_ each member of the local community makes his contribution, the potter bringing a new pot, the mat-weaver a new mat, the basket-maker a new basket, the carpenter a new wooden bowl; and at nine-thirty, when we went to the _Nellakki Nadubade_ or inner hall of the house – which amongst the ancestor-revering Coorgs serves as a family chapel – I saw the uses to which these things are put. At one end of the room the sacred brass wall-lamp, now lit, hung from the ceiling at face-level and directly below it the new mat was spread on the floor, touching the wall. On it stood the new basket, containing auspicious bitter-gourd, mango and peepul leaves, and also an old basket containing some of last year's paddy to welcome this year's crop. The new earthen pot held flour made from fried boiled rice, and beside it stood small bowls full of milk, honey, sesame and ground coconut. On a three-legged stool was laid the billhook with which Tim would cut the first sheaf, beside a dish-lamp complete with rice, betel leaves and areca nuts.
As we all stood before the wall-lamp Tim invoked the blessing of the god Igguthappa and the _Karona_ (family ancestor), and then each member of the family saluted him in the traditional way and received his blessings. At this point the _Koravakara_ 's wife becomes the most important person in the ceremony and Mrs Thimmiah, bearing the dish-lamp, led us in procession from the house to the fields.
We were preceded by several torch-bearers holding aloft blazing plantain stumps to light our way down the steep slope immediately below the house, and at intervals other stumps wrapped in oil-soaked rags flared beside the pathways, making the blossoms on the flower-bedecked archways glow with a strange, subtle radiance. All the time the tempo of the music was quickening and it reached a crescendo when we stepped from the shadows of the tall coffee-bushes and the paddy came suddenly into view, looking like a wide lake of silver beneath the brilliance of the tropical moon.
The swathes to be ceremonially cut had already been prepared and we approached them by walking in single file along the narrow tops of the dykes. Then Tim looked at his watch, poured milk and honey on the roots of a paddy clump, accepted the billhook from the youth who had been carrying it in a special bamboo container and, to a frenzy of music and exhilarated chanting, cut the first stalks of this year's harvest. At once a henchman rushed to the edge of the group and fired a single shot into the air to summon Igguthappa – and everyone began an immemorial chant to invoke the god's blessings on the crop. As I write this is still going on somewhere out in the vast, shadowy courtyard. The words mean 'Increase, O God!' and sound like 'Poli, Poli, _Deva_! Poli, Poli, _Deva_!' ' _Poli_ ' is said very quickly, while ' _Deva_ ' is almost drawled.
Next, the _Poludu Kuthu_ (a special wooden vessel) was filled with sheaves and placed on the head of the young man – Tim's son – who had been chosen for the great honour of carrying it back to the house. Other sheaves were handed to everyone present and I found it deeply moving to walk with the rest towards the threshing-yard holding those cool, dew-wet stalks, which collectively mean so much to some 500 million Indians. It is impossible, against the Coorg background, to think of this ceremony as merely 'a quaint local custom' or 'interesting old superstition'. Perhaps it is no more than that: perhaps all religious ritual everywhere is no more than that – who knows? But, if there is a God, then I think we came close to him tonight as we stood chanting in the moonlight.
Marking the centre of each Coorg threshing-floor is a plain stone pillar about four feet high, around which, for _Huthri_ , an elaborate pattern is drawn on the ground with white chalk. I took off my shoes at this stage, to join in the prayerful procession, and we circled the pillar three times before laying our paddy at its base while Mrs Thimmiah performed another _puja_. Then we picked the sheaves up again and climbed the steep path through the coffee back to the house, to lay them finally beneath the sacred wall-lamp. Before entering the house the _Kuthi_ -bearer paused on the threshold to have his feet washed by Sita – the unmarried daughter – and to receive from her a drink of milk. He then laid the _Kuthi_ on the mat below the lamp and, after a few moments, several young servants took some of the new paddy to weave it into garlands which were placed on every door-handle and window-latch in the house.
Having saluted his elders and received their blessings the _Kuthi_ -bearer went into the kitchen to mix a dough known as _Elakki Puttu_. This consists of rice-flour, fried gingelly seeds, bitter-gourd peel, grated coconut, mashed plantain, milk, honey and some tiny pebbles and coins, added for much the same reason as we add foreign objects to our barm bracks or Christmas puddings. I had followed the _Kuthi_ -bearer and I watched as he placed a little dough on six peepul leaves (one for each resident member of the family) and threw the leaves at the ceiling, calling the name of an ancestor at each throw. All the little balls stuck, which means the ancestors are well pleased with their descendants. And so they should be, in this family.
Meanwhile, two wooden trestle tables had been laid with shiny squares of plantain leaf in the _Nellakki Nadubade_ , and Sita was peeling a few grains from the new crop. She added these to a sweet porridge of which she placed a portion on a leaf – with a morsel from each of the seven ceremonial dishes we were about to eat – as an offering to the ancestors, and when we had all taken our seats Tim asked ritualistically, 'Shall we partake of the new crop?' We then did so, by eating a little porridge; and I came on a pebble and a coin which means I am to live long _and_ become rich.
I certainly feel rich tonight, though my new wealth has nothing to do with coins. Occasionally the traveller chances on an experience that seems enormously important, even if its significance cannot easily be expressed or explained, and though nothing could be simpler than these _Huthri_ ceremonies I know I shall never forget them. Altogether apart from the feeling engendered – which was so genuinely religious, in its joyous, primitive way – the sheer visual beauty of that paddy-cutting ritual was overwhelming. The Coorgs are a handsome race and all those fine faces, seen in profile against the darkness by the light of flaring torches, made a picture that would have inspired Rembrandt. Nor was there any intrusive twentieth-century detail to spoil the vision of Sita, superb in a Coorg sari of crimson silk, following her mother – a slim figure in silver – as Mrs Thimmiah bore that flickering dish-lamp along the narrow path while the workers' happy, rhythmic, full-throated chanting went echoing across the valley.
Probably, however, it is a mistake to consider the religious feeling and the visual scene as separate phenomena. Very likely they are interdependent, people responding to the one all the more readily because of the other. The builders of the great cathedrals seem to have known a thing or two about this matter, though my impression is that modern architects understand it only imperfectly. But perhaps thirteenth-century conservatives thought Chartres disgustingly eccentric and irreverent.
## DECEMBER 10TH
I woke at dawn this morning, despite having been so late to bed, and went for a solitary walk through the early freshness of coffee-plantation, paddy-valley and bird-busy forest. And I wondered, as I walked, what the _Huthri_ festival now means to Westernised Coorgs. More, I suspect, than Christmas now means to many Christians – though one might not think so to see the Thimmiahls lounging about in their jeans and T-shirts while sipping their cocktails, reading their _New Yorkers_ , listening to their stereo Johann Strauss and conversing in their Cambridge English (the first language of the Coorg elite). It interests me that so many Coorgs seem emotionally and intellectually capable of moving from East to West and back again without showing any sign of inner conflict or loss of integrity. This is a facility more usually found in practice amongst Muslims than amongst Hindus, though in theory the Hindu philosophy should be the more conducive to it.
As we sat on the veranda last evening, watching the dancers, I was very conscious of the chasm between Indian landowners and labourers; but later, when we were all in the fields, at the heart of the _Huthri_ ceremonies, I realised that at a certain level there is less of a chasm here than in Europe. Landowners and labourers recognise each other as being equally important, in different ways, and – at least where this family is concerned – are truly united in mutual loyalty and respect.
A Socialist would of course be appalled by the Coorg scene, which is as shamelessly feudal as anything I have ever come across. Tim talks cheerfully about 'allowing my people to smoke' or 'forbidding my people to gamble' as though democracy died with the City States. On the other hand, in addition to a just wage he gives 'his people' generous paddy rations for two meals a day, subsidises their weddings and funerals, pays their medical expenses when they fall ill and has so organised their lives that few of them are ever in debt though throughout India millions of agricultural labourers spend most of their lives in the grip of money-lenders. According to himself, Tim is an 'average' Coorg landowner and I would like to be able to believe this. He once stood for Parliament, causing the local Congress candidate to lose his deposit, but the wheeling and dealing of politics so disgusted him that he soon left the democratic arena to concentrate on doing his own feudal thing.
Contrary to my usual custom – but not surprisingly – I slept after lunch and woke to hear music in the distance. The bandsmen and singers had returned for a ritual praising of the family, from the founder-ancestor, called the _Karona_ , down to the youngest living grandson, aged three. As I write this (at ten p.m.) the musicians are still sitting on long benches against the wall in the prayer-room, chanting their strangely moving refrain, while the sacred lamp burns steadily before them. At intervals throughout the evening members of the assembled family went into the prayer-room and sat for a time, listening – and then returned to the veranda to get on with their game of scrabble. Tim has told me that tomorrow the ceremonial _Huthri_ Dance of Seven _Nads_ is to be held nearby. He added, sadly, that since the cinema came to Virajpet the locals have been losing interest in their festivals and the quality of both music and dancing has deteriorated. In an effort to encourage the boys to learn from the men, he himself sometimes tours the _nads_ ; but even in Coorg mass-entertainment is winning.
Rachel is five years old today and despite the inevitable shortage of cards and presents it was a most successful birthday, complete with home-made chocolate cake for tea.
## DECEMBER 11TH
This really is superb walking country, with climate to match. I spent most of today on the move: before breakfast with Sita, Rachel and the dogs, after breakfast with Rachel, and after lunch on my own. In all directions little tracks run to and fro and up and down, across the paddy and through the coffee and over the steep slopes. And every turn of every path presents a new combination of the region's beauties; blue mountains fortifying the horizon, protecting the peace of Coorg: long paddy-valleys lying between the dark green of the forested ridges like magic lakes of gold: wild heliotrope covering the open scrubland like a pale purple mist: neat acres of coffee fringed with lines of slim silver oaks and shaded by trees of an awesome height: and occasional handsome dwellings marked by warm red-brown tiles, gleaming white walls, groves of palms and plantains and cascades of bougainvillaea and poinsettia.
This afternoon, as I walked alone, I thanked Fate for having guided me to Coorg. With a five-year-old fellow-traveller I cannot seek out those remote areas which most appeal to me and it is rare indeed to find a 'developed' region free of brash advertisements, domineering pylons, strident petrol-stations, abundant litter, synthetic building materials and hideously artificial colours. But here, in this 'finest of the kingdoms of Jambudwipa' a civilised harmony still exists between landscape and people. So perfectly do the artistry of nature and of man complement each other that one feels miraculously restored to the Garden of Eden, to the world as it was before Eve ate the apple of technology.
At about half-past four I overtook several groups of friendly, curious, gracefully robed women who were also on their way to watch the _Huthri_ dancing, due to begin soon on a level expanse of grassy common land. Beneath the solitary, giant sampige tree in the centre of the common, Rachel was awaiting me with a swarm of young friends she had somehow acquired since lunchtime, and she announced that the local Harijans were about to perform an overture to the formal _Huthri_ dances.
Then, on the far side of the common, a quartet of weirdly comic figures came bounding on to the grass. The leader was almost black-skinned, smeared all over with white chalk and naked from the waist up – apart from a battered trilby, an elaborate garland of orange flowers and a blatantly false beard of goat-hair. Around his waist he wore a ragged cotton mini-skirt, held in place by a rope from which hung a dozen clanging pewter bells, and he had been kept well topped-up with a Arak during the past several days. He was followed by another man whose huge engaging grin revealed a magnificent mouthful of even white teeth and whose great bush of tangled hair may not have been as verminous as it looked. This character was clad in someone's cast-off army shorts and had a moth-eaten tiger-skin draped across his ebony torso. Like his friends, he was brandishing a long wooden staff and exuding Arak fumes. The other two performers were tall youths disguised as women and even without knowing the language one soon gathered that this entertainment would not have amused a certain Empress of India.
The adult Coorgs standing under the sampige rather pointedly ignored the Harijans as they gambolled, danced, yelled, sang, leaped high in the air and shook their long staffs. During a mock fight they rolled on the ground feigning mortal injuries (and feigning other things when the young 'women' fell beside them), while two small boys played a monotonous yet pleasing melody on long, curved horns. This boisterous, undisciplined clowning went on until the Coorg dancers appeared, forming a dramatic contrast to the Harijans as they crossed the common in a stately double line, their costumes immaculate, their bearing kingly, their movements, when the dancing began, stylised and gracious.
Forty-two men from seven villages were taking part and all carried short bamboo canes with which they duelled ritualistically while dancing in a circle to music provided by the drummers and horn-players. The leading pair wore white, the rest black, and as those handsome men circled rhythmically against a background of mighty trees I reflected that seldom, in the 1970s, is folk dancing performed for fun – not self-consciously, to preserve customs, or cunningly, to please tourists. But my pleasure can never be unalloyed when I chance upon such fragile and doomed links with the past. One knows that before Rachel is grown even Coorg will have opted for that pseudo-culture which 'kills time' (grimly significant phrase) but leaves the spirit starving.
Why do some people remain so passionately attached to traditional customs, while others can happily jettison them? The traditionalists, I suppose, are just silly romantic fools – or maybe cowards. It certainly frightens me to think that within my own lifetime customs which had survived for incalculable periods have been discarded in country after country, by race after race. Why should we assume that those links which previously bound the living to the dead are now worthless? It was only a few hours ago, under the sampige tree, that I glimpsed a possible answer to this question.
The dancers were still indefatigably dancing, though the clear evening sky had changed from pale blue to faint apricot, and then to a strange and lovely shade of violet. And suddenly it seemed to me that because our world has been so radically altered within the past half-century many of those things we were bred to value are, quite simply, no longer valuable; in modern society they have no place, they fulfil no function. So they must go, as the leaves in the autumn, leaving us, unprotected, to face the consequences of our own terrifying ingenuity.
Tomorrow we leave for a few weeks in the extreme south and Tim has guaranteed to have some suitably primitive accommodation organised for us on our return to Coorg.
CHAPTER EIGHT
# _A Glance at Kerala: Cochin's Kathakali Dance_
## DECEMBER 12TH. TELLICHERRY
This morning's journey from Virajpet to the Kerala State border was a continuous descent through dense forests where cardamom groves flourish in the undergrowth and not a trace of humanity is to be seen. On such roads I find it very hard to reconcile myself to bus travel.
The border consists of a shallow, clear green river running over elephantine boulders at the bottom of a deep ravine. In a one-street village on the Kerala side the Karnataka State-run buses turn around to go home, leaving their passengers to board the Kerala buses, which also turn around here. Kerala's rich green hills rise straight up from the village street and to the east looms the high blue bulk of the ghats. This is the sort of hidden-away little place, with a 'lost' feeling, which I particularly enjoy.
In the ramshackle mini-bazaar an astonishing amount of salted fish was on sale, and many baskets of fresh fish are brought every day by bus from the coast. At noon we went into a tiny eating-house and ate off plantain leaves provided by a little boy who carried them down the street on his head in a neat, freshly cut roll, tied with grass, and received ten paise for his labour. Before the food was served each customer carefully washed his own 'plate' with a tumbler of water – letting the water run on to the earth floor – and after the meal he tossed his leaf over the balcony towards the river far below. If it landed in the bushes on the cliff-side it was immediately set upon by the local cats and crows, watched enviously by the local pi-dogs, who could not cope with the precipice.
After lunch we set off to walk through lush magnificence until a bus overtook us. For a mile or so we had the river on our left and on our right were hibiscus and bamboo-clumps, marking the edge of the forest. Despite a total lack of cultivable land, quite a few little thatched dwellings, of mud-brick and/or coconut matting, had been erected along the edge of the precipice above the river. Their occupants were black-skinned, thick-lipped, curly-haired, bright-eyed and well-built. Most of them greeted us cheerfully, when they had recovered from their incredulity on seeing a more or less white woman and child strolling down the road, but the toddlers were terrified and fled shrieking to the shelter of mother's skirts.
In countries as developed as India one expects 'the media' to have by now given everybody an approximate idea of what everybody else looks like. But of course this is nonsense in the case of – for instance – Kerala's Ezhavas. Formerly these people were not merely 'untouchable' but 'unapproachable' and they are still a 'Depressed Class', to use the quaint official euphemism for impoverished groups who suffer from persisting (though now illegal) caste discrimination. The annual per capita income in Kerala is £26.30, so obviously the poorest class cannot afford to take their children to the coast, where they might glimpse foreign tourists or at least see pages from magazines, pasted on tea-house walls, which would give them some visual idea of white people.
We had been walking for about an hour when the countryside opened up. On every side stretched plantations of cashew and eucalyptus, groves of coconut-palms and plantains, low green scrub, stands of bamboo, patches of tapioca and the remnants of primeval forest where the black pepper vine thrives. One is overwhelmed here by the sheer abundance – the boundless exuberance – of Kerala's fertility. It is as though the Lord of Creation had given way, at this point, to the promptings of a wild and joyous extravagance.
We stopped at a crossroads to drink scalding sweet tea in the shade of a lean-to decorated with crudely printed Communist posters and a large picture of St Francis Xavier looking uncharacteristically soulful. The Hammer and Sickle marked the crossroads, fluttering merrily atop a high bamboo flagstaff, and opposite the lean-to some twenty barefooted boys and girls were sitting on the ground outside thatched schoolhouse, busily doing their English lesson. No teacher was in sight but they looked up from their studies only to help each other. I began then to believe all I had heard about the Malayalis' devotion to scholarship. And when the bus picked us up half an hour later we had just passed a large, tree-surrounded convent school from which hundreds of girls were pouring like lava down the sides of some intellectual volcano. Observing them, I wondered what effect that molten stream was destined soon to have on the Communistic, under-employed Malayalis. But – looking ahead – volcanic soil is very fertile.
From our seats at the back of the bus we had a good view, when the road began to descend to coast level, of the most densely populated region I have ever seen. Villages and towns merged one into another, people moved in throngs or stood talking in groups as big as a successful public meeting, the Red Flag fluttered gaily, gaudy wayside shrines contained smirking statues of the Virgin Mary, the Hammer and Sickle was neatly painted in white on ochre gable walls, Christian churches were frequently conspicuous and the hot, heavy air was laden with what a disdainful Coorg friend accurately described as 'the classic Malabar stench of shit, piss and rotting fish'.
Judging by the literature with which they were laden, most of our fellow-passengers were students. The lovely, flower-wreathed girl beside me cherished on her lap a gigantic tome of American provenance entitled _Industrial Psychology and Capitalism_. She gladly allowed me to look at it but the jargon was so way-out it might as well have been in Malayalam; and I did wonder how much of it was comprehensible to its present borrower from the college library. When we passed a gleaming new church – its grounds criss-crossed with bunting made of fresh blossoms – I asked our student friend if there was some special festival on and she explained the church was to be dedicated this evening. Then she sighed and confessed that she was worried. It was her new parish church and she longed to go to the dedication service, but her father was addressing a Communist rally in a nearby town at the same time and she had promised weeks ago to help with the refreshments for the visiting speakers. So what was she to do? When I suggested that she should go early to the rally venue, do her bit on the refreshments and hurry back to the church she immediately brightened. 'Of course! Why didn't I think of that?'
When we arrived in Tellicherry at five-thirty we walked the length and breadth of the town, looking for accommodation, and in seven hotels were told 'No room'. 'This is because India has too much population,' Rachel observed cheerfully. But I fear it is a bit more complicated than that. In three hotels an amiable youth at the desk had booked us in and was about to hand us the key when his paunchy Brahman boss appeared, gave us a hostile stare and said, 'All rooms are full!' However, remembering the racial discrimination once practised in India by Europeans I feel I must not complain. Although two Wongs don't make a white, as the Bishop of Hong Kong said to the couple with the blonde baby.
By seven-thirty the railway station – where I am writing this – seemed our only hope and we could have had a good free night's rest but for an unfortunate remark by the kindly station master to the effect that the nine-fifty night train to Ernakulam would solve all our problems. Apart from the daftness of travelling when the country is invisible, I can think of few things more hellish than an eight-hour nocturnal journey without a berth in a third-class Indian railway compartment. However, Rachel seized on the idea as a monkey on a banana and resolutely closed her ears to maternal words of wisdom; so I soon gave in, feeling she had earned this concession by being, on the whole, such a reasonable travelling companion.
In the ticket hall the male queue stretched for over fifty yards – its end was out of sight – but there were only two other women in the female queue. Inevitably I was asked to get a ticket for a man, which I gladly did. He was a very young father carrying a sleeping toddler of fourteen months and whimpering, newborn twins. Their mother, he explained pathetically, was still in hospital 'with a terrible complication – I sadly worry she will die'.
## DECEMBER 13TH. COCHIN
Between Tellicherry and here all my nightmares came true; and since Rachel enjoyed every ghastly moment of the journey it did not even serve the purpose of teaching her that Mother Knows Best. There was standing room only so she perched happily on my rucksack in the corridor when not sitting on the knees of strange men up and down the train, telling them her life-story. Apart from an hour's doze around midnight she never closed an eye, yet remained in high spirits. It is becoming noticeable that the rougher the going the better she copes, but the same cannot be said for her ageing mamma. I stood all night by an open door in the corridor swigging Koday's Rum and enjoying the waning moon behind the palms, while thinking how foolish it is to travel by train. Indian buses are as cheap as third-class on the railways and much more convenient from every point of view except speed (and, of course, safety).
We arrived here at five-thirty a.m. and went wandering around in a semi-coma of exhaustion looking for a hotel with a conscious _chowkidar_. Coming out of one narrow side-street, just as the darkness was turning grey, I walked straight into something white and hard and long and curved. Yes, an elephant's tusk. And beyond it, looming colossal in the dawn-light, was the owner, carrying a bundle of palm-fronds the size of a haystack in his trunk and an amused mahout on his neck. A collision with an elephant was just what we had needed to cheer us up and Rachel insisted on our following him. There was something almost eerie about the speed and silence with which that huge bulk moved through the greyness along the empty streets. Indeed, the speed was so considerable that even Rachel was willing to give up when we saw the door of a tea-house opening.
We emerged, refreshed, into full daylight and soon found this enormous new tourist hotel close to the sea. By our standards it is Hiltonian: Rs.10 for a single room with private Western loo and shower attached, and a fan and large table and comfortable chair. The bed has a foam-rubber mattress and everything is newly painted and scrupulously clean. By seven o'clock Rachel was asleep, but I can never sleep in the daytime when I have reached this point of exhaustion. So I shall now lie down and do some Kerala homework.
_Later_. According to legend, Kerala was raised from the sea by Parasurama, a Brahman incarnation of Vishnu who undertook to perform this labour with his battle-axe as a penance for having vengefully and destructively waged war against the _Kshatrias_. Yet the credit for Kerala's Golden Age is given not to Parasurama but to a demon, King Mahabali, whose reign ended when he was banished by the dwarf Vamana, another incarnation of Vishnu. Mahabali's reign represents the pre-Aryan era when the indigenous, caste-free peoples of Kerala were in control of their own destiny; and Vamana represents the fair-skinned invaders who imposed their own rigid social system on the dark-skinned and henceforth despised natives. Every August the Malayalis celebrate the imaginary return of Mahabali, during whose reign social equality, health and prosperity were enjoyed by all the people of Kerala. And surely it is no coincidence that in this State, which has dreamed for centuries of equality, the world's first elected Communist government came to power.
However, Kerala remains a stronghold of Brahman conservatism, for all its millions of Christians and Communists. The great nineteenth-century Hindu religious leader, Swami Vivekananda – champion of the Vedanta and founder of the Ramakrishna movement – became so confused and annoyed by the intricacies of Kerala's castes and sub-castes that he described the whole region as 'a lunatic asylum'. In his day – before the radical reforms brought about by that saintly Ezhava ascetic known as Shri Narayana Guru – the toddy-tapping Ezhavas had to keep sixty-four feet away from temples, thirty-six feet away from Brahmans, sixteen feet away from Nairs and twelve feet away from untouchables. Even today caste laws operate strongly here, not only among Hindus but among Christians and Jews. Over the centuries most of India's religious minorities have been inexorably – though unofficially – made to fit the Hindu mould. The Malabar Christians are divided into numerous hostile sects and sub-sects and apart from doctrinal and liturgical bones of contention many Christians further complicate the situation by remaining loyal to the hereditary Hindu castes and sub-castes of their remote ancestors. The Roman Catholics have added yet another ludicrous refinement; one sub-sect, claiming direct descent from St Thomas's first Indian converts, regards itself as much superior to the rest and not long ago, when a group of Ezhavas thought to improve themselves socially by becoming Roman Catholics (or Latin Christians, as they are called here), these 'Christian Brahmans' protested vehemently against their church being polluted by Ezhavas, however thoroughly baptised. So new churches had to be specially built for the new converts, many of whom – seeing that Christianity was not, after all, in favour of the brotherhood of man – relapsed into their former position at the bottom of the Hindu pile. Even today, when an Ezhava convert comes to the home of a 'caste-Christian' he may not enter but must stand outside and shout his message from the garden.
I hated wakening Rachel at ten a.m. but the alternative – to have her again awake all night – would ultimately have been more upsetting.
We spent the day exploring enjoyably though rather inefficiently. The local climate is not nearly as trying as I had expected, perhaps partly because there is so much water about and one spends half one's time on the motor-launch buses that operate between Ernakulam and the islands of Willingdon, Mattancherry and Mulavukad.
Before lunch we strolled through the Muslim quarter of Mattancherry where men were playing cards on cramped verandas and everybody greeted us cheerfully. The drab little rows of newish, solidly built one- or two-storeyed houses were plastered with slogans in English denouncing local capitalists, yet the worst of Cochin's poverty cannot be compared with what one sees in Bombay. Nor have I noticed here a single dirty person, of any age or condition. Even the inhabitants of the meanest hovels wear clean though often ragged clothes.
On all sides there is water – reeking, shallow canals, thick with slimy mud and crossed by rotting wooden footbridges: or the open, heavily polluted sea, always busy with boat traffic: or those fabled but (from what I have seen of them so far) much overrated backwaters. Little boys swam and played and splashed enthusiastically in the unspeakable canals but usually, I was relieved to notice, they gave themselves a shower, under a wayside fresh-water pump, before going home.
Turning one corner we came on tons of silver sardines being unloaded from long, slim boats into flat wicker baskets which were carried off to be weighed on the heads of sturdy small boys. As we stood watching, an old man sitting on a wooden crate beckoned us to join him and offered us glasses of tea. (In Indian towns a mobile tea-stall is rarely far away.) He spoke enough English to tell us that Kerala is India's chief fish-exporting state, landing more than 30 per cent of the national total of sea-food: and then he handed me a Communist pamphlet about the redistribution of wealth. When we were leaving the water's edge the young driver of a fish-delivery truck, who was shattering a mini-iceberg with an axe, gave us two huge lumps off the block and we went on our way through the early afternoon heat appreciatively rubbing our faces and arms to the intense amusement of the general public.
We next found ourselves in the Jewish Quarter, which consists of a long, narrow cul-de-sac with India's most famous synagogue at the closed end. A few of the tall, whitewashed, green-shuttered houses have antique-cum-junk shops at street level, run by mild, gracious men who would not dream of pestering the tourist but are happy to talk knowledgably about their wares, or about the history of the Malabar Jews. We chatted for over an hour to a pale, sad character with a long chestnut beard who was thirty five years old but unmarried because, being a White Jew, he could only marry a White Jewess and there are few of those left in Cochin. (Thousands of Indian Jews have migrated to Israel.) I was not in the least surprised when he explained that White Jews, Black Jews and Slave Jews (the three 'castes' of Malabar Jewry) cannot intermarry, and that the Slave Jews are regarded as outcasts by the others and up to a few years ago were forbidden to enter the synagogues.
The White synagogue was first built in 1568, burned down in 1662 and rebuilt with Dutch help two years later. (The Dutch had just captured Cochin from the Portuguese.) Our friend volunteered to give us a conducted tour of the building and I thought it a good mark for the neighbourhood that he had no fears about leaving his valuable stock unguarded. Together we admired the great chandeliers, and the blue and white eighteenth-century Chinese floor tiles, and the ornate golden crown presented to the community by some past Maharaja of Travancore, and, most precious of all, the ancient scrolls of the Old Testament. Then I turned to my companion and asked impulsively, 'Would you – could you – never consider marrying a Black Jewess? Because otherwise there won't be anyone, soon, to whom all this matters?' But he only looked at me blankly for a moment and then silently shook his head; he was unable even to consider such a shocking idea, preferring racial extinction to racial pollution. (Not that the Black and White Jews are necessarily dark and fair skinned.)
As we were walking back to our hotel a skinny little boy, wearing only a loincloth, came running after us. In most Indian cities I would have expected him to beg; here I was not altogether surprised – though very touched – when he presented Rachel with a hibiscus blossom, and us both with a lovely smile, before quickly running away. A tiny incident, but for me containing the essence of Kerala.
At five-fifteen Rachel heartily agreed that it was her bedtime. And now I must correct myself: this is no tourist hotel, but the Bharath Tourist Home, which means it is run by Brahmans for middle-class Indian tourists – conservative, vegetarian teetotallers who demand clean rooms, good plain cooking and a non-rowdy atmosphere. The enormous new building is staffed by charming young men who bound to attention at the touch of a bell, have at least two university degrees apiece and seem genuinely to care about the guests' welfare. Incredible value, for fifty pence a night. Admittedly, from the dissolute _mleccha_ 's point of view the absence of a bar is a slight disadvantage at the end of a long, hot day. But this defect is easily remedied by walking up a pleasant tree-lined road and fetching half a dozen bottles of excellent Bangalore beer from a liquor-store. Which is what I did when Rachel was abed, and then I settled down on the wide terrace-roof outside our fourth-floor room. Beyond the palmy islands across the bay the sun was sinking in a red-gold sky and when it had gone – so swiftly – a strange amber sheen lay on the water and I felt very aware of the _drama_ of day and night: something that passes us by in the twilit north. No wonder sun-worship has played such a part in the religious history of man.
Quickly the lights went on, encircling one of the world's finest natural harbours – for many centuries saluted as Queen of the Arabian Sea. The beginnings of Cochin's maritime glory are too distant in time to be seen, but Kerala teak was found during the excavations at Ur, and the Phoenicians, the Chinese, the Romans and the Arabs were regular visitors long before the arrival of the Portuguese, the Dutch, the French and the English. St Thomas the Apostle is said to have landed on the Malabar Coast in AD 52 and though much scepticism is expressed about this I see no reason why he should not have chosen to do his bit here. Certainly the first European settlement in India was established in Cochin in 1502 by Vasco da Gama, who died nearby on Christmas Day 1524; and on 16 December 1544 St Francis Xavier arrived on foot from the Coromandel Coast and had soon made many converts from amongst the untouchables and unapproachables.
## DECEMBER 14TH. COCHIN
Food is really scarce in Cochin at present: and an emergency can be said to exist when tourists notice a food shortage. Prices are proportionately high; bananas which elsewhere cost fifteen paise here cost sixty and such basics as rice, pulses, onions, tomatoes, potatoes, sugar, eggs and milk cost four or five times as much as in Karnataka and are often not available, at any price, to the ordinary shopper in the bazaar. (Large hotels like ours, which buy in bulk, can still get most of what they need, but yesterday there were no curds – an essential item of Hindu diet and Rachel's substitute for milk.) Today we unsuccessfully tried to get a simple rice meal in four restaurants, and since our return to the coast I have seen none of those piled stalls of fruits, vegetables and grains which are part of the normal Indian street scene. Also tea-house shelves, which elsewhere were laden with piled platters of sweet and savoury tidbits, are empty here at present. Yet the general impression is of a contented, quick-to-laugh people. Kerala's tradition of fish- and tapioca-eating must be responsible for the spectacularly superior mental and physical development of the average Malayali, as compared to his fellow-peasants from mainly vegetarian states. Hunger is not a permanent feature of Malabar life and one hopes this shortage will be temporary. In India one can never be sure such shortages are not contrived by racketeers who bribe or bully the relevant local authorities into submission.
I thought today how appropriate it is that the first book to have been printed in India was published at Cochin in 1577 by the Jesuits. Never have I seen such avid readers as these Malayalis, from the small schoolchildren who bend intently over paperback adventure stories as they travel between islands, to the wizened old rickshaw-wallahs who anywhere else in India would be illiterate but here read substantial, serious-minded daily papers. This afternoon I noticed three coolie-types on our crowded motor-launch who had obviously never worn shoes in their lives but were reading thick Malayalam volumes. These books – dog-eared and carefully jacketed in newspaper – had been borrowed, I discovered on enquiring, from college libraries run by the Shri Narayana Dharma Paripalana Yogam, an Ezhava welfare organisation founded in 1902, long before Gandhi began his campaign to better the Harijans. And on the train the other night, in our third-class compartment, several young men were reading imported Pelican editions of erudite experts which cost Rs.25 each – that is, the price of twelve vegetarian meals with all the trimmings. Kerala State has India's highest rate of literacy: 60.16 per cent. Granted, this need not mean much, but in Kerala millions of those 60.16 really are devoted to learning. A formidable army of secondary school and university students swarms all over Cochin, armed to the teeth with textbooks on everything from Architecture to Zoology. And I mean 'formidable army'. Most of these youngsters cannot hope for even the meanest sort of white-collar job but are unlikely to accept, with traditional Indian fatalism, their share of the subcontinent's misfortunes.
When we got back to our Bharath Home I insisted on Rachel's resting for an hour because tonight she is again going out on the tiles to see a performance of Kerala's unique Kathakali dance. According to the tourist office bumph, this is a '2,000-year-old Pantomime Kerala Dance'. Maybe it is – what are 2,000 years in India? – but according to the distinguished historian Nilakanta Sastri (who travels in my rucksack), 'Recent research has shown that the first Attakathas were composed towards the close of the fifteenth century.' Kathakali means 'story-play' and is specifically an educational religious dance based on the ancient _puranas_ , which recount the adventures and teachings of the gods and heroes of Indian mythology. Traditionally it is performed only by certain families belonging to the _devadasi_ community, a sub-caste associated with that temple prostitution which made so many mem-sahibs curl up at the edges. Tonight's performance is being given by the 'See India Foundation Troupe' which performs every evening, except Thursdays; so I suppose it will be a rather watered-down tourists' version. Yet the lives of the members of the troupe sound extremely gruelling and austere and not in the least commercialised. Training starts at the age of five and throughout the next fifteen years continues for twelve hours daily: two hours a day are devoted simply to exercising the eye-muscles. This Cochin troupe was founded by Guru Gopala Paniker, now ninety-seven years old, who last year received from President Giri the 'India's Greatest Artiste Today' award. His sons Shivaram, the world-famous dancer, and P. K. Devan, the director, are passing the tradition on – still assisted by their father, who continues daily to massage the student dancers by trampling on them with his bare feet. And now off we go, to see the result for ourselves.
_Later_. What to say? How to say it? I had read quite a bit about Kathakali – how ancient and awe-inspiring it is, how interesting and skilful and exotic. But no one had told me how exalting and humbling it is, how exhilarating and poignant, how quintessentially Indian, how triumphantly an affirmation of the Immanence of the Divine. I have often seen Indian dancing before and always enjoyed it but this was something quite different: less an entertainment than an escape into another sphere – and at the same time an encounter with an unfamiliar area of oneself.
The theatre is in the garden of a small bungalow up a narrow side-street and consists of a wooden outdoor stage, some ten feet by twelve, under an awning of coconut matting. In front of the stage a handsome brass pedestal lamp, four feet high and filled with coconut oil, burns brightly by way of footlights. Visitors are greeted on arrival by P. K. Devan – quiet, dignified, erudite – a man who at once makes it plain that all this is something more than tourist-bait. Significantly, too, the three musicians begin to play at the back of the stage about an hour before the dancing starts, for this whole ritual has a meaning and a purpose of its own, quite apart from the business of diverting the audience. Two of the musicians are drummers, using the _Chenda_ (played with two sticks) and the _Maddalam_ (played with the hands); the third is a singer with cymbals who tells the story as the dancers dance.
One hundred chairs had been arranged in rows before the stage, under the starry sky, but this evening the audience consisted only of ourselves and an elderly Danish woman. Normally an audience of three would leave those three feeling too embarrassed on behalf of the performers to enjoy themselves, and the performers too discouraged to give of their best. But one soon realises that ordinary criteria do not apply to Kathakali. Within moments of the dancers' appearing it is evident that to them it does not matter in the least whether three or three hundred people turn up on any given occasion. No one has a sharper nose than I for phoney tourist gimmicks and this Kathakali performance is unquestionably the work of men who feel the religious content of the dance to be of prime importance.
Before the dance began P. K. Devan outlined the story we were about to see enacted and simply explained the 2,000-year-old Kathakali technique. The language of gestures has been so developed that by using various combinations of the twenty-four basic hand positions over eight hundred words may be formed. Also, every movement of the eyes has a specific meaning intelligible to initiates, and the miming and footwork are equally eloquent. The elaborate make-up has to be applied by experts, a process which is gone through slowly and systematically, in solemn silence, and takes two or three hours. Each face is painted all over: green for good characters, black for bad, red for villains and pink for women and saints. These colours must be procured by crushing certain rare local stones or powdering the bark of sacred trees: and when they have been applied the dancer pauses for a moment, to pray with uplifted hands, before moving out of the dressing-room. The fantastic, heavily jewelled brocade costumes are themselves works of art which have passed down from generation to generation. Their weird loveliness is so strange that Rachel exclaimed, 'These must be magic clothes!'
Indeed, magic is perhaps the best word with which to sum up this whole experience. I felt utterly bewitched as time passed and the spell was woven more and more intricately around us. Kathakali dancer/actors make no sound, apart from a few animal-like grunts occasionally emitted by the villain, and in comparison with their slight, exquisitely stylised movements even the most inspired ballet-dancing seems crude. Without having seen them I could never have believed it possible to produce, through the controlled use of eye, face, hand and foot muscles, such an effect of ineffable beauty, adding up to what can only be described as a prayer in movement.
CHAPTER NINE
# _Pilgrims at Cape Comorin: Family Life in Tamil Nadu_
## DECEMBER 15TH. TRIVANDRUM
Statistics mean something to me only when I can see them, as you might say, and I could certainly see them today during our 136-mile bus journey from Cochin to Trivandrum. In area Kerala is one of the smallest Indian states (38,855 square kilometres), but its population of twenty-two million puts it amongst the most densely populated regions in the world. Moreover, one-third of its area is forest and mountain so some districts have 1,124 people to the square kilometre. Along the coastal strip each village merges into the next and little seems to have changed since lbn Batuta wrote – some five centuries ago – 'The whole of the way by land lies under the shade of trees, and in the space of two months' journey there is not one span free from cultivation; everybody has his garden and his house is planted in the middle of it.' But in one respect things have been changing for the worse: as the people increase, erosion is diminishing the land area.
Yet Kerala is not depressing; the Malayalis look far better developed than the average crowd to be seen on a European beach and since men and children wear the minimum of clothing (or none) one can fully appreciate their magnificent physiques. (Incidentally, it is only quite recently that Ezhava women have been allowed to cover themselves above the waist in the presence of the Brahman and Nair castes.)
Trivandrum is a hilly, higgledy-piggledy city full of trees and quite attractive, though no urban conglomeration of some 400,000 people can truthfully be said to excite me. Outside the bus stand an ebony-skinned youth – barefooted and extraordinarily handsome – offered to guide us to a good but cheap hotel and led us up a broad street, all the while begging me to hire a coolie to carry my rucksack. He said he hated to see me shouldering it yet could not possibly carry anything himself – not even my water-bottle or canvas bag of books.
Soon we had been installed in a twin-bedded room, with its own primitive shower and latrine, for Rs.5 plus another Rs.5 deposit, which I suppose is intended to ensure the guests don't make off with the bedding. When I handed fifty paise to our guide he waved it aside and smiled and bowed, and said it was his joy to help us, and vanished. No doubt the hotel rewards him, but how often in India does a barefooted boy decline a tip? I could not help reading a certain significance into his use of the word 'joy' where most Indians use 'duty'. It seemed a nice illustration of the average Malayalis' light-hearted approach to life.
We spent the afternoon drifting around talking to people rather than systematically sightseeing. In some respects the southern princely states of Mysore, Cochin and Travancore were far more advanced at Independence than British India – Travancore, especially, had a reputation for being prudently progressive without being pseudo-European. For generations its rulers had treated state revenues as public funds rather than as their own private property and less than 5 per cent was kept for the use of the Maharaja and his mother, through whom (the state being a matriarchy) he had come to the throne. The 'palace' was a simple white house on a hill, and throughout the 1930s one-fifth of the revenue was devoted to education.
The last Dewan of Travancore, Sir C. P. Ramaswami Aiyar, courageously changed the law to allow Harijans into the temples and made possible Kerala's present-day industrial expansion. But he was an autocrat who for years strangled every popular political movement at birth. During the pre-Independence controversy about the fate of the Princely States he announced peremptorily that when power was transferred Travancore would become a sovereign state: whereupon there was a spontaneous revolution and an attempted assassination of the Dewan, followed by his resignation and a hasty announcement from the Maharaja that his _rajyam_ would of course become part of the Indian Union.
We spent a couple of hours strolling through the green and pleasant university grounds, talking with students and staff. Here in the midst of their problems it is easy to sympathise with Kerala's Communists, who of course are not in the least like non-Indian Communists. Their strongly held political beliefs seem to co-exist quite comfortably with a fervent devotion to Harihara, pilgrimages to Guruvayur and Sabarimala, an unquestioning acceptance of made marriages and the pronouncements of astrologers, reunions for joint-family _pujas_ – and so on and so forth. In fact I can't think why they don't call themselves something else.
India's two Communist parties (both of which claim to be the One True Party) are known as the Right Communists (Soviet) and the Left Communists (Chinese). The General Secretary of the Left, for all India, is an outstanding political genius called Elamkulam Manakal Sankaran Namboodiripad. (Who must surely say to his friends, 'Call me El.') This gentleman comes of the highest sub-caste in Kerala, a most rarefied elite of academic aristocrats, and while chief minister of the first Communist government he was worshipped by millions as a 'holy man'. This was even before his 1969 Land Reform Act, which prescribed the lowest land ceiling in India, allowing no more than five standard acres for one person, ten for a family of between two and five members, and one acre each extra for every additional member, after five. The young economics lecturer who provided me with these figures insisted on writing them down himself in my notebook. 'You must not forget,' he said. 'Our Communist government really did give "the land to the tiller" – not just _talk_ about doing it. Now we have no landless peasants – nobody can be evicted – the cultivator has full ownership. But next it is most important to make him have less children.'
This morning in Cochin we woke to a grey sky and all day the air felt deliciously cool. Then at sunset we heard our first rain since leaving home, exactly a month ago, and it is still slashing down with monsoon-like fury.
## DECEMBER 16TH. CAPE COMORIN
This evening I have come to the conclusion that India – the whole Indian _dharma_ – is peculiarly tourist-proof. By which I mean it is too individual, too absorbent, too fortified by its own curious integrity, to be vulnerable to those slings and arrows of outrageous vulgarity which have killed the loveliness of so many places since tourism became big business. I had expected to find Cape Comorin despoiled, yet it remains first and foremost a place of pilgrimage: a holy place, as it has been for centuries beyond counting. Like so many of Hinduism's less accessible pilgrimage sites, it is marked by an extraordinary atmosphere of quiet excitement, of devout gaiety; and added to this is its own unique flavour. From the bus one suddenly sees the sea – or rather, three seas – and a temple on a rock about half a mile off-shore. And that's it. One has reached the end of India.
Although we arrived on a Sunday afternoon, in the midst of a local Roman Catholic festival, the crowds were not excessive and there was not one other non-Indian to be seen. Having booked into a Rs.5 windowless cell – swarming with ants – we dumped our kit and hastened to the sea. Cape Comorin is emphatically final – a tapering point of rock which is unmistakably farther south than the rest of the coast. Here steps lead down to the confluence of the Gulf of Mannar, the Indian Ocean and the Arabian Sea; and in this water, regarded as most sacred by Hindus, the pilgrims 'take bath' and do _puja_. Fierce cross-currents and occasional sharks make the sea hazardous, so massive boulders have been cleverly rearranged to prevent pilgrims (or Irish swimming fanatics) from being swept away or eaten alive. A memorable bathe is the result, as during the north-east monsoon swimmers are tossed to and fro like corks within this safe area of swirling foam and crashing waves. And while being tossed one inevitably thinks of that other frontier, of rock and eternal snow – the long base of the Indian triangle, 2,000 miles away – and of the 1,138,814 square miles and almost 600 million people in-between. And then one marvels at the durability, elusiveness and strange beauty of that mixture of rank superstition and refined metaphysics which unites the shepherds of the snow-bound Himalayan valleys to the fishermen of the sun-flayed Coromandel Coast.
Rachel had a blissful time making castles in a sandy cove just west of the bathing-pool, but to avoid a popular public latrine we had to keep well below the high-water mark. The sand around Cape Comorin is famous throughout India and pilgrims buy tiny bags of it to take home. It is not simply golden, but – in patches – pure white, rose pink, pale yellow, charcoal grey and dark red. Scientists describe these sands as monazite and ilmenite: Hindus say they represent the various dishes once served here at a wedding of the gods.
Throughout the afternoon I repeatedly plunged back into the bathing-pool since in my estimation the entertainment value of sand is not great, however variegated its hues; and I appreciated the pilgrims not objecting to a _mleccha_ using their sacred pool blatantly for fun. In fact no Indian was using it today, because of the storm; instead they were ritually ducking themselves off Rachel's bit of sandy beach. Everyone was welcoming, though to decent Hindus a woman in a bathing-suit is a most shocking sight. Hindu women always enter the water fully dressed and when they emerge, with their thin saris clinging to their bodies, they reveal a great deal more than I do in my black, ultra-decorous, Edwardian-style costume. Most of today's pilgrims seem to belong to the well-off elite and this evening I have spoken to people from Bombay, Ludhiana, Delhi, Lucknow, Calcutta and Madras. All but the Madrassis have to use English as their only possible means of communication with the Tamil or Malayalam-speaking locals; there is considerably more resemblance between Hindi and Irish than between Hindi and Tamil.
Traditionally sunrise and sunset are the most solemn moments at Cape Comorin, as the sun may be seen rising out of one ocean and sinking into another. Therefore at six o'clock we joined the small crowd who had gathered on a huge, smooth black rock against which great green rollers were hurling themselves, sending up curtains of spray thirty feet high. Because of cloud nobody actually saw the sun setting, but the whole western sky became a glory of fast-changing colours – lovelier than it could possibly have been if cloudless. This, however, was no consolation to those for whom it is important to witness the sun touching and being quenched by the ocean.
Having supped in a tiny vegetarian restaurant we stepped out into the darkness and saw, on the east shore of the Cape, a vision seemingly from fairyland. For a moment I was dazzled into incomprehension by the bewildering beauty of the spectacle; then I realised that thousands of brilliant, multi-coloured electric bulbs were outlining the pseudo-Gothic Catholic cathedral against the blackness of the sea. The Indians are very good at this sort of thing and Rachel became quite breathless with excitement. We decided to find our way back to the hotel by the cathedral and went stumbling over piles of excrement, on a pitch-dark _maidan_ , before finding a narrow street thronged with excited, jostling, shouting Christians – and their low-caste Hindu neighbours – on the way to the evening's festivities.
Inside the church hundreds of pilgrims, their faces aglow with love, were queuing to touch the feet of a gaudy statue of Our Lady of Mount Carmel, whose feast-day this is. They kissed their finger-tips when they had laid them on the worn plaster feet, and then they touched the feet again and, placing both hands on the tops of their heads, bowed low and retreated backwards from the Virgin's 'presence'. Some had tears trickling down their cheeks as they frantically invoked the statue's help; others laughed joyously as they stroked the toes or caressed the robes of their beloved. These people are amongst the poorest of India's poor, descended from the _sudras_ and untouchables baptised by Portuguese missionaries over four hundred years ago, and it is plain that they have close personal relationships with their favourite statues – relationships of which some theologians might not approve. But what matter? If the Divine is everywhere it is in chunks of plaster and good luck to those who can find it there.
The general scene within that vast, unfurnished church reminded me of a typical Indian railway-station platform between trains. Many pilgrims were lying asleep on the cool stone floor, their cotton wraps covering their heads; many others were squatting about in family groups, eating meagre suppers out of banana leaves, and some were just sitting cross-legged, staring into space. Our arrival electrified the majority and as usual Rachel was seized and cuddled and tickled and pinched and the pretence of kidnapping her enacted. This is the commonest Indian game with a small child and though Rachel knows it to be a joke she still finds it slightly alarming; obviously the mere thought of being separated from mamma in a foreign land is classic material for five-year-old nightmares. This evening she kept a stiff upper lip but I could see her peering anxiously at me from amidst a tangle of dark arms and legs and faces, lit by white teeth and flashing, laughing eyes. Indians can be quite rough in their play and sometimes she emerges from this sort of fracas with slight scratches or bruises. During the past few days I have noticed her becoming increasingly irritated by the Indians' obsessive compulsion to handle her – which is an understandable reaction on her part, but I have explained she must try not to hurt their feelings. I suppose her colour fascinates them. By now she is as brown all over as a Punjabi, but that still leaves her a good deal lighter than most South Indians.
## DECEMBER 17TH. TIRUNELVELI
Because of Rachel having been up so late last night we just missed the 6.06 sunrise and got to the bathing-pool as the pilgrims were performing their important morning _pujas_. Against the sombre background – a grape-dark sky, black rocks and a jade ocean – brilliant saris were fluttering like so many silken banners in the gale: or 'cyclone', as they melodramatically call it here. The oceans were churning around the Cape as though being stirred by a thousand giants and a group of pilgrims, having decided discretion is the better part of devotion, were simply pouring water over their heads from brass jars; so again I was alone in the pool. To east and south the sky had become a solid-seeming mass of dark purple and above me I could see towering, bottle-green breakers rushing towards the smooth, glistening rocks to send giant columns of pure white spray leaping into the sky. It is years since I have enjoyed a swim so much; but these clouds were not there for nothing and at nine-fifty the storm broke.
Within seconds everything and everyone in sight had been saturated so I simply put my shirt and shorts over my bathing togs and left Rachel as the good Lord made her. Yesterday's experience taught me that here it is futile to attempt to dress modestly. There are lots of corners, and relatively few people, yet a crowd of men, women and children pursues one to the farthest corner of all and stands staring, with pathological insensitivity, while one attempts, if one is fool enough, to cover one's nakedness. Last evening, being without a towel, I made no such attempt and the sight of my bare bottom provoked cyclones of laughter. It is nice to be able to cause so much innocent amusement by the use of the most basic raw material.
We got a tourists' luxury coach to Tirunelveli (spelt Tinnevelly in British days), where I hoped to find an accumulation of mail from home. This coach cost almost twice as much as our usual peasants' bus but was by no means twice as comfortable. Before we started, a richly dressed lady in the front row (the purdah quarter) raised hell when the conductor tried, most politely, to persuade her to tolerate an equally richly dressed gentleman in the adjacent seat. The conductor then tried to persuade Rachel to sit beside the lady, so that the gentleman could sit beside me. But on the basis of the lady's strident rejection of the gentleman Rachel had already deduced she was not nice to know and refused even to contemplate sitting beside her. So I moved, and Rachel beamed delightedly to find herself with a male companion instead of boring old Ma. The gentleman proved to be a Professor of Sanskrit from Benares University who entertained her with innumerable Rama stories told in immaculate English. But I could discover nothing about the lady, who was plainly appalled to find herself beside a filthy foreigner and resolutely pretended I didn't exist.
In South India one notices many young couples of all castes separating on buses or in restaurants and affecting not to be acquainted until the journey or meal is over. No wonder Indians are so deeply shocked by hippies kissing and petting in public.
Yesterday, coming from Trivandrum, we passed the end of the Western Ghats – extraordinary hills of dark rock, scattered with patches of earth and scrub. They rise sheer from a level plain, creating a most dramatic effect, and the narrow valleys that run between them made my feet itch. We passed them again today, as our road returned to a little junction town some ten miles north of the Cape, and then forked right to run along their eastern flanks. They are superb, rough, chunky mountains, with an atmosphere about them that is still tantalising my wanderlust. If Rachel were a little older we would be sleeping up one of those valleys tonight.
Perhaps, however, it is just as well that we are not doing any such thing, for soon after we left Cape Comorin the heavens opened again, in true monsoon style. Visibility was immediately reduced to thirty or forty yards and the flat land on either side of the road became flooded, as we gazed at it, to a depth of two feet – the water perceptibly creeping up the trunks of the immensely tall palmyra palms. Our bus, despite its exalted status, leaked like a sieve. As water went sloshing around the floor everyone took their bits and pieces on to their laps and several passengers who were sitting under roof-leaks raised umbrellas, to Rachel's huge amusement. The richly dressed lady and myself were sharing a leak but she made sure her most superior umbrella would not become polluted by giving shelter to the _mleccha_. As the drops splashed down my neck the bus trundled hesitantly on through an unnatural twilight, with sheets of water spraying out from the wheels. Then suddenly, half an hour before we got here, the rain stopped, the sun shone and excremental odours arose so strongly from the countryside that one almost expected to see them.
Tirunelveli felt very humid and its streets were mini-lakes. When I asked the way to the post office of an amiable-looking man – tall, slim and dark – he offered to guide us and introduced himself as Mr Luke, a Christian. According to him this is the most Christianised district in India, with a CMS that was established in 1820 and an Anglican Diocese founded in 1896. But I wonder if he is right; the 1971 Census says there are almost four and a half million Christians in Kerala and only about half that number in Tamil Nadu. However, it may be that most Tamil Christians are concentrated in this area.
Mr Luke made consoling noises when the postmaster explained that no airmail has been coming in from Europe recently, because of a strike, and advised me to call back next week. It seems worthwhile remaining within reach of Tirunelveli until Christmas Eve, if necessary, since Rachel is expecting all her birthday _and_ Christmas cards. But we cannot remain beyond the 24th as she has long since been promised a Christmas visit to Periyar Game Park in lieu of the hectic seasonal excitements she is missing. Actually this delay could have happened in a much worse place; Tirunelveli was put on our itinerary because Ernest Joseph, an old Indian friend of mine, now lives some thirty-five miles away in a village called Ittamozhi.
Amongst the pile of Indian mail awaiting me was a letter from Ernest in which he gave the address of a friend, Mr Mathew, with whom we were to stay the night before catching the morning bus to Ittamozhi. I read this letter in the ironmongery-cum-printing works of Mr Luke, where we had been invited for coffee, and it only slightly surprised me to find that Mr Luke knows both Ernest and Mr Mathew quite well. This sort of thing is always happening in India, despite those teeming millions.
We are now installed in Mr Mathew's home, a decrepit little bungalow on the outskirts of the city. I have never before stayed with an Indian Christian family and it is a most interesting experience; no one would suspect this household of not being Hindu but for the fact that on the walls biblical texts replace oleographs of the gods. Most of the attitudes, routines, prejudices and customs are indistinguishable from those of middle-class, conservative Hindus. Even beef-eating is frowned on, ostensibly because one cannot buy wholesome beef locally. (Possibly this is true, but I get the impression some good excuse would be found for not eating even the best Irish beef.)
At sunset the rain started again and ever since has been coming down in torrents. The roof leaks so badly it is impossible in this tiny parlour to find dry spots for our flea-bags and Rachel's is already sodden, though she continues to sleep peacefully. As the latrine and bathroom are in the garden I got soaked through when nature called me out just now. Most Indian white-collar-workers live in what seem to us slum conditions and amongst this large section of the population there must be a painful degree of frustration: perhaps more than amongst the millions who have less to eat but no ambitions and no special abilities.
There are two children in this family, a nineteen-year-old son and a seventeen-year-old daughter. The boy is in his second year at Madras University and was picked last week for Tamil Nadu's State hockey team. He is bitter because the frequent university strikes seriously hinder his work. At present the Madras students are striking to have Tamil Nadu's Chief Minister dismissed and, while it may well be that the gentleman in question deserves dismissal, it does seem absurd to have students involved in politics to this extent.
In the past month I have talked to several so-called graduates who could not possibly pass the eleven-plus in Britain. (Probably I couldn't, either, but we won't go into that.) Many Indian graduates simply bribe their way through and others get by because professors do not wish their own ineptitude to be underlined by a high percentage of failures. The son of this house admits that when he graduates he will almost certainly have to take up some menial job totally unconnected with his studies. I can only suppose the Indian's paranoid determination to acquire worthless degrees is some sort of spin-off from thousands of years of Brahmanical idealisation of learning: a most commendable notion, but unfortunately India has a flair for so radically distorting commendable notions that they breed serious social problems.
I hardly saw the daughter of the house, who is studying hard for her university entrance examination. Her brother told me she will never be allowed to mix with the male students and soon after graduating will be married to the young man of her parents' choice. When I asked what would happen if he himself wished to marry a girl not of his parents' choice he found it difficult even to imagine this situation. After a moment's silence he shrugged and said it would be impossible to do such a thing 'because my mother would cry and put pressure on me until I gave in, and for me the most important thing is not to upset her'. A typical Hindu answer from a Christian boy; what Indian women lose on the wifely swings they gain on the motherly roundabouts. Even when they appear to be demure, timid, characterless or positively down-trodden, their influence within the home is tremendously strong.
Yet the convention of deference to the male has to be carefully preserved and this evening no one ate until Father came home from work at eight-thirty – two hours late because of flooding on the streets. Then, to my embarrassment, I alone was fed in the tiny bedsitter in which we had been talking, while the family – plus three visiting relatives who had called to meet me – hovered around urging the guest to eat more and more of this and that. Very good it was, too: a typical South Indian meal of rice, dahl, hot vegetable curry, curried fried sardines, omelette, plantain and excellent Coorg coffee.
I suspect the Mathew family treated us as VIPs because we had been introduced by Ernest Joseph. Ernest is a distinctively Indian phenomenon, although brought up in Burma and educated at an English public school. Born of a South Indian Christian father and a Rajput mother famed for her beauty (an elopement, surely, since such a marriage would never be arranged, or even condoned), he has evolved a personal religious synthesis which seems to suit him admirably. His father – a teak millionaire – went bankrupt when Ernest was a young man; there were complicated political overtones and the case caused something of a furore. By then Ernest had already established himself as a painter of widely recognised talent whose pictures give many people an uncanny feeling. To me they seem like messages from another world, rather than human creations, and I am not sure that I could live with them.
Ernest is a bachelor in his early sixties. When I first met him he had long since decided it would be immoral to use his artistic gifts to make money and was living in a one-room shack in a Delhi slum without visible means of support. I myself feel he is wrong not to accept gracefully and use honestly the gift with which providence has endowed him, but that does not lessen my admiration for the steadfastness with which he upholds his curious principles. He is a truly patriotic Indian – of whom there are not a vast number – and his refusal to paint for profit may well be an illogical emotional reaction to the gigantic cesspool of Indian corruption. Also, of course, he is an eccentric of the first order. Every day he shaves his head, he habitually wears a monocle (and in hot weather very little else), he believes firmly in telepathy, astrology, palmistry and graphology and under no circumstances will he speak to anybody about anything on Saturdays – 'my day of silence'. As I have said, he is distinctively Indian.
## DECEMBER 18TH. TISAIYANVILAI
At ten o'clock this morning the rain at last stopped and the sun came out as we got on the Ittamozhi bus; there was a strong breeze, instead of yesterday's sticky heat, and water lay refreshingly in sheets all over the level countryside.
The battered bus took us back some fifteen miles along the main road to Cape Comorin, before turning left for the east coast. It was full of peasants with flattish noses, thickish lips, remarkably low foreheads and near-ebony skins. Compared with Kerala, this coastal corner of Tamil Nadu seems to have dourer people, duller scenery and bonier cattle. Hundreds and thousands of palmyra palms grow tall and straight from pastures where the grass is a quarter of an inch high, and patches of thorny scrub support countless goats. The large cattle herds are devoutly decorated with bells and ribbons, and have coloured ropes wound around their carefully painted horns, but they look in miserable condition, as do many of the humans. This has always been one of the poorest areas of South India, scourged by almost intolerable heat for ten months of the year and inhabited mainly by primitive pearl-fishers, toddy-tappers, jaggery-makers and deep-sea fishermen, to whose ancestors St Francis Xavier devoted the best years of his life. Judging by the few villages and people to be seen, it is not overpopulated; and yet I suppose it _is_ , in relation to what its thin, grey, desiccated soil can produce. We saw only occasional small patches of paddy and it was hard to believe that Tamil Nadu now produces more rice from one hectare than any other rice-growing state and expects soon to have a surplus for export.
It often happens in India that the poorer a region the more jewellery is displayed and on our bus were several women plainly suffering from chronic malnutrition but literally weighed down by their gold ornaments. Rachel was fascinated to see the elaborate tattooing on their necks and arms and the saucer-like earrings that hung from their misshapen ears. But then, true to form, she began to fret lest that weight depending from the ears might be causing – or have caused – some pain.
As we approached Ittamozhi lakes of brown floodwater could be seen reflecting the deep blue sky. To reach Ernest's hovel, half a mile from the village, we had to wade and slither through deep pools and sticky mud – an 'adventure' enormously to the liking of my daughter. The hovel was built by Ernest's father as a medical dispensary for the local Harijans but it is many years since any doctor has been willing to work for such people in such a place. Recently, during Ernest's absence, the structure was much depleted by vandals and previously it had lain empty for many years, being adversely affected by wind and weather, so it may not unfairly be described as an uninhabitable ruin.
Ernest nevertheless finds it quite comfortable, though in view of Rachel's age and – compared with her mother – fragility, he has decided we are to spend our nights with friends of his at this little town of Tisaiyanvilai, five miles west of Ittamozhi. (Incidentally, Ittamozhi is pronounced 'Ittamolly', for some reason best known to the Tamils.) Rachel did not at all approve of this arrangement, having fallen in love with Ernest at first sight. But when he invited her to spend the day painting with him tomorrow, while I explore St Francis Xavier's village of Manapad, she was Ittamollified. (It was Ernest who said that – not me.) Small children seem to have a special affinity with a certain type of unselfconscious eccentric, and with people who are in any way psychic, or genuinely detached from the things of this world. Today, seeing Ernest and Rachel together, I knew that on some plane inaccessible to me they had at once established an exceptionally close relationship. Oddly, they seem to complement each other.
In twenty-five years I am only the second non-related guest to have stayed a night with this Hindu family. Ernest of course is the other, and it is a mark of the family's regard for him that his two wandering _mleccha_ friends have been admitted to such an exclusive home. The household consists of a retired doctor and his wife, their eldest son – now the local GP – his wife and four shy children, and his equally shy unmarried sister who is his partner in the practice. The large, handsome house was designed by the old man and built only a few years ago on the outskirts of the town. We are in the spacious, never-used-before guest-room, which has been hastily but most adequately furnished for our benefit with two camp-beds and a table and chair. The unglazed, heavily barred windows have splendid teak shutters and the door leads on to a wide roof from which one looks into the sunset over the neat yard with its cattle shed, or into the sunrise across a flat grey-green landscape broken only by straggling lines of palms. It would be impossible to exaggerate the warmth of our welcome here and the anxiety of the whole family to make us happy and comfortable, so I hope not to be misunderstood when I say that this evening I am very aware of having been thrown into the Hindu pool at the deep end.
## DECEMBER 19TH. TISAIYANVILAI
Today a septic mosquito bite on my right ankle immobilised me, but I must be thankful it came to fruition within reach of a good doctor.
I spent most of this cloudy, breezy day sitting out on the terrace roof with my foot up, savouring the quiet of my daughterless state and reading _A History of South India_ by Nilakanta Sastri (OUP). This is probably the best book there is on the subject but it makes no concessions to human weakness and read at home would seem tough going. Read in South India, however, it becomes positively entertaining. I find it a good policy to tackle such tomes while travelling through the country concerned.
Rachel returned at four o'clock, a vision of glory in a Madrassi little girl's costume of ankle-length full skirt and low-cut bodice with short puff sleeves; most attractive, if not very practical for our sort of travelling. She herself had chosen the flowered cotton materials in Ittamozhi bazaar, and then the village tailor's eleven-year-old apprentice had most expertly made it up. The total cost of the outfit was Rs.4.
To test my foot, I accompanied Ernest and Rachel to Tisaiyanvilai's bazaar, to buy new sandals, and nowhere else has our advent caused such a sensation. Within moments of our stopping at a shoe-stall I was astonished to see the whole main street become a seething mass of shouting men and boys, pushing and shoving to get closer to us. So fascinated was the populace that the Tirunelveli bus simply had to stop, its strident blaring having been ignored. This over-excited throng was of course entirely good-humoured, but the atmosphere it generated had a perceptibly primitive quality and I found myself wondering how it would behave should something occur to change its mood. I suppose our entertainment-value may be seen partly as a measure of the total monotony of village life and partly as an indication of how few foreigners visit South India. One thinks of India as being an important World Tours attraction but its tourist centres are mere dots on the vastness of the subcontinent and anyway are mainly in the north.
Having failed to find any sandals to fit we went to have tea with Christian friends of Ernest who own the local rice-mill. There are several children in this family so Rachel at once disappeared and as we adults nibbled delicious home-made tidbits, while talking about inflation in relation to wedding ceremonies, it again struck me that the _mleccha_ feels not one degree closer to the Indian Christian than to the Hindu. Almost, indeed, one feels further away, since certain aspects of Hindu-impregnated Christianity seem even less comprehensible than Hinduism itself to outsiders with a Christian background.
Within the past twenty-four hours I have developed a real affection and respect for our host family, despite the formidable and, I fear, insurmountable barriers that divide us. I now feel at home in this household to an extent I would not have believed possible last evening and I long to be able to define the dividing barriers, though I cannot hope to overcome them. They have nothing to do with provincialism, as we understand the term, since the absence of such narrowness is one of the chief distinguishing marks of educated Hindus, however physically circumscribed their lives may be. Perhaps I am especially sensitive to barriers in this family because it is – if one can to any extent compare the two civilisations – almost exactly on my own social, intellectual and material level. Therefore where we do diverge, on what can only be called the spiritual level, our divergence is very evident. It leaves us mutually invisible on opposite sides of that wide chasm which for many foreigners, including myself, is amongst India's main attractions. One suspects that if one could only _see_ to the other side – it would be nonsense to think in terms of _getting_ there – one might be a lot better off for the experience.
No one could describe the witty and forceful women of this family as docile or down-trodden, yet they adhere strictly to the immemorial Hindu formalities governing the social behaviour of their sex. While Rachel and I eat with the two men, in the dim, cool dining-room beside the kitchen, the two wives stand by the connecting door, poised to replenish our stainless steel platters whenever necessary, joining animatedly in our conversation and affectionately exchanging jokes with their husbands. By now I should be quite accustomed to this business of being treated as an 'honorary male' – it happens in many non-European countries – yet I still find it slightly disconcerting in households where one is surrounded by mod cons and educated conversation. In a muddled sort of way I feel guilty and ill-mannered about being waited on by the old lady – who is very much a _grande dame_ – and the repression of my urge to leap up to relieve her of some heavy dish becomes quite a strain. Neither she nor her daughter-in-law ever at any time sits in the presence of their menfolk – this evening they stood conversing happily for an hour and a half – and they eat (in the kitchen) only when the men have finished. The young doctor works very long hours among the poor, for minimal or no fees, and, being deeply religious, will not dine until he has locked up the dispensary, bathed to purify himself after the inevitable polluting contacts of his professional life and gone to the nearby temple to pray. Therefore his wife and mother must often wait until nine or ten o'clock for their evening meal; but presumably such restrictions do not matter to most Indian women, who surely could not appear so serene and relaxed if full of hidden resentment. Incidentally, none of the several servants employed about the place ever appears in the kitchen or dining-room, so I conclude they are of too low a caste to be allowed near the family's food.
In the morning we are going to the little coastal town of Tiruchendur, some thirty-five miles away, to see a famous seashore temple dedicated to Subrahmanya, the god of war. We plan to stay overnight in the pilgrims' hostel run by the temple trustees and to return here next day. A leaflet issued by the Board of Trustees reports that the temple also runs 'a free Siddha dispensary for the benefit of the worshipping public' and 'an Orphanage with 67 Orphans'. It owns four hundred and forty-four acres of wet land, eight hundred and fifty-five acres of dry land and approximately Rs.25,000,000 worth of gold, silver and jewels.
CHAPTER TEN
# _On the Coast of Coromandel_
## DECEMBER 20TH. TIRUCHENDUR
Not being blessed with either a good ear or a good memory, I am sorely tried by many South Indian names. But one must look on the bright side. Things could be worse. For instance, until the sixteenth-century Tiruchendur was known as Tirubhuvanamadhevi Chandurvedhimangalam.
The landscape en route from Tisaiyanvilai was flat and harsh; gaunt palmyras stood erect in their thousands everywhere and the dusty grey plain was varied only by acres of thorny scrub, hedges of prickly cactus and occasional fields of plantains at all stages of development. (I am told the banana plant is not a tree but a vegetable which in six months grows from scratch to its full height of eighteen or twenty feet.)
We first saw Tiruchendur's nine-storey temple from many miles away, over the plain, and by ten-thirty we had booked into the hostel (Rs.2 for a single room) and been told that non-Hindus are permitted to enter the temple only between three and eight p.m. 'Fair enough', I thought; I have always deprecated hoards of camera-clicking tourists swarming through churches during services. Then, after paying our respects to the two sacred temple elephants – an adult and an adolescent – who are elaborately stabled in the precincts, we went to swim off the long, smooth, curving beach.
At one-thirty we made our way to the centre of the town through a mile-long arcaded bazaar that begins in the temple courtyard and is lined with ancient statues of the gods, their stone features blunted by the affectionate caresses of generations of devotees. Tea-shops are interspersed with stalls displaying a scatter of cheap trinkets or a few bunches of plantains and a small tray of fly-blown tidbits, and religious oleographs, framed and unframed, lie on the ground beside shop-soiled bales of cotton 'going cheap'. According to the temple trustees Tiruchendur means 'a sacred and prosperous town of Victory' but nowadays one gets no impression of material prosperity. However, the atmosphere is friendly and the citizens seem in no way predatory, possibly because 99 per cent of Tiruchendur's visitors are very poor.
It was difficult to get tea as milk is scarce and Indians refuse to credit the possibility of milkless tea. Eventually we found a cavernous eating-house beneath the arcade where a milk delivery was expected within moments, so we sat down to wait. (This lust for tea was caused by my having forgotten to bring our water-pills from Tisaiyanvilai.) The eating-house seemed without any stock of food and, as he waited for something to occupy him, the slim, barefooted serving-boy went to stand before a wall-niche containing a statue of Ganesh and prayed fervently.
'Indians pray a lot,' observed Rachel. 'Why do they pray more than we do?' To which I replied, rather ambiguously, 'They are at a different stage of development.'
Happily a water-carrier rescued me by stopping his cart beside us at this moment, to deliver the day's supply from the well, and Rachel immediately wanted to know why there was gold paint on the horns of the enormous pure white humped bullock. I explained (if it can be called an explanation) that pure white bullocks are very sacred and therefore merit gold paint, rather than the red or blue or yellow seen on the horns of lesser cattle. Then the milkman arrived, carrying on his head a little brass churn containing a gallon of no doubt heavily watered milk. As this was being boiled in a large copper cauldron over a wood fire we watched the bullock being unharnessed, tied to a pillar of the arcade, stroked reverently on the neck and given a bundle of paddy-straw. Next the water-carrier – a seemingly frail old man – emptied the gigantic wooden barrel on his cart by repeatedly filling a brass jar and carrying it on his head to a row of rusty tar barrels in a corner of the eating-house. And so life goes on, much as it did 2,000 or 3,000 years ago.
At present a most regrettable concrete extension is being added to Tiruchendur's temple but, though materials have changed for the worse since the temple was first built, methods of construction have remained virtually unchanged. On our way back to the beach we saw nine small sweating men, one hundred and fifty feet above our heads, hauling up a huge concrete roof slab which had been roped by four men on the ground. Three giant bamboo poles leaning against the wall provided support for the slab on its way up and, as a product of the Crane Culture, Rachel was fascinated by this display of muscular Hinduism. Indian physiques are often misleading, especially in the South, where apparent fragility can conceal the strength of an ox. Yet the effects of a vegetarian diet show in the lack of stamina, which is said to be one reason why so few South Indian hockey players are picked for the national team, despite their renowned speed and skill. (Another reason, according to our hockey-playing friend in Tirunelveli, is the deep-rooted anti-South prejudice of North Indians.)
The temple trustees' leaflet, mentioned above, is a good example of the Hindus' attitude – or perhaps one should say 'non-attitude' – to history. It is intended to be factual and informative and in Europe a comparable bit of bumph would concentrate on giving precise dates. But in India we are cheerfully told, 'The date of the temple is hidden in the Puranic past. The nucleus of the structure however has been here for more than 2,000 years as the Tamil classics refer to.' And again, 'The Gopura is said to have been constructed about 100 years ago by Desikamurthi Swami, an Odukkath-Thambiran of the then Maha-Sannithanam of Tiruvavadutharai mutt.' And also, 'Kavirayar belonged to the Mukkhani comunity [ _sic_ ] and lived perhaps in the eighteenth century.'
A people's concept of time lies at the root of their whole philosophy and much incomprehension of India is probably related to the antithetical notions of time held by Hindus and Westerners. We see time as a conveyor-belt, eternally carrying the present moment out of sight for ever. But the Indian sees it as a wheel, eternally revolving, and can believe he will at some stage, in some reincarnation, return to the present moment. For him time is divided into ages ( _yugas_ ) which perpetually recur in cycles. So nothing is new and nothing is old and even Hindus of high intelligence, with trained minds, find it possible to believe that 2,000 years ago their ancestors invented aeroplanes which in due course – as that _yuga_ declined – ceased to be used.
Since Herodotus, creative minds in the West have been taking an interest in history. But naturally no such interest arose in India, where the most respected human being is the _jivanmukta_ – the man who, having freed himself from Time, can perceive the nature of ultimate Reality. Hinduism positively encourages a man to forget his historical situation rather than to look to it, as we do, for guidance in the present, a deeper understanding of human society and some increase in self-knowledge. And of course this attitude is closely linked with what outsiders see as Indian passivity and fatalism. If ages _recur_ , instead of _passing_ , one obviously only has to wait long enough and the Golden Age will come again; an improvement in social conditions has nothing to do with the efforts of individuals or generations to better the age in which they happen to find themselves.
On the beach this morning I talked to a very articulate young man – a Tamil farmer's son now studying medicine at Madras University – who told me his father has for some years been using the new rice seed, of Green Revolution fame, but has just decided to give it up because it needs too much expensive fertiliser. This snag had been interpreted by both father and son as a sign that, despite the starving millions, India's rice crop _should not_ be increased at present. To try to swim against the cosmic current of this _yuga_ – to try to outwit Destiny – was _avidya_ (ignorance), which might be described as the only form of sin recognised by Hindu ethics. This conversation did nothing to change my long-held opinion that FAO are well and truly up against it in India – especially South India.
On our way up to the temple at three-thirty we were joined by a brisk, elderly little man, covered in _puja_ after-effects of ash and coloured powder, who insisted on talking to us volubly in Tamil – which did no one any good that I could see. Tamil is the oldest surviving Dravidian language and has, I am told, a wonderful literature. It is, however, prodigiously difficult. Usually even I can master 'Please' and 'Thank you', or words to that effect, but by Tamil I am totally defeated.
At the temple entrance a notice said 'Admission Rs.1 only' and here our companion held out his hand and indicated that he would get our ticket. At the time I believed he was being disinterestedly helpful and we followed him to the gateway to the Inner Sanctum, where two rough-spoken temple guards in khaki uniforms abusively objected to my entering. They thought I was a man (I was wearing grey slacks and a shapeless grey bush-shirt), and men are allowed in only if stripped to the waist. Our guide quickly signed that they must be given a rupee each, at which point I would have begun to argue had not Rachel's tight grip on my hand told me she was terrified of the guards' aggressiveness. So to spare her I paid up.
Then began a whirlwind tour around many brilliantly lamp-lit shrines through scores of worshippers. It is no exaggeration to say that I have never in my life felt so embarrassed; and I have rarely felt so angry. I had wanted simply to pay my rupee and quietly go wherever _mlecchas_ are allowed, leisurely observing all I could. Instead, I was rushed around the entire temple, to the understandable fury of orthodox worshippers, and given no time to observe anything. And when we emerged – both striped on our faces and arms with all sorts of ash and powder – I was less Rs.12 and in that sort of choking bad temper caused by the realisation that one has been taken for a ride.
This was the best-organised exercise in co-operative conmanship I have ever encountered. As our guide took us to various forbidden places the guards or priests (or both) simulated anger and outrage, and the guide then quickly indicated that only by donating another rupee could I appease their alarming (to Rachel) wrath and make amends for having intruded. My puzzled readers may wonder why I did not simply turn around and walk out, but this temple is so vast and complex that we were soon lost and I had no wish to start a riot by inadvertently stumbling into some Holy of Holies. (Remember how the Mutiny was sparked off!) What most upset me was that so many genuinely devout people were distressed by our involuntary gate-crashing and must have been scandalised to see _mlecchas_ going through the sacred rituals as – apparently – a tourist stunt. And the intrinsic beauty of those rituals heightened my frustration. If only we had been able to move around slowly, and as unobtrusively as possible, this could have been a wonderful experience.
Outside the temple our guide confidently demanded another Rs.10, as his personal fee. When given a few unprintable home truths instead he became speechless with rage and stood wordlessly opening and shutting his mouth, making funny wheezy noises like a toy steam engine. Then he followed us, at a little distance, up the beach; so I asked Rachel to sit guard over my clothes and money while I swam far beyond the surf to work off my ill-temper.
As I swam I thought how right St Francis Xavier had been when he wrote to his colleagues in Rome, after an encounter with the Brahman priests of this very same Tiruchendur Temple:
There is a class of men out here called _Bragmanes_. They are the mainstay of heathenism, and have charge of the temples devoted to the idols... They do not know what it is to tell the truth but for ever plot how to lie subtly and deceive their poor ignorant followers... They have little learning, but abundance of iniquity and malice.
Not that St Francis could afford to be too critical; he himself was hopelessly ignorant on the subject of Hinduism and chose always to remain so. He seems never even to have heard of such basic concepts as _karma, yoga, bhakti_ and _maya_ and his years on the subcontinent were devoted to loving the poor and lambasting idolatry. Yet even in his own century several distinguished Roman Catholic theologians had agreed with John Capreolus that idolatry need not be as silly as it looks because 'God of His absolute power could assume the nature of a stone or other inanimate object, nor would it be more incongruous to say that God is a stone than to say that He is a man, because He is infinitely above both natures.' (The Revd Capreolus might have added, 'It would be no more incongruous to say that God is a stone than to say that He is a piece of bread.')
St Francis seems to have been in some ways singularly gullible for an ex-professor of the Sorbonne. This is his own description of an encounter he had in 1544 with 'more than two hundred _bragmanes_ ' in the pillared courtyard (unchanged to this day) of Tiruchendur's temple.
I delivered an exhortation on the subject of Heaven and Hell, and told them who go to the one place and who to the other. After the sermon, the _bragmanes_ all rose and embraced me warmly, saying that the God of the Christians was indeed the true God... God gave me arguments suitable to their capacity to prove clearly the immortality of the soul... One must avoid scholastic subtleties in reasoning with such simple folk... Still another of their questions to me was whether God was black or white... As all the people of this land are black and like the colour, they maintain that God too is black. Most of the idols are black. They anoint them constantly with oil and they stink abominably. They are also appallingly ugly. The _bragmanes_ seemed satisfied with my answers to all their questions...
Poor St Francis! Clearly these 'simple folk' had a marvellous time pulling his leg, and no doubt they went to their homes chuckling over the primitive reasoning of this simple wandering preacher... Not one of them, I need hardly say, became a Christian.
As we walked back to the bazaar, in quest of more tea, Rachel noticed that the young temple elephant was having his make-up put on. Blue and gold circles were being painted on his ears and trunk, and white stripes on his forehead, and then (big thrill!) he was caparisoned in red, blue and gold tasselled brocade – his Sunday Best, as it were. Next a thick silken rope with heavy brass bells on both ends was thrown over his back, he was given a small piece of wood to hold in his trunk and off he went towards the main temple entrance. 'Let's follow him!' said Rachel, almost stuttering with excitement – though a quarter of an hour earlier she had been complaining of acute dehydration. So we did.
On the way the proprietors of several little food-stalls came rushing out to present Babar – as I had somewhat irreverently named him – with bananas, buns or pastries. Before accepting these he had to hand (not quite the _mot juste_ , but never mind) the piece of wood to his attendant, which meant a check was kept on what he ate: and I noticed oranges were _verboten_. When he received coins he carefully handed them to his attendant and then laid his trunk on the donors' heads to bless them: so he, poor brute, has also been co-opted. I must say he is beautifully trained. On arriving at the main temple entrance, where he was directly opposite the image of Sri Subrahmanya in its central sanctum, he slowly knelt – giving an uncanny impression of reverence – then raised his trunk and solemnly trumpeted three times in greeting to the god. Being a sacred elephant his touch is greatly valued and Lakshmi-alone-knows what he earned during the next hour as he stood by the main entrance with his attendant squatting beside him. Many people presented him with food, which he delightedly popped into his mouth, but he had been trained to give his blessing only for cash. I handed him ten paise, to find out what an elephantine blessing feels like, and it is quite a pleasant sensation to have that sensitive tip of trunk laid gently on one's head.
The next excitement started just after sunset, as I was trying to prise Rachel away from Babar. On the edge of the beach, near the temple, was a big, ugly concrete shed with padlocked corrugated iron doors – and suddenly these swung open to reveal, astonishingly, a glittering golden chariot. To it was attached a pair of prancing, life-size silver horses and Rachel stood transfixed, obviously half-expecting the fairy tale to unfold and the horses to gallop out of the shed. An Indian crowd gathers incredibly quickly and moments later we were surrounded by most of the townspeople and hundreds of pilgrims. A small boy who spoke excellent English (he attends one of the last outposts of intelligible English in India – a convent school) told us the chariot-shrine was a new acquisition costing two lakhs (Rs.200,000), and that it was to be used this evening for the first time to carry the temple's most precious image of Sri Subrahmanya around the building three times in procession.
This elaborate example of the work of contemporary Madrassi goldsmiths proves that their art, at least, is not dying. In its every delicate detail Subrahmanya's new chariot is truly a thing of beauty and the countless tiny figures adorning it are not mere replicas of traditional images but have a life and vigour of their own. Unfortunately, however, technology has overtaken it, in the form of electricity. One doesn't actually see any bulbs, these having been so cleverly arranged that the whole mass of gold looks as though it were radiating its own light, but when the procession started four men had to push a clumsy, reeking generator behind the chariot. (I still have in my nostrils the warring smells of jasmine and generator fumes.)
It was a most memorable experience to watch the Lord Subrahmanya, wreathed in blossoms and enthroned in glory, moving slowly through the blackness of the night. The mile-long path around the temple is rough and in parts quite steep, so several torch-bearers held aloft blazing brands of oil-soaked wood. These gave off an incense-like aroma and both alarmed and thrilled Rachel by occasionally sending showers of sparks cascading into the crowd. Three bands of musicians accompanied the procession – but did not mingle with it, being Harijans – and all around us the fervent, uncoordinated chanting of various pilgrim groups added to the atmosphere of elated devotion.
I was particularly struck by the number of young pilgrims, most of whom were completely absorbed in their worship. Then, observing the whole scene, I felt a sudden conviction that India's civilisation will be the last in the world to capitulate to our sort of materialism. And I saw an analogy between the beauty of the golden chariot, locked away in that ugly concrete shed, and the worth of the Hindu tradition, guarded by a corrupt priesthood.
As the only foreigners present, we were not only permitted but encouraged to walk close to the chariot and when I tired of carrying Rachel piggyback (at ground level she could have seen nothing) there were many volunteers eager to take her over. From the broad shoulders of a Trivandrum engineer she beamed down at me, her face glowing in the golden light, and said, 'Isn't India fun?'
## DECEMBER 21ST. TISAIYANVILAI
Before catching our noon bus we spent a few hours in or near a Parava settlement about a mile down the beach from Tiruchendur's temple. The Paravas are a Coromandel Coast community of pearl-fishers whose ancestors were baptised _en masse_ between 1535 and 1537, a few years before St Francis came on the scene. For many previous centuries these gentle, primitive people had been bullied and exploited by both Hindus and Muslims, so they were impressed when an Indian Christian from Calicut argued that conversion would strengthen their position by gaining them the protection of the then powerful Portuguese. But as no available missionary could speak Tamil the original 'converts' received not even the most elementary instruction in their new faith and, despite St Francis's subsequent efforts (he was no great linguist himself), their descendants give the impression of being – shall we say – a unique sub-caste of Christianity.
Those whom we met today seemed not unlike their sixteenth-century ancestors, described by the Portuguese as a simple, humble, handsome race; they quickly made friends with Rachel but were rather shy of me. Their homes are cramped, palm-thatched huts built on the beach, well away from the edge of Tiruchendur, and they keep their antique catamarans – each sporting a pair of rough-hewn wooden horns on its prow – parked outside their front doors, as you might say. The evident ill-health of the little community was a surprise, where everybody must at least have enough fish to eat; but I suppose no unbalanced diet is healthy. This settlement is dominated by an incongruously large, once-white seventeenth-century church of obviously Portuguese provenance which has fallen into a serious state of disrepair. We found all the doors open and it seems to be in daily use, yet the interior was completely unfurnished and undecorated, apart from a few chipped, conventional plaster statues. About the whole settlement there was an unmistakable ghetto atmosphere, but I have been warned against generalising from this one example of how the Paravas live. Apparently many of their villages are lively and thriving, and their 'capital' – Manapad – is said to be an exceptionally prosperous and progressive little town with a fine, well-kept church.
As we left Tiruchendur my only regret was that I had seen nothing of Shanamukha, deliciously described in our trustees' leaflet as 'the Bhaktas Idol, the cynosure of all eyes and the Chief attraction of the commonality.'
The paradox inherent in Indian attitudes to animals is at present greatly exercising Rachel; how can a mainly vegetarian race be so callous about suffering animals? On the bus today she was very worried when she saw several pitifully bony cows whose horns had been tied to their legs, securing their heads in the grazing position so that they could not eat the young plantains. And she fretted too – quite unnecessarily – about the many goats we saw with long sticks attached horizontally to their collars to prevent them from breaking through fences of stakes.
To my mind, however, the treatment of small children and babies on pilgrimage beaches is far more disturbing. Both at Cape Comorin and Tiruchendur I saw many infants being carried into the rough sea, kicking and screaming with terror, and being dipped three times under the water, the parents pausing between dips to roar with laughter at the spectacle of their hysterically frightened offspring. Tonight those scenes are haunting me; there is something very disquieting about parents deriving amusement from the deliberate terrorising of small children. One hears a lot about the security enjoyed by the Indian young, who are breast-fed for years, and picked up whenever they cry (because crying is believed to weaken the whole constitution), and who spend so much time close to their mothers' bodies. But how real can this security be if one of the most basic functions of the maternal instinct – to protect a child from fear – remains inoperative? And if some mothers actually _inflict_ terror? And, most baffling of all, if they even _enjoy_ inflicting it? This behaviour is perhaps connected with the Indians' unawareness of themselves or other people as individuals – or it may be a symptom of acute frustration. Many young couples are still living in joint families, where they must unremittingly defer to their elders; and possibly those who resent this restriction find some release for their tension in bullying the only people with whom they can feel themselves to be independent adults, in control of a situation.
Or am I overreacting? Most Indians, after all, regard me as a monster of heartless cruelty because Rachel is normally left alone in a bedroom from 6.30 p.m. until 8.30 a.m., without my even once opening the door to make sure she is still alive. In this household, the three-and-a-half-year-old – who shrieks with terror every time she sees us – spends much of her day on mamma's hip and the rest of it on grandmamma's lap and all her night in mamma's arms. She is a tiny, dainty little thing, no bigger than Rachel was at two and always immaculately dressed.
When one considers how most Indian children are reared, it is not really surprising that in their company Rachel should sometimes speak and act as though brought up under the personal tuition of Lord Curzon. An alarming number of Indians have an unfortunate way of provoking the mildest Europeans to behave autocratically, and for this the blurred outlines of the average Indian personality are very likely to blame.
## DECEMBER 22ND. TISAIYANVILAI
This morning we went into Tirunelveli to mail-hunt unsuccessfully – but the postmaster is confident our letters will have come through by the 24th – and to do a little Christmas shopping, since Tisaiyanvilai's bazaar offers no toys or gift articles of any kind. Tirunelveli, being the market centre for a wide area, was jammed with people, and across the main shopping streets hung banners wishing everybody a Merry Xmas and a Happy New Year. Christmas is celebrated throughout this district much as Whitsun is throughout Britain, where little thought is given over that weekend to the Third Person of the Trinity.
Rachel is beoming increasingly critical of certain aspects of Indian life and today her comments on the treatment of Hindu women got us involved in the whole doctrine of re-birth. I explained that women are considered inferior because they would not have been born as women but for sins committed in a previous life, which means they deserve no better treatment than they get. Rachel didn't think much of this theory but conceded grudgingly, 'I suppose it _might_ be true.' Then, after a few moments' silence (an extremely rare occurrence in our joint lives), she exclaimed, 'Won't it be _interesting_ to be dead! Then we'll know everything. Would you like to be dead?'
'Not particularly,' I said. 'I'm quite happy with my mortal coil. And there's always the possibility that far from knowing _everything_ , we'll know nothing!' Which of course led me into still deeper waters, but these need not concern us here.
Another of Rachel's current grievances – particularly since a gob of phlegm landed on her bare shoulder the other morning – is the Indian habit of spitting in the street. This is the sort of thing I took for granted on previous visits to India but, as I have already mentioned, my daughter is much more fastidious than her Ma. And now I come to think of it, it _is_ a bit uncivilised at least not to look before you spit, if spit you must.
I used to assume vaguely that Indian spitting was simply a consequence of Hindus being inexplicably chesty and peculiarly devoid of any spark of Civic Spirit. Recently, however, I have discovered that the habit is closely linked with their pollution laws, which are complex beyond anything a simple Western mind could imagine. To us many of them seem outlandish, though others contain obvious elements of common sense. For one thing, all bodily discharges are regarded with extreme horror and fear; and saliva, phlegm and mucus, which are believed to be 'spoiled semen' (even today semen is popularly supposed to be stored in the head), are thought of as having an especially powerful polluting effect. Therefore the body must be cleared of these ghastly menaces at the first possible moment, and it doesn't matter a damn where the discharge lands or who else is polluted in the process.
## DECEMBER 23RD. TISAIYANVILAI
After breakfast we set off to walk the five miles to Ittamozhi. Having spent a week in this little corner of the extremity of India – one of the world's oldest inhabited areas – I now feel quite fond of it. At least during this season, it has a certain muted charm. Mid-December to mid-January is the one enjoyable month, weather-wise; by March nobody ever feels comfortable and by May even the locals regard it as hell on earth. But that was hard to imagine this morning, as we walked under a gay blue sky, strewn with a few high, white clouds, and relished a pleasantly hot sun tempered by a boisterous wind off the sea. After the recent rain the wayside was studded with tiny, brilliant wild flowers and butterflies zigzagged excitedly from blossom to blossom and the bird-life was so dazzling one almost doubted one's eyes. 'If there were monkeys here it would be perfect,' said Rachel. 'Why are there no monkeys?'
We followed a little road built under the personal supervision of Ernest's remarkable Rajput mother during the heyday of his family but which has fallen into such disrepair that few motor vehicles now use it. It must be fascinating here when the toddy-tappers are at work, shinning up and down all those palmyras every few hours to extract the sap for making jaggery. Much ploughing of the rain-softened paddy-fields is now going on and several men, wearing only ragged _lunghis_ and untidy turbans, were driving yokes of small, emaciated oxen along the road while carrying wooden ploughs on their heads: a measure both of the primitiveness of the ploughs and the strength of their neck-muscles. Turning to look back at one such man – young, neatly built, almost black-skinned – we found that he, too, had stopped to stare, and was standing using a hand to balance his plough while gazing at us not with curiosity, amusement or suspicion, but with an expression of the purest astonishment. For a moment we stood thus, on that wide, bright, silent landscape – Europeans of the twentieth century confronting an Indian of no century, a man whose life is contained in a mould that would be perfectly familiar to his pre-Aryan forebears. And then, wordlessly, we turned away from each other and moved in opposite directions.
Beyond a doubt one has to walk or cycle really to appreciate the flavour of a place. Bus journeys are all very well in their way, but they are not true _travelling_.
Between Tisaiyanvilai and Ittamozhi we counted five little churches or chapels of various Christian denominations and, this being Sunday, all of them were open. In an impoverished toddy-tappers' village most of the children were suffering from malnutrition and/or worms, and many had that rough, dead, brownish-red hair which amongst people naturally black-haired means severe vitamin-deficiency. But even here one of India's heroic malaria-eradication teams had sprayed and meticulously marked each wretched dwelling.
As we were approaching Ittamozhi we heard weird, rapid chanting and rhythmic handclapping coming from a well-built, palm-thatched house a little way off the road. There was no other building in sight and the chanting and clapping, accompanied by frenzied drum-beating and cymbal-clashing, created a hypnotic effect that seemed tribal African rather than Indian. Rachel and I were equally intrigued and decided to enter the compound through a little wooden gate in its high hedge of prickly pear. Then we sat on a rough-hewn chair placed, unexpectedly, just inside the gate, and went on listening in fascinated bewilderment until a young woman in a white ankle-length gown with long sleeves – which look very odd here – came hurrying down the road. She was carrying an armful of Christian prayer-books and I was irresistibly reminded of the White Rabbit as she hastened past us, her pace not slowing for an instant and her eyes fixed on the hut. However, her gestured invitation was quite clear and although her expression had told me that she suffered from some severe emotional disorder we followed her into the building – and none of the rapt congregation appeared to notice our alien presence.
The chapel measured some twenty-five feet by fifteen and neat strips of coconut matting were laid on the polished mud floor. A few biblical texts in Tamil hung on the walls and the only furniture was the preacher's desk, behind which stood a tall, heavily built Tamil of about forty, wearing the sort of simple vestment favoured by Low Church clergymen in all countries. When we entered he was leading the hymn-singing (if you can call it that) in a not too abnormal manner, but I soon realised that the congregation's odd lack of interest in our arrival had a slightly sinister explanation: all those present were in a trance of some sort, having been completely mesmerised by their clergyman.
It was not difficult to count heads. On the males' side were four men – one a hideously deformed idiot – and two youths: on the females' side were twenty-three women – the majority young, and all dressed in white – plus five school-girls and an assortment of sleeping (incredibly) infants. One of the men was beating the drum, one of the women was clashing the cymbals and everybody else was loudly clapping hands and singing while rocking to and fro on their heels. At first glance one might think the whole scene rather touching: simple folk expressing their devotion as best they knew how, and so on... But it soon became apparent that we were in on something very peculiar indeed.
At a given signal the tempo of the music, chanting, clapping and swaying quickened dramatically. Then, as it reached crescendo point, the preacher suddenly threw back his head, roared like a wounded tiger, thrust his clenched fists into the air and stood shaking them at the ceiling, and sweating and panting and heaving, and screaming in a voice that had become curiously shrill while his congregation went berserk.
Poor Rachel was so terrified by this Scene from Clerical Life (Tamil translation) that I had to take her in my arms. By now the women – shrieking like witches at a Sabbath – were gyrating cross-legged around the slippery floor, working themselves into a frenzy in which sexual excitement was unmistakably interwoven with religious hysteria. Meanwhile the 'clergyman' (by now I felt he had qualified for inverted commas) continued to scream, tremble, sweat and shake his clenched fists, never once taking his eyes off the ceiling. Several women now began to foam at the mouth and a few soon slumped into unconsciousness, overcome by the intensity of their emotion. I have twice witnessed Tibetan shamans going into trance, but that was merely uncanny. This morning's session had a nauseating aura and when two women leapt to their feet and began to loosen their robes I decided it was time to go, before Rachel witnessed something not suitable for five-year-olds.
When I asked Ernest to explain our experience he said we had attended the last half-hour of the regular two-hour Sunday morning service at the local chapel of the Pentecostal Church of Ceylon. I enquired if 'service' could be assumed to have a double meaning in this context, but he would not commit himself. It seems this sect is quite popular, chiefly amongst young women whose husbands belong to other Christian sects in the remoter regions of South India. The Pentecostals wear only white, eschew jewellery of every sort and condemn all fun and games except those involved in their weekly receiving of direct messages from the Holy Ghost, on the hot line described above. No doubt there is a link between the predominantly female attendance and the repression of Indian women. Whatever else may be said about this morning's service, it certainly took the lid off everybody's repressions.
Incidentally, Ernest has been enlightening me about the sexual morals of the local Harijans, Sudras and toddy-tapping Christians. Apparently pre-puberty intercourse is freely indulged in by both boys and girls, and tacitly condoned by their elders. But this means the girls have to be virtually imprisoned between the times of their reaching puberty and being married, since the majority do not revert with ease to chastity. The marriage age is often illegally low in this remote region, yet unmarried mothers do exist. However, contrary to the custom in higher castes they are treated leniently and 'a little error' – even of indeterminate paternity – is not considered a serious obstacle to matrimony.
This morning Rachel produced the Saying of the Week, if not of the Year. Having listened attentively but unprofitably to a breakfast-time discussion on the Bhakti movement in South India, she suddenly announced, during a lull in the conversation, 'I think I'm too young to understand Hinduism. Will you explain it again when I'm eight?'
CHAPTER ELEVEN
# _Fever in Madurai: Wildlife in Periyar_
## DECEMBER 30TH. MADURAI
The seven-day break in this diary is attributable to a nameless fever.
On Christmas Eve morning, when we left Tisaiyanvilai, I felt slightly peculiar but thought nothing of it – until suddenly, as we waited at Tirunelveli Junction for a train to Madurai, I became really ill. We were waiting for a train because we had just missed the bus; and we had missed the bus because we were waiting at the post office for a delivery of foreign mail that again failed to come; and, as a final complication, I had also missed the bank, which on that day closed at noon by way of celebrating Christmas.
This was the first time I have ever been literally penniless – our last paise had gone on the train tickets – and I found the experience interesting. It underlined the extent to which even the poorest of us depends on what little money we have as an essential prop to our personalities; and I began to see the begging type of hippy, who has voluntarily made a vow of poverty, from a new angle. Not for nothing do most religions regard poverty as a prerequisite for the perfection of sanctity.
Our train, marked EXPRESS in giant lettering up and down its sides, left Tirunelveli at four o'clock and took five-and-a-half hours to cover ninety-five miles. It was almost empty because the railwaymen had been on strike up to that morning and the general public had not yet realised the strike was over.
By the time we arrived here I was too feverish to articulate and Rachel also was sickening fast. However, in the Tirunelveli waiting-room we had met a kindly young Swiss couple – our first foreign fellow-travellers since leaving Goa – and by some means these guardian angels got us installed in Madurai's Travellers' Bungalow, just beyond the station yard. I dimly recollect stumbling across row after row of railway sleepers in pitch darkness under the noses of gigantic steam engines ( _c_. 1910) which hissed menacingly while Rachel vomited over my legs. Then I was on a bed and she was on a couch in a high-ceilinged room well furnished with rosewood pieces – and haunted by generations of ICS officers on tour to inspect their Empire.
I had heard our Swiss friends urging the pudgy, puzzled little caretaker to get us a doctor from somewhere without delay – the irony of it, hours after leaving a doctor's house! – but this man proved more than slightly obtuse and from ten p.m. on Christmas Eve to eleven a.m. on Stephen's Day no one even put a head around the door to see if we were still alive. Mercifully our gallon water-bottle had been almost full when we arrived and I suppose Rachel helped herself; she tells me she slept most of the time and never had a headache. Meanwhile I dosed myself with fistfuls of codeine which had no effect whatever on any of my symptoms. The worst of these was a headache so excruciating that at times I half-believed myself to be dying of meningitis. And the noise off-stage did nothing to help.
Indians love noise and habitually amplify their degraded cinema pop music to truly diabolical proportions. In this case I have no idea where the original sound came from, but an amplifier had been attached to the roof directly above our window and it is no exaggeration to say that during the first two days and nights in that room I was driven almost insane. Only those who have personally suffered Indian pop music at close range will be able to give me the sympathy I deserve. Occasionally there was a lull in the inferno and I almost wept with relief, but no lull lasted longer than it takes to change a record. Perhaps Richard Lannoy was right when he commented in _The Speaking Tree_ – 'Indian pop music... pervades the lives of the Indian masses as does no other form of entertainment... Here is a people... distracted from the human predicament by the highly organised mass media. The pop arts of India merely block individuation, alienate people from personal experience, and intensify their moral isolation from each other, from reality, and from themselves.'
By eleven a.m. on the twenty-sixth I had realised that if I were not to die of neglect some action must be taken. Leaning on the wall I made it to the veranda and tried to persuade three passers-by that I genuinely and urgently needed medical attention; but they all insisted that I must go to a clinic or hospital as no doctor would come to me. However, I knew it would be suicidal to go doctor-hunting in a steady downpour of cold rain with a high temperature, so I tottered despairingly back to my sweat-sodden bed.
Then Rachel appeared beside me, in a rather genie-like way. 'I'm better,' she said, 'and I'm hungry. May I go out to look for food? Why don't you get a doctor? You look terrible. Have you no medicine? Why am I better?'
I mumbled that no doctor was available, whereupon Rachel said, 'Why don't you write a letter to a doctor and get a servant to take it?'
'What doctor? What servant?' I muttered muzzily.
'Any doctor and any servant,' said Rachel, impatiently.
I raised my head and began to take her seriously. She brought me pen and paper and in shaky capitals I appealed to a 'Dear Doctor' while she trotted off to fetch 'a servant'. Moments later she was back with a young cycle-rickshaw-wallah she had found sheltering on the veranda. His English was unintelligible but he seemed to understand when I explained that if he returned with a doctor I would give him Rs.5 before I left Madurai. Pocketing my note he disappeared and less than fifteen minutes later showed an elderly Indian woman doctor into the room. She was from a Christian maternity hospital scarcely five minutes' walk away and she assured me that had we gone there on Christmas Eve we would have been given a very warm welcome and appropriate treatment.
But what was 'appropriate treatment'? Despite heavy doses of fabulously expensive British-made drugs my temperature remained between 101º and 104º for the next few days, while my headache resisted every available painkiller and I developed a strange racking cough – quite unlike bronchitis – which almost caused me to faint with exhaustion.*
Obviously I could not be moved, but my faithful doctor called four times a day – no doubt she feared further ghastly complications – and ordered the caretaker to provide fresh bedding and two-hourly pots of tea. She also brought her senior partner, Dr Kennett, to examine me, which I gathered was a significant measure of her concern. Dr Kennett is an astonishing eighty-year-old who has done so much for the poor of this city that a main street has been named after her. Following her visit, the attitude towards us of the caretaker and his staff changed from polite indifference to a respectful eagerness to please.
Apart from all this professional attention, both these doctors were motherly kindness personified. They lent me Rs.100, regularly sent a servant with tempting little delicacies from their own kitchen, and provided Rachel with an abundance of Christmassy snacks, toys, games and balloons. Then yesterday Dr Kennett's car took us to the hospital, where we are now installed in a two-bed cubicle amidst the howls of the newly born. Today my temperature is at last normal, and if it remains so we plan to go to Periyar tomorrow afternoon to convalesce in the depths of the wildlife sanctuary.
## DECEMBER 31ST. KUMILI
This morning I rose and shone. Fifteen watt, as you might say, but an improvement on the blackout of the past week.
After breakfast we set off with our cycle-rickshaw friend to see what is perhaps the most impressive of all Hindu temples. The morning was a perfection of clear golden sunshine from an azure sky – after several dark days of non-stop monsoon rain – and the building that came into view in the distance, as we crossed the high railway bridge, seemed almost unreal in its alien loveliness. It is in fact a whole complex of buildings and one could spend days exploring and admiring – though that might overtax Rachel's interest: she was happy enough to leave after five hours. Moreover, since the Madurai Temple is one of South India's main tourist attractions _mlecchas_ are courteously catered for and racketeers of every sort rigorously suppressed.
On the way back to the hospital we called at the bank – always a long-drawn-out procedure – and by the time we had packed, said grateful goodbyes and caught the two-thirty bus I was feeling decidedly feeble. And so – I suspect – was the ever-uncomplaining Rachel, who is still suffering from that odd cough and has not yet regained her appetite. She has had no treatment for our nameless disease because I am very against children being stuffed with antibiotics.
This afternoon's journey took us south-west, through a region where the density of the human population was matched by a staggering number of cattle, mainly the much-revered humped whites. There were also hundreds of buffaloes and several herds of minute donkeys which are commonly used as baggage-animals and too often beaten savagely. Naturally none of these beasts looked well fed, yet even on this rather arid plain I saw no starving animals, as one frequently does in North India. Rachel was distressed on the donkeys' behalf and not consoled when I told her that according to Hindu mythology the ass is the steed or vehicle of Sitala, the goddess of smallpox (one of the ten aspects of Kali), and so is regarded by most Indian peasants with a mixture of fear and contempt. Under the Mughals, no Hindu of the North-West frontier province – now Pakistan – was allowed to ride anything but an ass. I cannot understand why donkeys are universally scorned, despite their being so useful. Perhaps their voice is against them. Luckily Rachel did not notice that many of those we passed today had had their nostrils slit, it being the erroneous belief of Indians that this mutilation modifies the bray.
For miles our narrow road ran between low, grotesquely shaped, rock-strewn hills towards the high blue wall of the ghats. Then, having crossed the Tamil Nadu–Kerala border at the little town of Cumbum, we drove straight at the apparently sheer mountain barrier that here rises abruptly from the plain. 'There must be a tunnel!' said I to Rachel. But instead there was a dramatic road which I would have immensely enjoyed on foot though I did not greatly relish it from the seat of an overloaded Indian bus.
When we got here just after sunset the air felt cold. Kumili is a single-street village, 3,300 feet above sea-level and four miles from Periyar, and in the larger of its two doss-houses we are occupying a cubicle in which I can only move crabwise between our cots. An icy draught is sneaking through a broken window and I have just come face to face with my first South Indian bedbug (now deceased). I feel so exhausted the New Year will have to see itself in without me, but I dare say 1974 will be none the worse for my non-attendance at its birth.
## JANUARY 1ST, 1974. THEKKADY, PERIYAR WILDLIFE SANCTUARY
If the denizens of Kumili celebrated our Western New Year I did not hear their celebrations, or feel their draughts or bedbugs, or suffer any other interference with my ten-hour sleep.
By seven-thirty this morning we were on the way to Thekkady, which is the administrative and tourist centre for the sanctuary. Near the lake the wildlife preservation officer has his headquarters in a little bungalow, and an inconspicuous wooden landing-stage has been built for the small motor-launches that take visitors on game-watching expeditions.
'How far is it?' asked Rachel, as we walked away from Kumili through the crisp early morning mountain air.
'Four miles,' I replied.
Rachel looked at me sardonically. 'I thought we were supposed to be convalescing,' she said. 'I don't call carrying your big rucksack four miles _convalescing_. Is there no bus?'
'No,' I said firmly – hoping one would not overtake us, for 'The whole area of the Sanctuary abounds in natural scenery,' as my tourist brochure puts it. Soon we saw a troop of Nilgiri langurs, and then that most lovely creature, the Indian giant squirrel, and Rachel forgot all about the snags of convalescing with mamma. At the sanctuary border-post an amiable young policeman asked – without getting up from his breakfast – if we were carrying any guns, and then made a sign that we could duck under the barrier and proceed.
The Kerala Tourism Development Corporation owns both Thekkady's hotels. One is the expensive, Western-style Aranya Nivas, where a bottle of beer costs Rs.9, and the other is Periyar House – clean, comfortable, spacious, efficiently staffed, teetotal, vegetarian and only Rs.10 for an airy, well-appointed single room overlooking jungle and lake. Tonight Periyar House is almost full and the guests include half a dozen semi-hippy European youngsters and a party of elderly Prussians with thick guide-books and severe sunburn. But the Aranya Nivas, not surprisingly, is empty. I have been told it depends almost entirely on rich Americans and the flashy, hard-drinking type of North Indian who is out to impress his benighted Southern cousins. A pleasing feature of Thekkady is that one can without difficulty avoid one's fellow-tourists; even on the motor-launch this morning there were only four Madrassis and a camera-obsessed Japanese youth.
Periyar Lake is twenty miles long and was formed in 1895 by the construction of a dam across the Periyar River to help irrigate large tracts of Tamil Nadu. Its maximum depth is about 140 feet and, as my brochure explains, 'When the Lake was formed, tree-growth from the water-spread area was not completely removed and therefore a large number of dead tree trunks still exist within the lake. They get submerged or exposed by the fluctuating water-level. These dead trees, though sometimes a hazard to navigation enhances the scenic value of the locality and allows the nesting and roosting of several water birds.' I am not sure that I agree about the enhancing of the scenic value; the cumulative effect of so many dead trees is slightly depressing and they serve as a nagging reminder of the lake's artificiality. However, if they solve the water-birds' housing problems they are well worth keeping.
Our two-hour tour was good value for Rs.4 and the enthusiastic pilot identified many birds for us as we chugged slowly along, enjoying the warm sun sparkling on the water, and the cool breeze, and the faint yet thrilling possibility of seeing some big game. At the edge of the water in the near distance we eventually saw a herd of elephants; but obviously touring by motor-launch is not the most efficient way of animal-watching, though this trip is well worth taking for its own sake.
After lunch I left Rachel playing in the jungle near the hotel – where there were two tame elephants and lots of non-shy langurs to entertain her – while I walked halfway back to Kumili in search of the wildlife officer, a pleasant young man who readily agreed to our spending two nights at the Manakkavala Forest Rest House, six miles away. The Government of India Tourist Office in London had provided me with an excellent sketch-map of the sanctuary, on which all rest houses and footpaths are clearly marked, so I argued that we needed no guide, only the key. But the officer thought otherwise and in the morning a trainee wildlife officer is to meet us outside the hotel at eight o'clock.
## JANUARY 2ND. MANAKKAVALA
The trek here perfectly illustrated how one should _not_ travel with a small convalescing child. All would have been well had we been able to go at our own pace, devoting the whole day to the six-mile walk, but our unwanted guide arrived three hours late, which meant that when we started Rachel had already expended a considerable amount of her at present meagre store of energy and I was in an occidentally bad temper because I detest unpunctuality. On being asked 'Why so late?' the smartly uniformed guide, who was accompanied by a barefooted fourteen-year-old, replied that he had been looking for a companion as he would be afraid to return alone to Thekkady – an excuse which did nothing to raise him in my estimation. Then it transpired that our guides were in a hurry, and Rachel was not equal to hurrying over the roughest terrain she had ever encountered. In brief, the whole thing was a disaster, not enjoyed by either of us.
However, to be on our own in this remote rest house compensates for the day's tribulations. It stands near the top of a steep, jungle-covered ridge, overlooking one of the lake's many narrow arms, and about a hundred yards away, across the still water, is a tree-covered peninsula with a long shore of grassland between forest and lake. There, at sunset, I saw seven gaur (the Indian bison) coming to drink and then quickly melting away into the shadows under the trees. These splendid creatures, with their spreading upcurling horns and massive sleek bodies, are aggressively anti-human and by far the most dangerous animals in the sanctuary; but because of their shyness the visitor is extremely unlikely ever to encounter one at close range. There are said to be sixteen tigers and many leopards here though these are rarely seen.
## JANUARY 3RD. MANAKKAVALA
Today we did some serious convalescing. My original plan had been to trek out from here, but this morning neither of us was up to it. However, as we lay around on the nearby lake shore we probably saw more than if we had been on the move. Scarcely thirty yards away a gaur cow and calf crossed a grassy glade between two patches of jungle: lots of wild pigs and piglets dug vigorously for their lunch during the forenoon: bonnet macaques and lion-tailed macaques swung and screamed in the trees above us: two flying-squirrels played tip and tig for quarter of an hour: a fiercely handsome fish-eagle caught and ate his prey on the opposite shore: darters dived frequently into the water, looking like something out of a fossil museum – and towards sunset eleven elephants, including two young calves, strolled down to bathe in the lake. But alas! – to our great disappointment they turned a corner before submerging, and because of the calves it would have been unwise to follow them.
It feels strange to be the only factory humans in a world of animals, knowing that every movement and sound is caused not by a member of one's own species. Periyar must be one of the most satisfying game sanctuaries in the world. It is totally uncommercialised – apart from Thekkady on its fringe: and even Thekkady has not yet been spoiled – and when you walk off to a forest hut there are ( _pace_ that sketch-map!) no discernible paths, no tiresome little signposts, no fussy picnic-sites, no concessions of any sort to mankind, until the hut itself is reached. It is just you and the animals, in a setting of incomparable natural loveliness, blessed by silence. But of course silence is the wrong word; what I mean is the absence of artificial noise. Except during a couple of noon hours there is very little silence, day or night, in an area that teems with bird and animal and insect life. Even when one can see nothing, it is fascinating simply to listen to the complex pattern of jungle sounds being woven against the stillness of a region undisturbed by man.
## JANUARY 4TH. THEKKADY
The return trek on our own was an unqualified success and when Rachel said, 'It seems to me you're a better guide than those other two' I felt bound immodestly to agree. Not that it was easy to negotiate either the uncomfortable elephant-bogs or the steep, slippery slopes that in places rise straight up from the lake and had been the main cause of Rachel's alarm on the way out. The latter hazard we avoided today by leaving the lakeside and cautiously following animal paths through the jungle, stopping at intervals for sustenance under a gooseberry tree. The elephant-bogs, however, were another matter. These are swampy stretches of land at lake level, dotted with huge clumps of tough grass which act as stepping-stones, and the penalty for missing one's footing is partial immersion in gluey black mud. To Rachel's delight I soon slipped and, being weighted with a rucksack, sank so fast I lost both shoes. (They were falling to bits anyway, so this was not the economic disaster it might have been.)
It was interesting to observe the impact of animals on the environment in an area where man never interferes. (Though the fact that he deliberately never interferes is itself a form of interference with the balance of nature.) Many of the trees had recently had branches and bark ripped off by elephants, whose gigantic droppings were all over the place, and several grassy ridges looked as though newly ploughed by the wild pigs, of whom we saw dozens today, some quite close and not particularly nervous. We also saw fresh gaur droppings and passed a few of their resting-places, where the undergrowth had been trampled down and shaped. And to Rachel went the glory of noticing a tree from which much of the bark had been scraped by feline claws – a leopard, judging by the height of the marks. But to me – luckily – came the shock of seeing a long, thick snake just in time to arrest my bare foot inches from its back as it crossed our path.
'Why do you look so queer?' asked Rachel, staring up at me. 'Is that why you won't let me go first?'
'Probably it was harmless,' I said briskly. (I notice one always tells oneself this immediately afterwards, doubtless by way of counteracting the shock.)
'How soon would you die if it was harmful?' asked Rachel, indefatigably athirst for scientific data.
'I don't know,' I said shortly.
All day a strong cool breeze sent small white clouds cruising across the sky and stirred the golden elephant grass; and the warm sun sparkled on the lake – from which we never strayed too far – and glistened on the fresh green grass by the water's edge; and all around were powder-blue mountains, rising just beyond the splendour of the forest – a pink-brown-green expanse of noble trees, their colours vivid in the clear air, with the fiery flowers of the Giant Salmalias blazing like distant beacons.
We got back here at two-thirty, having made the six-mile walk last for seven hours, and I shall remember this Periyar interlude as one of the highlights of our journey. The feeling of remoteness, the beauty of jungle, lake and grasslands, and the novel awareness of being a mere visitor in a world of animals, add up to something very special.
After a late lunch I left Rachel playing near the hotel and hitched a lift into Kumili to replace my lost shoes. By the time I had walked back the only available pair were lacerating my feet but as they cost less than Rs.6 1 can afford to replace them tomorrow. Trying to shop in a tiny place like Kumili – or even in a bigger town like Tisaiyanvilai – reveals how little cash circulates in rural India.
At supper I got into conversation with a family from Delhi – parents, two adolescent sons and paternal grandmother. Despite their staying in this modest hotel the husband must be a government official of some importance, as they have a State car and a retinue of liveried minions who travel in a jeep. The whole family spoke rather patronisingly about South Indians, as North Indians are wont to do, yet they were charming to me and I found myself talking to them with a freedom one does not normally feel amongst South Indians, however fluent their English.
This takes us into a not very savoury labyrinth. How much thicker is blood than water? Why am I aware of being with my own people – in the most basic sense of that phrase – when I am talking to fair-skinned, Aryan, North Indian Hindus, and aware of being with strangers when I am talking to dark-skinned, Dravidian, South Indian Christians? I suppose the short answer is that blood is indeed a lot thicker than water.
Yet this is not simply a shaming confession of racism: something a good deal more complicated is involved. The expressive cliché 'on the same wavelength' is needed here. One does not always approve of, like or wish to be with those of one's own race, but one understands their emotions and thought-processes by some primitive system that seems not to operate with other races. This lack of instinctive understanding must be at the root of racism, though in itself it is not racism; people fear what they cannot understand, and dislike what they fear.
The Hindu caste laws could be described as an elaborate contrivance for making colour prejudice look respectable and the immutability of the Aryans' disdain for Dravidians is very striking. Whatever anti-discrimination laws may be passed, and however rapidly India may become a genuinely secular state, I cannot see Indian colour prejudice ever being eradicated. Throughout history it has been a dominant factor here and it does make one question the wisdom of having a single, unwieldy, politically united Republic when a number of smaller independent states would be more manageable from a practical point of view and culturally more realistic. Even in this EEC era no one suggests that Italy and Denmark should be parts of the same nation because they both have a Christian tradition and belong to the same land-mass.
However, I must admit that on the whole I find South Indians far more likeable, outgoing and friendly than North Indians. Just as I find the Tibetans and the Ethiopians far more congenial than certain notoriously pure-blooded European Aryans I could mention.
## JANUARY 5TH. MUNNAR
In Kumili this morning everybody denied the existence of a Munnar bus so we had to stand shivering for over an hour beside a faded little signpost saying 'Munnar: 110 km.s' and pointing up a steep, rough road not marked on my map.
'Why are we standing here?' asked Rachel, her teeth chattering pathetically. 'The men _said_ there was no bus.'
'Don't worry,' I replied confidently. 'There's a bus to everywhere in India if you wait long enough.'
An Indian street-scene is rarely without entertainment-value and to divert us this morning we had the spectacle of some two hundred Alleppy pilgrims doing battle for accommodation on three decrepit forty-seater buses. These men had come up from the coast yesterday, to attend a festival at a famous local shrine, and they looked a wild lot. Despite the bitterly cold morning air most were naked from the waist up, with sandalwood ash streaked across their dark torsos, bulky marigold garlands around their necks and bed-rolls slung over their shoulders. On their heads were balanced sacks of Shiva-knows-what, topped by a couple of cooking-pots and another garland. Their struggles to fit the human quart into the pint vehicle were at last successful, as such struggles normally are in India, and with much chanting of prayers, clapping of hands and blaring of horns the three antique buses swayed slowly off to tackle an extremely tricky ghat road.
Our own bus, when eventually it arrived, looked no less decrepit but was not unduly crowded. It was going most of the way to Munnar and took four and a half hours to cover forty miles through the Travancore Hills – Kerala's highest mountains. I was so cold for the first two hours that my numbed hands could not find my handkerchief in my pocket and I was unable fully to appreciate the grandly beautiful ranges we crossed, and the dark, densely forested ravines that sometimes dropped away for five hundred feet from the edge of our narrow road.
The surface was so rough and the tyres were so worn that we had two convenient punctures, which allowed us to stretch our legs and admire the view. This is such a thinly populated area (by Kerala standards) that we passed only one town and three large villages – each sporting several pairs of nuns and an array of neatly painted hammers and sickles on the walls of huts and houses.
At one-thirty we were deposited outside a tea-house at a cross-roads and told the Munnar bus would come soon. It did, but was so crowded I had to stand and therefore missed the approaches to this enchanting town, which lies in a green bowl of tea-plantations, rimmed by soaring blue mountains – including Anaimudi (8,841 feet), the highest peak in India south of the Himalayas.
As we were extricating ourselves from the bus a slim man about forty years old, who introduced himself as Joseph Iype, stepped out of the crowd and said we must have tea and biscuits in his electrical equipment shop. Soon we had been invited to spend the night with the Iypes and were being escorted to their bungalow by eleven-year-old Chuta, at present on holidays from his Ooty school. We went part of the way by bus, as the Iypes live on a steep, tea-green mountainside some three miles from the town, overlooking the river valley and directly opposite the blue, rounded bulk of Anaimudi. There is a little colony of British-built bungalows here but few British residents remain. Yet the tea-plantations are still British-owned – which is fair enough, as our host remarked, since the British were entirely responsible for organising the clearing of the jungly mountainsides and building the local roads.
English is the Iypes' first language and they are, as our host's first name indicates, Christians. Their seventeen-year-old daughter is in her last year at a Coimbatore boarding-school and Mrs Iype laughingly admitted it is no coincidence that so many two-child South Indian families have a five- or six-year gap between children. In this part of the subcontinent there is such a strong boarding-school tradition that even not-very-well-off middle-class families send both sons and daughters away at five or six years old; and when the adored first-born departs – sometimes to a distance of several hundred miles – his or her heartbroken mamma naturally tends to think in terms of a replacement.
Leaving Rachel with Chuta, I set off after tea to walk along the narrow crest of the 5,000-foot ridge on which these bungalows are built. (Munnar town is at 4,500 feet.) On both sides I was looking straight down into dizzying depths, with fold after fold of soft blue mountains fading away into the southern distance and Anaimudi lying royally against the northern sky, dominating Munnar's valley – which also holds a swift, tree-lined river and a cricket-pitch where tiny, darting white dots were just visible. I wish we could have accepted the Iypes' generous invitation to spend a few days here, but the Thimmiahs expect us back on the 10th.
Before dinner the Iypes' closest friend called. He is a most endearing and prodigiously well-informed Muslim whose wife – unexpectedly – is an Indian Christian. Recently he started a toy-factory on the nearby mountainside and to my horror he presented Rachel with a large, angular, heavy and beautifully finished wooden truck which will not make life any easier for the beast of burden over the next few months. Despite our non-Christmas, Santa somehow managed to function only too efficiently and I am now carrying, as part of our permanent equipment, three elephants, two large dolls, one tiger, one spotted deer, one kangaroo, the dolls' dinner-service and a sketching-pad accurately described on the cover as 'Monster!'
## JANUARY 6TH. UDUMALPET
Today began badly for poor Rachel, who before breakfast had to have a minute thorn removed from the ball of her right foot. Overnight it had set up quite a nasty infection and I only hope I got it all out.
I spent the forenoon walking – and climbing a little – in the nearby mountains, while Chuta entertained Rachel. When I set out at eight-thirty an improbable light frost was glittering on the grass but the air soon warmed up and by ten o'clock I was sweating, despite the strong breeze that swept the heights. I hope some day to return to that Idukki District of Kerala, where one could spend weeks happily trekking.
By a pleasing coincidence, Mr Iype and the children were also travelling towards Coimbatore today: otherwise I might never have plumbed the mysteries of the regional bus service. Because of the state of the local roads Munnar is ignored by Kerala's buses and depends on a few privately owned vehicles of infinite whims. Today the Udumalpet bus chose to leave at 2.40 p.m., but tomorrow it may leave at noon, or at dawn. And yesterday it didn't bother to leave at all so its would-be passengers had to hire a truck.
The drive down to the plain, over an 8,000-foot pass, was magnificent – tremendous peaks, densely forested slopes strewn with colossal boulders, deep green valleys noisy with dashing young rivers and a few spectacular waterfalls. Mr Iype had ensured us front seats and as the driver never dared to exceed fifteen miles per hour we had time to appreciate the landscape; yet inevitably I resented being in a motor vehicle.
At the State border we had to endure a forty-minute delay because for some utterly baffling reason an old man was trying to smuggle one live rabbit into Tamil Nadu in a basket of oranges. Having completed our descent to the border by the light of an almost-full moon, the driver went much too quickly for safety over the level road to Udumalpet. It was exactly eight p.m. when he stopped for our benefit outside the Dak bungalow, so the fifty-four mile journey had taken us five hours and twenty minutes.
We are all sharing the one room that was vacant here, but whereas the Murphys intend to sleep comfortably, stretched out on the floor, the three Iypes have uncomfortably squeezed themselves on to a single bed. I never can understand why most people imagine a bed – some sort of bed: any sort of bed – to be a prerequisite of sleep.
## JANUARY 7TH. OOTACAMUND
On the subject of Ooty I am afraid I disagree with Murray's _Handbook to India_ , which observes that 'The astonishing charm of its scenery seems likely to survive modern developments, which include extensive hydro-electric projects, a vast new Government factory for the manufacture of cinema film and a population that now tops 50,000. Its climate has long been famous. As early as 1821, Europeans began to build their homes there.' To my mind, no scenic charm can survive this sort of development.
In 1974 the keynote to the whole Nilgiri region is nostalgia. Around Ooty, in every direction, rise Christian churches of various denominations, and enormous boarding-schools and military barracks, and the innumerable handsome homes of retired Indian Army officers or senior civil servants – with neat signposts pointing up steep paths to individual houses and saying 'Col. and Mrs This', 'Brig. and Mrs That' or 'Mr and Mrs T'other'. During the late afternoon many residents may be seen with the naked eye, wearing heavy overcoats over their saris if female and thick tweeds if male, and carrying shooting-sticks or (inexplicably) umbrellas. Those also carrying dog-eared books are obviously on their way to the palatial Ootacamund Public Library, which stands grandly in its own spacious grounds opposite the main church, St Stephen's. The average age of these senior citizens seems to be eighty and when greeted they usually smile at one a little sadly, a little vaguely. This of course is Ooty's closed season; when the hot weather comes to the plains there will be an enlivening infusion of children and grand-children.
To me, the library is Ooty's most exciting feature. There are now only ninety-six subscribing members and the wistful, veteran librarian who gave us permission to browse cheered up no end when I went into ecstasies about the fabulous collection of nineteenth-century first editions which just happen to have accumulated on these shelves, where one finds few volumes published after 1939.
Also near St Stephen's are rows of enormous shadowy shops that must have done a roaring trade forty years ago and are still pretending to operate with mainly empty shelves. Their ancient, dusty owners peer listlessly from unpainted doorways across the rooftops of the bazaar to the lines of fir trees on the highest crest of the Nilgiris. If they lower their eyes to observe a scruffy white woman and her even scruffier child walking down the otherwise deserted street they bow obsequiously and I am overcome by gloom. Then to cheer myself I reflect that, depressing as Ooty is now, it must have been even more so when infested with mem-sahibs who enjoyed being fawned on by 'niggers'.
Yet I am glad we came here, because of the journey up from Coimbatore. We left Udumalpet early this morning – still with the Iypes – and for two-and-a-half hours drove straight across a densely populated, dull plain where many bullocks were ploughing poor soil. Then we said goodbye to our friends and took another bus, heading for the tremendous blue wall of the Nilgiris. The road soon began to climb gradually through plantations of palms, which are oddly unattractive when grown en masse. Then suddenly it was climbing so steeply that within minutes the air felt chilly and the plain we had just crossed looked like a view from an aeroplane; no wonder the Nilgiris were almost deified by the heat-demented British! Again we had front seats, which gave Rachel a good view of the scores of half-tame rhesus monkeys who sat by the roadside cheering the bus on, as it seemed. Every acre of these precipitous slopes is heavily forested and I have never before seen such an extraordinary variety of gigantic trees.
When at last we emerged on to the grassy, treeless highlands I could have fancied myself back in the Himalayas had this whole area not been so built-up. Ooty is at an altitude of 7,440 feet so even at midday, in winter, it is quite cold when one is out of the sun, and now, at seven p.m., it is perishing. As we carry no woollies I have had to wrap both my flea-bag and a blanket around me. We are staying in what is absurdly called a 'Tourist Bungalow', run by the Tamil Nadu State Board. In fact it is a multi-storey hotel, opened in 1963, and it compares very unfavourably with similar establishments in Kerala. When we were shown into our Rs.10 single room there was no water either in the carafe or in the bathroom, the latrine was filthy, the wardrobe door was broken, the sheets were dirty and there were revolting stains on the wall over the bed. All these seemed unnecessary drawbacks in a place that advertises itself far and wide as the 'Ideal Tourist Home', but to give the management its due a brigade of servants appeared within moments of my complaining, to rectify matters.
I am a little worried tonight about Rachel's foot. This afternoon I had to carry her down from Elk Hill – she feels even heavier than usual at over 8,000 feet! – and I don't quite know what to do next. I have a logical distrust of unknown Indian doctors, some of whom buy their degrees without ever opening a medical textbook, so if possible I would prefer to postpone treatment until we get back to Coorg. But at the moment Rachel is tossing and muttering in her sleep, obviously half-conscious of the pain.
## JANUARY 8TH. GUNDLIPET
This morning Rachel insisted that her foot felt better, but it looked worse. I was therefore relieved when the bearer who brought our sloppy tray of lukewarm bed-tea told me 'a very smart doctor' was staying in Room 87. Praying that this gentleman's smartness was mental rather than sartorial I carried Rachel to him and he assured me the foot needed only a washing in salted water and a plain gauze dressing. Having given it this treatment I left the patient doing a jigsaw with the doctor's ten-year-old twins and went off on my own to explore.
As one walks through Ooty's less lovely areas a great deal of poverty is evident, and poverty always seems more harrowing in cold weather. Quite apart from the foot complication, I would not have wanted to spend more than twenty-four hours in this tomb of the Raj. But it does have a good Bata shop where I bought strong walking shoes for Rs.25. I also found a small bookshop where imported paperback porn stood shoulder to shoulder with austere tomes on Hindu philosophy and a fat collection of Radhakrishnan essays cost me only Rs.6.
After lunch Rachel limped the two miles to the bus stand without complaining, but despite her cheerfulness I still feel uneasy. Experience has taught me that she is incredibly stoical about personal pain, though she will burst into tears if I accidentally tread on the cat.
The descent to the Mysore Plateau was no less beautiful than yesterday's ascent and quite different: India's landscapes are endlessly varied. But by now I really have had a surfeit of just _looking_ at the countryside and never coming to grips with it. Beyond Ooty, to the north, stretched mile after mile of open downland with fine plantations of firs and eucalyptus. Then begins the descent, around a series of brilliantly engineered hairpin bends. As one Indian said to me recently – 'It was worth having the British to stay, if only for the roads they left behind them.' (Had the Indian Empire never existed, who would now be building India's roads? China? Russia? America?) Far below we could see an immense brown plain stretching away to the horizon: Karnataka State's wildlife sanctuary of Bandipur, which is 3,000 feet above sea level.
Bandipur cannot compete with Periyar; most parts are accessible to jeeps and it is a well-organised tourist centre. However, we enjoyed the golden-brown forest and saw a peacock strutting across the road and lots of monkeys, some of whom made Rachel's day by climbing into the cab at octroi posts. We also saw several working elephants going about their Forestry Department business and a mongoose disappearing into the undergrowth.
The sun was setting as we left Bandipur and came to undulating, cultivated land where dark red earth glowed in the hazy golden light and the glossy green of palms, plantains and wayside banyans stood out against a deep blue sky. Then a purple-pink tinge dramatically suffused the whole scene as the sun dropped lower, and its last slanting rays burnished the classical brass water-jars that were being carried across the fields on the heads of slim women in vivid, graceful saris. At such moments the simple, timeless beauty of rural India can be very moving.
It was almost dark when we arrived in this little town and I felt dismayed, though not surprised, to observe Rachel's silent suffering as she hobbled across the road to the nearest doss-house, where there was a vacant cell just inside the street-door. Mercifully, we are due tomorrow at the Hugheses' place in Sidapur, to which we were invited when we met Jane and David at Byerley Stud, and I know a good doctor works in the new hospital near Sidapur, which is partly subsidised by South Coorg's coffee-planters.
## JANUARY 9TH. MYLATPUR ESTATE, NEAR SIDAPUR
This has been a day I should prefer to forget, though I am unlikely ever to do so. From midnight neither of us got much sleep, as poor Rachel tossed and turned and whimpered, and by dawn her foot was at least twice its normal size. No water was available in our reeking doss-house wash-room, so I decided it would be more prudent not to remove the bandage in such spectacularly unhygienic surroundings but to concentrate on getting to Sidapur as soon as possible. Accordingly we caught the seven o'clock bus and arrived at the big village – or tiny town – of Sidapur at twelve-thirty. The Hugheses had explained that Mylatpur is five miles from the village so I tried to ring them, but I had no success because the Indian telephone system is one of the two greatest technological catastrophes of the twentieth century. (The Irish telephone system is the other one.) Rachel then volunteered to walk half a mile to a hitch-hiking point on the outskirts of Sidapur, and though her foot was far too swollen to fit into her sandal she did just that, hobbling on her heel. (If VCs were awarded to five-year-old travellers she would have earned one today.) After standing for only a few minutes we were picked up by a neighbour of the Hugheses, but we arrived here to find the family gone and my letter announcing the date of our arrival on top of their pile of mail. However, they were expected back at tea-time and their kindly old bearer did all he could for us.
I at once put Rachel to soak in a hot bath, boiled a safety-pin and scissors, punctured the menacing yellow balloon, squeezed out a mugful of pus, cut away inches of festered dead skin and was confronted with a truly terrifying mess. Not having the slightest idea what should be done next, I simply disinfected and bandaged the wound and at that point Rachel reassured me by announcing that she was ravenous. She added that her foot felt fine now, though a bit tender, and having eaten a huge meal she went to bed at five o'clock and has not stirred since. (It is now ten-thirty.) But of course she must have medical attention and Jane has said that first thing in the morning she will drive us the ten miles to Ammathi Hospital to see Dr Asrani, a US-trained doctor in whom everybody has complete confidence.
## JANUARY 10TH. GREEN HILLS, NEAR VIRAJPET
Everybody is right about the inspired skill of Dr Asrani, but that did not lessen the shock when he said Rachel would have to have a general anaesthetic this afternoon to enable him to probe her foot fully, clean it thoroughly and dress it efficiently. We both still have the residue of our Christmas infection and he admitted he would have preferred not to put her under with a partially stuffed nose: but to do so was the lesser of two evils. At this point my nerve broke, though I regard myself as a reasonably unflappable mother where things medical or surgical are concerned. I hope I maintained an adequately stiff upper-lip, in relation to the general public, but Rachel at once sensed my inner panic and was infected by it. She herself has absolutely no fear of anaesthetics, having twice been operated on in Moorfields Eye Hospital, yet the moment her antennae picked up the maternal fear she went to pieces and a very trying morning was had by all.
As the patient had finished a hearty breakfast at nine o'clock she could not be put under before two p.m., so Jane volunteered to take us back to Mylatpur, return us to Ammathi after lunch and arrange to have us collected from there by the Green Hills car. She has been a friend beyond price today and I bless the hour we met her. When she had filled me up with a quick sucession of what she called 'Mum's anaesthetic' (rum and lime-juice) I began to feel quite sanguine about Rachel's chances of survival and to marvel at the good fortune that had provided us with such a capable doctor in such an unlikely place.
It is not Dr Asrani's fault that the local anaesthetic techniques are fairly primitive; when it came to the crunch I had to hold Rachel down while a beardless youth clapped a black mask over her face and I begged her to breathe in. No foreign body was found in the wound, nor was it manufacturing any more pus: so I felt secretly rather proud of my do-it-yourself surgery. (Had I not been a writer I would have wished to be a surgeon and I always enjoy opportunities to carve people up in a small way.)
To my relief Dr Asrani did not suggest any form of antibiotic treatment but simply advised me to steep the foot twice a day in very hot salty water, keep it covered with dry gauze and leave the rest to nature. His skill is such that Rachel came to – in an immensely cheerful and conversational mood – precisely eight minutes after the bandage had been tied. Half an hour later she was her normal self again and we set off for Green Hills where I found, as though to compensate me for the morning's trials, my first bundle of mail since leaving home. There were ninety-seven letters, if one includes bills, advertisements, an appeal for the Lesbians' Liberation Fund and a request for advice about how to cycle across Antarctica.
* Some time later, routine malaria blood-tests incidentally revealed that we had both had brucellosis: so Rachel was lucky to have recovered within three days.
CHAPTER TWELVE
# _Ancestor Veneration in Devangeri_
## JANUARY 11TH. DEVANGERI
It is remarkable how easily in Coorg past and present blend together. As we drove this morning to Devangeri, I noticed side by side on the back seat of Dr Chengappa's car a stethoscope and an ancient, heavy dagger for cracking coconuts. Every Friday morning the doctor goes to his Devangeri _Ain Mane_ (ancestral home) to honour his forefathers by cracking six coconuts before the sacred brass wall-lamp in the prayer-room and ceremoniously spilling the milk while chanting appropriate _mantras_. Then he returns to his Virajpet clinic to give scores of lucky patients the benefit of his first-rate, up-to-date medical skills: and one is aware of no conflict between his roles as _Karavokara_ and as South Coorg's most eminent physician.
Dr Chengappa, one of Tim's oldest friends, is our Devangeri landlord – or rather, our absent host, since no Coorg would accept rent from a stranger. He is tall and handsome, with that air of soldierly authority which marks even those Coorgs who have always been civilians, and he has most generously agreed to let us occupy two rooms in this empty joint-family house four miles north of Virajpet. As soon as I saw the place I knew it was absolutely right for us; Tim has proved himself a man of imaginative understanding by ignoring those who said that foreigners _must_ have running water and electricity.
Three miles from Virajpet the narrow road divides beside a small rice mill and, taking the left fork, one continues for another mile until a dirt track branches off to the right. Following this down a slight slope, between low stone walls and tall tamarinds and palm trees, one soon comes on a wide, neatly swept expanse of pinkish earth in front of an imposing, two-storeyed, brown-tiled house, freshly painted white, with verdigris pillars, balcony-railings and window-surrounds. On the left, as one approaches, are two solidly built granaries; on the right is the well – some eighty feet deep – and beyond it stand three whitewashed thatched huts where the Harijan field-labourers live. Moving around to the side entrance, opposite these huts, one sees roomy stone cattle-sheds and two threshing-floors now overlooked by great glowing ricks of rice-straw. And all around, at a little distance, stand majestic trees that must be centuries old – some bearing enormous, cream-coloured waxen blossoms with a powerful scent which fills the air at dusk.
The house faces east, like all Coorg dwellings, so it is quickly warmed after the cool mountain night and never gets too hot during the tropical afternoon. A long paddy-valley stretches away in front – slightly to the left, as one looks out from the main entrance – and is bounded in the distance by high forested ridges. At this season it is a sheet of pale gold stubble on which cattle may unprofitably graze.
Because of the Coorgs' emphasis on ancestor-veneration, their ancestral home is also their main temple. Apart from the compulsory return home for _Huthri_ (which applies not only to family members and servants but to any cattle which may be on far-off grazing grounds), the _Ain Mane_ is the scene of every important spiritual and social event in the life of a Coorg. Traditional _Ain_ houses usually stand on a height, overlooking the family's paddy-fields, and because the majority are invisible from the motor-roads passers-by imagine this countryside to be underpopulated.
The Chengappas' _Ain Mane_ was built in 1873 and does not exactly follow the traditional pattern. One steps from the portico into a long, high-ceilinged sitting-room, dominated by portrait photographs of splendidly attired ancestors – all good-looking, proud and keen-eyed. Behind is an even longer but windowless dining-room, containing the sacred wall-lamp, and five doors open out of this room, one of them into the kitchen. At the far end, on the right as one enters from the sitting-room, is a steep double ladder-stair. The right-hand ladder leads to another high-ceilinged room, forty feet by fifteen, which was completely empty when we were escorted upstairs by Dr Chengappa and Tim. It is a most splendid apartment, lit by five tall, wide windows which open inward and have occasional panes of red, green and yellow glass mixed with the 'penny plain' in no particular order. Outside, the slope of the tiled portico roof is directly below and each window is protected by a row of strong perpendicular iron bars. At the far end of the room from the stairs is a most attractive double door, with what looks like a Georgian fanlight imported direct from Dublin. It leads to our bedroom, which has a decrepit bed in one corner, complete with supports for a mosquito-net, and in another corner a pretty little rosewood revolving bookcase containing a complete set of _The Gentleman's Magazine_ for 1882. The big arched window also sports several coloured panes – which in Devangeri a century ago must have been the ultimate in status symbols – and the disintegrating cupboard contains numerous bundles of letters addressed to one of the Chengappas and posted in Cambridge in the 1890s. Our ceilings are of wood, our plaster walls have recently been painted a cool shade of turquoise and our earth floors are polished dark red. The whole house is beautifully kept as the family maintains a permanent caretaking staff. At present this consists of a tubercular, pock-marked little man called Subaya, his attractive eighteen-year-old daughter Shanti and his listless nine-year-old son who is no bigger than Rachel. None of the family speaks English – only Kodagu (the Coorgs' language), Kannada (the Karnataka State language) and some Hindi (which is totally unlike either Kodagu or Kannada and has an entirely different script).
When Tim and Dr Chengappa had departed Subaya furnished our living-room by carrying upstairs a small table, three wooden camp-chairs and two tiny stools (for kitchen furniture). To reach our latrine and wash-room one goes down the ladder, through the kitchen and out to the compound. But fortunately what I have been referring to as 'the kitchen' is really a sort of pantry-cum-dining-room; if it were the true inner sanctum kitchen, where the fire burns and the cooking is done, I could not walk through it without causing a havoc of pollution. The sun-worshipping Coorgs are also, very logically, fire-worshippers, and the kitchen fire is considered sacred. Like the wall-lamp, it is seen as symbolising the power, unity and strength of the family and when a Coorg dies his funeral pyre must be lit with embers from his own kitchen fire.
Here the fire burns in a low mud stove, which has two holes, one behind the other, for saucepans. It is fuelled with long, fairly thin branches which lie on the floor and are pushed farther and farther in as they burn – or are withdrawn, should it be necessary to lower the heat. All this I observed this morning while standing outside the kitchen doorway watching Shanti boiling water to steep Rachel's foot; and since it is not my intention to use the caretakers as servants (even if they would condescend to serve _mlecchas_ , which seems doubtful), I immediately realised that because of pollution complications I would have to buy myself a little kerosene stove.
It must be frustrating for Rachel not to be able to race around exploring our new home, but with her usual stoicism she has adjusted uncomplainingly to being a semi-invalid and she did not object to being left alone this morning while I went into Virajpet to shop. Dr Chengappa had given me the local bus times (the bus stop is a mile away, where our road joins the Virajpet road at what is called Mill Point), and I decided to catch the eleven o'clock 'in' and the one o'clock 'out'.
Between our house and Mill Point are two long, low, substantial buildings, standing on their own about a furlong apart. These are Devangeri Middle School and Devangeri High School, the former built about seventy years ago by Dr Chengappa's grandfather, the latter built in 1966 by Dr Chengappa (who paid half the costs) and a group of other Devangeri farmers. The Coorgs have never believed in waiting for some outside authority or central government to provide what they felt they needed; they do it themselves. And you can see this spirit of vigorous independence in the very way they walk and talk and behave.
I did not wait at Mill Point, knowing the bus would stop anywhere to pick me up, but happily no bus appeared. The little road switchbacked through dark green coffee, golden paddy-valleys, grey-brown scrubland and patches of forest. Sometimes I passed a tiled whitewashed house, guarded by plantains and palms, and usually the pale blue mountains were visible, not very far away, against a cobalt sky. Coorg now looks autumnal: the coffee-berries are turning red and in the forest many leaves are tinged pink, yellow, crimson, brown, or orange – though here green always remains the prevailing colour. A fresh breeze blew, a couple of round white clouds drifted south, and the silence was broken only by bird calls and an occasional creaking ox-cart carrying rice to the mill or straw to the market. As I walked along I rejoiced to think that I am no longer merely passing through this glorious region but have become a temporary resident, to whom each curve of the landscape will soon seem familiar.
Virajpet is attractively spread out at the foot of Maletambiran Hill, a prominent mini-mountain visible for miles around. The town's full name is Virajendrapet; it was founded only in 1792, by Dodda Virarajendra, to commemorate the meeting between himself and General Abercromby during the first campaign against Tippu Sultan in 1791.
A disconcerting Gothic-cum-Baroque Roman Catholic church is visible from afar as one approaches Virajpet. Since its foundation the town has had a colony of several thousand Roman Catholics, most of whom speak Tamil, Malayalam or Konkani. At least the Lingarat rajas were not guilty of religious bigotry and when Tippu Sultan began to persecute his Christian subjects these fled to Coorg and were given a free gift of lands. In his correspondence on this subject with Catholic clergy, the Raja always referred to the Bishop of Bombay as 'your High Priest', and under the British the Church lands were registered in the revenue accounts in the name of 'the Chief God of the Christians'.
My kerosene-stove cost me Rs.10; like most Indian factory-made goods it looks very ill-made but may just last for two months. Sugar is rationed and costs the equivalent of twelve pence per kilo, or twenty-two pence on the black market; this means that only the rich can afford it, even at the legal price. Other prices per kilo are: dahl fifteen pence, coffee forty-five pence, mutton sixty pence, honey forty pence, baker's bread sixteen pence. Small eggs are three pence each (I remember they were half an old penny each in North India ten years ago), ground-nut salad-oil is forty-five pence per litre, inferior curds are four pence per litre and heavily watered milk is ten pence per litre – and not always obtainable at this season. Only fresh fruit and vegetables remain relatively cheap – for us, though not for the unfortunate Indians – and a kilo of delicious tomatoes cost me only two and a half pence.
I got home soon after three o'clock feeling very arm-weary: again the expected bus had not appeared. Rachel seemed quite unruffled by having been abandoned for over four hours in strange surroundings; I suspect she becomes so involved in her own affairs of the imagination that she fails to notice time passing. As I scrambled up the ladder she said, 'I like the sounds here' – and I know exactly what she means. Urban sounds merge into a distressing blur of noise, but each rural sound is separate, distinct and comprehensible – the soft trot of cattle-hooves on dust, the tossing of rice on a wicker tray, the crowing of a cock, the squeaking of the pulley as water is raised from the well, the harsh disputes of parakeets, the shouts of men urging oxen around the threshing-floors, the barking of a dog, the grinding of grain in stone hand-mills, the laughter of children, the thud of a coconut falling – and now, as I write this at eight p.m., the unearthly howling of jackals.
On the way home from Virajpet I met an elderly gentleman with an old-world manner who introduced himself as Mr P. A. Machiah, the husband of a cousin of Dr Chengappa. Later he and his wife called, to make sure we 'lack nothing essential', and I soon realised that we certainly do not lack good neighbours. Mrs Machiah – tall, slim and briskly kind – is such a practised granny that Rachel adored her on sight. She eyed our establishment appraisingly and then said she would lend us a slop-pail, a basin, a jug, a large spoon and two saucepans. I really warmed to this couple, who have invited us to visit them tomorrow. As they were descending the ladder Mr Machiah paused, beamed approvingly up at me and said – 'Anything in excess of what you need is luxury!'
## JANUARY 12TH
I woke at six-thirty to hear an exotic dawn-chorus of jungle-birds and see a silver sky turning blue behind the trees. A thick mist lay on the paddy-valley and moisture was dripping to the ground like slow rain, from the leaves of the immensely tall palms.
Rachel has become much addicted to bed-tea so I got the stove going and for want of a teapot made an excellent brew in a saucepan, tea-house style. At present milk dilution is my only worry. One expects it to be diluted in India, where a variety of desperate governmental anti-dilution measures have merely provided new and better opportunities for bribery and corruption. But if our suppliers, who live on the edge of the compound, are diluting the Murphy half-litre with unboiled water from the well we may soon be in serious trouble because of Rachel's refusal to drink boiled milk. I have assured them I will pay the same for a quarter-litre of neat milk as for a half-litre of milk and water, but I fear the watering habit is too ingrained to be eradicated overnight.
Although I might not choose to live permanently without the modest mod cons available in my own home, I do positively enjoy a spell of the simple life; one needs it, to keep in touch with what are still the realities of life for the majority of human beings. It is also worthwhile rediscovering how superfluous, though time-saving, most of our possessions are; and it shocks one to realise how much we waste. Here every banana-skin is eagerly devoured by some bony passing cow, and every discarded sheet of newspaper has a use, and every empty tin, bottle or box is treasured.
Rachel is now able to hobble around our rooms at top speed, but until her wound is healed she must avoid infected dust so she rode piggyback this morning to visit the Machiahs. We were guided by a little old Harijan woman, with teeth that have been broken and blackened by a lifetime of betel chewing, who lives in our compound. She does errands for anybody who will give her a few paise, and Mrs Machiah had instructed her to show us the way.
Crossing the farmyard behind our house we came to the Devangeri maidan, and then to a rough, dusty, hilly track running west for about two miles through paddy, scrub and forest. It forks at a settlement of substantial Muslim cottages, barns and cattle-shelters – Coorg seems to have no slummy shacks or hovels – and turning right here one descends to a level expanse of stubble, beyond which rises a steep ridge. On this stands the Machiahs' house, surrounded by richly scented rose-bushes, many varieties of flowering shrubs, and papaya, orange and supporta trees draped with black pepper and loofah vines. The Machiahs spent most of their working lives in Bombay, where Mr Machiah was a senior railway official, and I have rarely met a couple who are so zestfully enjoying retirement.
While we sat on the veranda, drinking our _nimbu pane_ , Mr Machiah explained the exact significance of the Coorgs' sacred brass wall-lamps. All important family decisions and events must take place before the lamp and agreements made, or loans given or received in its presence, require no signed document or other formality since it is an unforgivable sin to break a promise to which the lamp has been 'witness'. In each household the sacred lamp must be lit morning and evening and it is unlucky to say, 'The lamp has gone out.' Instead, one says, 'Make the lamp glow more.' The prayer-room should never be defiled in any way, so when passing through it at Devangeri we must always take off our shoes.
Mrs Machiah invited us to stay for lunch, but I made an excuse about having to go to Virajpet as I hope to establish a casual two-way dropping-in relationship, on the Irish pattern. However, we were sent off laden with sun-warm fruit – a colossal papaya, a hand of bananas and a dozen supportas.
Butter and cheese are virtually unknown here, but we have both become enslaved to the fabulous Coorg honey. It tastes, in truth, like a food of the gods – which is not surprising, given the variety of flowering trees from which the local bees operate.
This afternoon, in Virajpet, an enthusiastic young man in the South Coorg Honey Co-operative told me there are more than 16,000 beekeepers in Coorg, where it is the main cottage industry. But he complained that the average production of honey per hive was only ten to fifteen pounds, compared to almost fifty pounds in the United States. 'Never mind,' said I (who know nothing whatever of sericulture), 'perhaps you can't have both quality and quantity.'
The young man sighed. 'You think not? Then it is better to have quantity and get more money – don't you agree?' And he looked baffled when I replied coldly that I did not.
Already I am being made to feel a part of Devangeri. As I walked home several strangers stopped me to ask how Rachel's foot is today, and how long we are going to stay here, and why I like Coorg so much. The Coorgs seem always ready to stop for a chat, instead of staring suspiciously, as so many Indians do, or turning away to laugh at one behind their hands.
Tonight I have a sore tooth – the penalty for excessive thrift. I bought the cheapest dahl in the bazaar and it was so lavishly adulterated with fine gravel that I am lucky to have any teeth left. Tomorrow I shall present the rest of the dahl to Shanti, who doubtless is more expert than I at the skilled work of unadulterating grain.
## JANUARY 13TH
An uneventful day, full of beauty and contentment. This morning we went for a three-hour walk through the splendidly untouched forest north of Devangeri and – today being Sunday – passed several huntsmen carrying guns and hoping to go home with a deer, a wild boar or at least a rabbit. I had not thought there were any rabbits in India, but the locals assure me there are. Perhaps they were imported to certain regions by the British. As the Coorgs were never bound by the Indian Arms Act they have remained keen _shikaris_ , which explains the total absence of monkeys in these forests; unlike most Hindus, the Coorgs do not regard monkeys as sacred animals but as crop-destroying pests and good meals.
The few people we met all wanted to know why I was walking briskly towards nowhere in the heat of the day with a large child on my back. When I explained that I was simply walking for fun, to enjoy the landscape, they plainly either disbelieved me or thought I was at an advanced stage of mental decomposition.
On our way home we came on three _Ain Manes_ and, when we investigated these, were of course observed and invited in to drink coffee or _nimbu pane_. A typical _Ain Mane_ is approached by a long, narrow, winding lane – an _oni_ – cut deep through the reddish soil of a coffee-plantation, with seven-foot-high banks. At the end of this _oni_ are substantial red-tiled cattle-sheds and outbuildings – often two centuries old, yet kept in perfect repair – and then comes a paved threshing-yard with a slim stone pillar in the middle and mango and flame-of-the-forest trees around the edge. Half a dozen stone steps lead up from the yard to a long, deep veranda – the _Kayyale_ – which is reserved for the elders of the family, who gather there to relax, chat, play cards, confer, drink, arrive at decisions and receive guests. Usually the sturdy wooden veranda pillars are lavishly carved with gods, cows, birds, fish, lizards, snakes, elephants and flowers.
The traditional _Ain Mane_ is a handsome, massive, four-winged structure; in far-off days it often served as a fortress, like the Nair houses of Kerala. Half a century ago, before families became so fragmented, it was not uncommon for one _Ain_ house to shelter seventy or eighty people, perhaps representing five generations, while it was normal to have forty or fifty family members living permanently under one roof. Yet the process of fragmentation began long ago, under the Lingayat Rajas, who feared the power of some of the richer and more enterprising families. These Rajas actively encouraged the establishment of separate homes by Coorgs who had come into property through marriage, or who for some reason had had to leave the ancestral _nad_ , and the British presence and the development of coffee plantations accentuated this tendency.
At the first _Ain Mane_ we chanced on, our hostess took us indoors to see the general plan of the house. 'Indoors', however, is not quite the right word, for on passing through the heavy, intricately carved main door one is in the _Nadu Mane_ , an enormous square hall open to the sky in the centre, where four pillars stand at the corners of a deep depression in the floor – looking not unlike an empty swimming pool – which is of great importance during wedding ceremonies. Formerly the _Nadu Mane_ was used as a dormitory by the young unmarried men of the family, and the kitchen, bedrooms for married couples, guest-rooms, children's rooms and prayer-room all lead off it. Most of the rooms are small, with high, raftered ceilings and beaten earth floors, and though they are kept scrupulously clean their ventilation and lighting are poor.
Each _Ain Mane_ has either a _Karona Kala_ or a _Kaimata_ quite close to the house. The former is a raised earthen platform built around the trunk of a milk-exuding – and therefore revered – tree, and reinforced with stones, rather like the Nepalese porters' resting places. Here, however, such platforms are for ancestor-veneration and the little shrines built on them face east, sun-worship being so closely interwoven with the Coorgs' religious life. The _Kaimatas_ seem to be a fairly recent development of these ancient _Karona Kalas_. They are substantial single-roomed 'chapels' dedicated to particular ancestors who died bravely in battle, or otherwise distinguished themselves, and they often contain Islamic-type gravestones though the ancestors in question have usually been cremated and cast upon the waters. Within most _Kaimatas_ crudely carved stones represent the ancestors and on all important occasions a little meat curry, rice and Arak are offered to these on a plantain leaf. There is an annual Day of Propitiation, too – known as _Karona Barani_ – when special offerings of food and liquor are made. And, not content with all this, some families – like the Chengappas – have evolved their own particular forms of _Karona_ -worship, adjusted to the individual characters, noteworthy deeds or possible present needs of their forebears.
We spent the late afternoon sitting in our own backyard, watching the threshers through a haze of golden dust. Nothing could be more primitive than their methods. Each sheaf of paddy is beaten on a long, flat stone, just as a _dhobi_ beats clothes, and as the grain falls to the ground it is swept up with a grass broom and shovelled into a sack. Because of the threshing our yard is more populated these days than it normally would be and we are a marvellous added attraction – something like a sideshow at a circus. At all hours people wander up to our apartment to observe the odd habits of foreigners: but they never stay long or handle anything – just study us shyly from the top of the ladder.
To add to the charms of Coorg, there are no insects in this house apart from an occasional housefly. No mosquitoes, no ants, no fleas, bedbugs, cockroaches, spiders, lice or weird unnameables such as afflicted me in my Nepal home when I wrote – as I do here – by candlelight, near a broken window. Outside, of course, there are various types of large and vicious ants. Probably the red tree-ants inflict the most excruciating bite. I absently sat on some this morning, while resting in the forest, and as a result I now find it very hard to rest anywhere.
## JANUARY 14TH
The fact that I do not recoil from Coorg's curiously anglicised atmosphere must be partly owing to the unusual historical process that brought Coorg under the British. It was never subjected to Government of India laws unless these had been made specifically applicable to it and the Raj, having been invited to stay, wisely adopted a policy of 'Coorg for the Coorgs' and gave most of the subordinate jobs in the government service to the scions of old Coorg families. (The senior posts were of course never open to Indians, however able they might be.) Thus the local British ghost is quite unlike the spirit that lingers in Ooty or Simla, though during the second half of the nineteenth century the Coorgs enthusiastically adopted the English educational system – not to mention hockey, cricket and whisky.
In the November 1922 issue of _Blackwoods_ , Hilton Brown, an ICS officer, wrote: 'There is just one disconcerting feature about the Coorgs – their ready willingness to be dominated by the outsider... The Coorg's profession is all to the contrary, but the fact remains... It is very puzzling, for it is just what one would _not_ expect... The Coorg can think for himself, and he ought to; but very often he won't.' I wonder, however, if Mr Brown was altogether right. It is arguable that the Coorgs have a history of being dominated by outsiders not because of any innate tendency to submit but because they have never been able to unite effectively for the good of their country. Up to the beginning of the seventeenth century this tiny region was never ruled by any one dynasty but by numerous princelings and chieftains owing allegiance to bigger outside powers.
My old friend the _Gazetteer_ emphasises the benefits conferred on Coorg by the Raj, yet during the restless 1920s the Coorg Landholders' Association was formed to demand – unsuccessfully – a greater share in the running of the province. Then in 1940, as part of a government economy campaign, Coorg became 'a self-sufficient unit with all the offices located within its territory and was governed by a full-time Chief Commissioner'.
So the scene was set for much post-Independence political agitation in a province where the powerful Coorg minority wished their land to remain 'a self-sufficient unit', while many of the less influential non-Coorg majority favoured a merger with Mysore (now Karnataka) State. From March 1952 until November 1956 the province had what was known as a 'Popular Government' with a two-man ministry; but 'popular' proved a very inappropriate adjective and by 1956 many previously staunch separatists had become so disillusioned by the inefficiency and corruption of their own Coorg politicians that they, too, advised a merger.
However, most Coorgs still bitterly resent their loss of independence; walking into Virajpet this morning I met no less than three men who made a point of telling me what a fine place this once was, when not being manipulated by the bureaucrats of Karnataka for their own ends. One middle-aged man, clad in patched pants and a threadbare shirt, gloomily quoted Abraham Lincoln – 'You cannot strengthen the weak by weakening the strong.' I do not know how real local grievances are, but one does see many signs of a recent decline in the region's traditional level of prosperity. For seventeen years the State government has been siphoning off, through taxation, a considerable proportion of Coorg's income and the Coorgs argue that it is grossly unjust to expect them to prop up the less fortunate areas of Karnataka. At first glance this reluctance to share their wealth seems ungenerous, but at second glance one realises that Lincoln was right. Applied to the vastness of Karnataka State that stream of wealth which would suffice to keep Coorg happy and healthy makes little impression, while its deflection from Coorg has already had perceptible ill-effects.
One is very aware, here in Devangeri, of witnessing a society in transition. This evening Dr Chengappa arrived with his eighteen-year-old daughter whose duty it was, as the eldest maiden in the family, to initiate the storing of this year's crop by carrying a basket of paddy on her head from the threshing-yard to the granary. She is an extremely sophisticated young woman who speaks faultless English and, as I sat on a window ledge, looking down at that elegant figure ceremoniously crossing the compound with its unaccustomed burden, I wondered if her daughter will in time do likewise, or if she represents the last generation of tradition-observing Coorgs.
## JANUARY 15TH
We lunched with the Machiahs today and on arrival found Mr Machiah sewing up big sacks of paddy to be sent to his three married sons in Bombay. One daughter-in-law is a Cochin Christian, but the Machiahs seem as fond of her as of the two Coorg girls whom they themselves chose. Although the Coorgs are so proud of being a race apart, they are more socially flexible than most Indians. No doubt they are secretly saddened when their children marry non-Coorgs, but the majority warmly welcome outsiders into their little community. Such marriages are now becoming much commoner and there is a danger that eventually the 80,000 or so Coorgs may lose their identity amidst India's hundreds of millions.
We had a delicious lunch, cooked by Mrs Machiah, and everything on the table was home-produced: steamed rice, fried chicken, cabbage so cunningly cooked it bore not the slightest resemblance to what we call boiled cabbage, egg and tomato salad, rice bread, crisp, subtly flavoured potato-cakes (these specially prepared to honour the Irish), fruit salad and coffee. Unlike most South Indians, the meat-eating Coorgs do not care for very hot foods and are such good cooks that I foresee my middle-aged spread getting altogether out of control here.
To my annoyance – and to the great glee of all onlookers – the antique well in the compound utterly defeats me so someone else must fill my bucket and keep the great earthen water-pot in the latrine topped up. Because of caste laws, this is a slightly complicated situation. No Harijan can draw water from our well, and no non-Harijan will enter our latrine. So I myself have to top up the latrine container with water drawn by Subaya or Shanti, poured by them into the large brass wash-room jar, and transferred by me into the latrine container. It would be only too easy unwittingly to do something dreadfully polluting – like borrowing a cooking vessel from the kitchen – which would involve the family in an elaborate and expensive purification ceremony. One is therefore permanently on the alert, watching out for disapproving glances.
## JANUARY 16TH
I realised today that I have not yet adequately described Devangeri. It is a typical Coorg non-village, consisting of our house – the manor, as it were – the two schools already mentioned and a few score homesteads and thatched labourers' cottages, scattered over an area of two or three square miles. Behind our house is a long, two-storeyed building with an outside stairs at one gable-end leading up to the local Co-operative Society's offices and storerooms. The ground floor of this building accommodates the tiny post office – which opens only for brief periods at irregular intervals – and the village tailor's workshop, and a mini tea-house where card-players gather, and a twilit general store too small to hold more than one customer at a time. Anybody who happens to be expecting a letter saunters along to collect it during the forenoon, or sends a servant to fetch it, and so far I have heard no complaints though the battered and rusted metal box to which one entrusts outgoing mail has been _in situ_ since the reign of Queen Victoria. I buy my kerosene (a litre in an Arak bottle for one rupee) from the store: but nothing else, as village hucksters charge at least 20 per cent more than bazaar merchants, and adulterate even such unlikely things as soap and candles – which have probably been adulterated once already, before leaving their respective factories.
At a little distance from the Co-operative building, on the edge of the forest, stands our 'local', a ramshackle cottage from which Subaya every morning procures my breakfast litre of palm-toddy – in another Arak bottle – for fifty paise. (Where else, nowadays, could one buy a litre of beer for two and a half pence?) This potation is taken from the toddy-palm at dawn, in an earthenware pot that was attached to the top of the tree by a tapper the previous evening, and it arrives in our room fermenting on the wing, as you might say, with numerous dead ants almost blocking the neck of the bottle. If one neglects to drink it within a few hours it is said to do terrible things to the innards, so at last I have an excuse for drinking beer with my breakfast. It is most refreshing, whitish in colour and with a low yet perceptible alcohol content. The Coorgs think it so health-giving that even elderly female pillars of respectability habitually have a glass (but not, admittedly, a litre) before breakfast.
At all hours of the day, Devangeri's alcoholics may be seen sitting on benches outside the local, clutching tumblers of neat, potentially lethal, home-distilled Arak. According to sacred Hindu laws the drinking of alcohol is a most grievous sin, for which the orthodox atonement is suicide by drinking boiling spirits – though it seems unlikely that anyone impious enough deliberately to drink alcohol would afterwards feel remorseful enough to take his own life. At all events, the Coorgs have never heeded this prohibition and excessive drinking is undoubtedly their worst collective fault. Often men stagger home at lunchtime, unable to keep upright without assistance, and local reactions to this spectacle remind me very much of Ireland. People are mildly amused, or affectionately chiding, or ribaldly witty, or occasionally slightly impatient – but never critical. (Except of course for the more responsible members of the community, who think about the drunkard's wife and children.)
I was diverted this evening by the section on Prohibition in the 1965 _Coorg Gazetteer_. Passages are worth quoting: and the reader should bear in mind that the Prohibition Laws have since been allowed to fall into disuse.
It has been laid down in the Constitution as a directive principle of State policy, that the State shall endeavour to bring about Prohibition of the consumption – except for medical purposes – of intoxicating drinks and drugs which are injurious to health. Drink has generally been responsible for the poverty and misery of man, sinking him lower and lower into depths of danger and despair. There is no gainsaying the fact that prohibition is a social as well as an economic necessity and it acts as the fulcrum and force in our economic programme for social amelioration... Though prohibition was formally inaugurated on the 2nd April 1956, effective enforcement began only on 25th April 1956, leaving reasonable time for consumers to adjust themselves to the new circumstances... [And to make Other Arrangements]... Permits for possession and consumption of liquor were issued only in exceptional cases; they were issued to (i) those who were accustomed to take liquor, (ii) non-proprietary clubs for sale to such of their members as held permits and (iii) the church authorities for sacramental purposes... Government have sustained a loss of about twelve lakhs of rupees annually, consequent on the introduction of prohibition in the district... As is to be expected, illicit distillation followed in the wake of prohibition... The incidence of illicit distillery cases was high in the year 1962, 1,846 cases [in tiny Coorg!] having been detected during that year.
The introduction of prohibition has already brought a change in the social outlook of the people who were once accustomed to drink. It has brought peace to their homes and enabled them to save money, pay old debts, purchase new clothes, eat better food and lead healthier lives... The general feeling among the public, however, remained that... the prohibition law was contravened on a large scale and the percentage of convictions was very low... it has to be admitted that the number of permits issued appears to be large. Action is being taken to restrict the number, only to deserving cases.
But alas for the prohibitionists, those 'deserving cases' soon came to form the majority of the population of Coorg, and eventually the whole dotty though well-meaning experiment was tacitly acknowledged to be no more than a breeding ground for bribery and corruption. I dare say something similar would happen if anybody tried to enforce prohibition in Ireland.
Reverting to the Hindu sacred law on alcohol: for years I have wondered why it was so fanatical (by any reckoning, suicide as an atonement is going a bit far), and at Cape Comorin I got a plausible explanation from a splendid old Brahman scholar with whom we watched the sunset. It seems that when the Aryans arrived in India they were confirmed _soma_ addicts, and because they assumed their gods must also enjoy this psychedelic drink they decently fixed them a _soma_ whenever they made a ritual sacrifice. By the end of the Vedic period _soma_ drinking had come to dominate their religious ceremonies and the severity of the anti-alcohol laws was part of a successful attempt to have harmless rhubarb juice substituted for the juice of the extremely dangerous hallucinogenic red-capped mushroom, which is now accepted by most experts as the source of _soma_. Neat _soma_ is a deadly poison, but blended with honey, milk and water it becomes palatable. Its addicts were evidently not too fussy about flavour since laymen commonly collected for their own consumption the urine of _soma_ -drinking priests.
Virajpet's post office is the oldest such establishment in Coorg – and looks it. This morning, when I patronised it for the first time, a clerk became excessively agitated at the prospect of having to register four airmail letters to Ireland, and the unruly behaviour of the crowd around me did nothing to help him regain his composure. It had taken me fifteen minutes to establish myself in a position of negotiation, to the forefront of this crowd, and in order to retain my advantage I had to grip the shelf in front of me very firmly: otherwise I would have been pushed beyond reach and sight of the clerk. Meanwhile he, poor man – looking not unlike a harassed rabbit, behind his wire netting – had to thumb through two grimy volumes, and do intricate calculations on blotting-pads, to enable him to arrive at some plausible conclusion about my letters. While he thus did his duty several of the rowdier members of the crowd yelled abuse at him and demanded to be given fifteen paise stamps _at once_. It was easy to see how their minds were working. _They_ only wanted one stamp each, for which they were clutching the right number of coins in their fists, whereas _I_ wanted to transact an infinitely complicated piece of business which might take hours. (In fact it took precisely forty-three minutes.) To placate them the clerk at intervals pushed a few fifteen paise stamps across the shelf, which naturally encouraged another importunate scrum to form around me. There must have been at least fifty jostling, shouting men on that veranda when suddenly one tall, elderly Coorg appeared and said a few sharp words. Instantly the crowd fell back and was silent, not advancing again until I had finished my business. I do not know who this gentleman was, but there could be no more striking example of the Coorg community – minority though it is – or of the enduringly feudal structure of Coorg society.
## JANUARY 17TH
This morning Rachel suddenly announced, 'I think I'll be able to walk properly today' – which she was, though wearing only a sock over the thick bandage on her injured foot.
After lunch we went to the Machiahs in quest of eggs, Mrs Machiah having agreed to become our supplier. But today there were none because during the past few nights a mongoose and a jackal have between them decimated the hen population. Early this morning Mr Machiah shot the jackal and gave it to a local outcaste eccentric who relishes jackal flesh – a rare taste, even among outcastes. It is less easy to eliminate a mongoose, and anyway these pretty little creatures kill so many snakes and rats that they deserve an occasional banquet of chicken. We saw one this afternoon, racing across the path near the Machiahs' house. The culprit, no doubt.
Today's domestic excitement was the purchase of twenty large sardines for one rupee. I bought them from a ragged youth found sitting on the back doorstep and unmistakably they were fresh, but had I known the wretched things would take an hour and forty minutes to clean I might have felt less enthusiastic. The minute scales proved extremely adhesive, first to their owners and then to everything in the kitchen corner of our living-room. Also, if not gutted very delicately they went to pieces in me 'and, and their multitudinous fins required no less skilful treatment. By the end of that session I had had the simple life and could entirely see the point of buying tinned sardines.
On the whole, however, I am enormously enjoying the rhythm of these Devangeri days. Nothing much happens here, or is ever likely to happen, and if one did not have a lot of reading and writing to do one would no doubt feel bored; but I consider it the ideal life. When I hear Subaya locking up after sunset, and going off to wherever he and his family sleep, I reflect that now it's just the Murphys and the Chengappa ancestors in residence. And if one can go by the 'feeling' of this whole huge silent house, lit only by the two candles flickering on my table, those ancestors are most amiable and welcoming. I am totally unpsychic, and not abnormally suggestible, but in a most curious and pleasing way I am aware of not being quite alone here. The house is companionable: let us leave it at that.
## JANUARY 19TH
This afternoon Mrs Machiah took us to meet cousins of hers who live just up the road but have been away during the past few weeks. The family consists of Lieutenant-Colonel (Rtd, and for some years past a coffee-planter) and Mrs Ayyappa, their twenty-year-old daughter Shirley and a fourteen-year-old son now at school in Ooty. The new Ayyappa bungalow – very handsome, with teak floors and rosewood ceilings – stands beside their old _Ain Mane_ but on a lower level, since no dwelling must overshadow the ancestral home. Mrs Ayyappa is a fanatical gardener who has created – starting from bare ground – what can only be described as a mini-Kew. Both she and Shirley are rather shy and very gentle and we are invited to drop in whenever we feel like it.
As we drank our coffee the talk was of inflation, civil disorder, food-adulteration and the oil-crisis. Colonel Ayyappa showed me a paragraph in today's _Deccan Herald_ , where India's Defence Minister, Jagjivan Ram, is quoted as having said, 'The Indian Penal Code provides the death penalty for murder by physical force or weapons, but those who kill people by adulterating medicines or food go practically untouched. Yet the gravity of the crime is far greater in the latter case and warrants a proportionate penalty.' Makes one think, as one goes forth into the bazaar with one's shopping basket. My only real fear is powdered glass in the sugar – a not unusual phenomenon, since some merchants think nothing of poisoning customers if they can thereby rake in a few extra rupees. Several (Hindu) friends have strongly advised me to buy only from Moplah (Muslim) merchants in Virajpet.
This evening, as I read Rachel's bedtime stories – from _The Heroes_ and _The Arabian Nights_ – it struck me that in future such stories are going to seem much more real to her. Grinding the day's supply of flour, drawing water from the well, going into the forest to collect firewood to cook the evening meal, fetching bales of cloth home from the bazaar on one's head, yoking the oxen, shaping and firing bricks to build a new home, hunting for meat, trimming the lamps at sunset, making offerings to the gods – all these are commonplace activities here, though weirder than space travel to Western children of the Technological Age.
CHAPTER THIRTEEN
# _Caste in Coorg_
## JANUARY 21ST
Last night I came across a remark made in a letter home by a newly arrived ambassador to India. 'No one,' he wrote, 'is allowed to marry outside his own caste or exercise any calling or art except his own.' That ambassador was the famous Megasthenes, whom Seleucus appointed some 2,300 years ago as his envoy to the Mauryan court of Chandragupta, and I thought of him again this afternoon when Rachel appeared at the top of our ladder in bewildered tears, sobbing that Subaya was very angry because she had been trying to persuade her Harijan friends to come upstairs to play with her toys.
Rachel is not easily reduced to tears so I can only suppose she had been frightened by something she could not understand – Subaya's outraged fury at the very thought of Untouchable children putting a foot over this threshold – and hurt by what, from her point of view, was the injustice of his reprimand. She has, after all, been brought up to invite anyone she likes into her own home, and I should have warned her that in India things are different.
In Indian cities, a foreigner might now live for weeks amongst Westernised Hindus without realising there was such a thing as a caste-system; yet one cannot live for twelve hours in rural India without having to accommodate it, and in the cities it has merely been modified – not abolished. Few 'twice-born' Hindus – however Westernised, atheistic, socialistic or liberal they may profess to be – would feel completely at ease sitting in a bus beside a latrine-cleaner.
As aggrieved Sahibs used to point out, when accused of maintaining a colour-bar, the inter-racial barriers in India were first erected by Hindus. (Though it is true the British did eventually become as socially exclusive, in their way, as any Brahman.) What I tried to convey to Rachel today is the strange fact that the majority of Hindus value the caste system just as much as we in the West now value the ideal of social equality. It is not an affliction they helplessly endure but an institution which gives an essential cohesion to their unique and otherwise disparate society. Hence the declaring illegal of Untouchability by the Indian Constitution can at present be little more than a formal salute to an alien concept. Many criticised Gandhi's singling out of Untouchability for abolition, leaving the rest of the caste structure intact, but the Mahatma well knew that the caste system could not exist without a foundation of Untouchables to take upon themselves those impurities which otherwise would pollute the whole of society.
Although Hinduism is renowned for its ability to absorb outside influences, and change them more than it is changed by them, it may now have reached a crisis point at which its genius for assimilation can no longer operate. Richard Lannoy has suggested 'institutionalised inequality' as one definition of the caste system and it is hard to see how the official Indian government policy of social equality can either be absorbed into Hinduism or democratically imposed on hundreds of millions of citizens to whom it is repugnant. Something, it would seem, has to give – and this time it may be Hinduism. But not yet.
At present – especially in South India – a man's caste, rather than his personal talents, determines the degree of political power he can obtain: and this is having a disastrous effect on the national morale. India's parliamentary democracy has of course given the uneducated but numerically more influential sub-castes an unprecedented opportunity to dominate their local scene; yet this opportunity is often wasted because caste still matters more than the interests or opinions of the individual voter.
Gandhi, among many others, argued that those verses from Hindu scripture commonly quoted in support of Untouchability were interpolations or misrepresentations – which is probably true, since one can hardly imagine any religious scriptures, however primitive, prescribing the degradation and exploitation of millions. But it is too late now to oppose the day-to-day working of the caste system with academic arguments. Our neighbours here in Devangeri are not concerned about Vedic authority, or about the compromises that may have been arrived at three millennia ago between Aryan kings and Harappan high priests. What matters to them is the magico-religious code they have learnt at their mothers' knees. This includes the lessons that faecal pollution is a spiritual and social calamity of the first magnitude, as is the slightest physical contact with a menstruating woman or an outcaste. And the Harijan child is taught, equally emphatically, to avoid contact with caste Hindus. Many Indian mothers habitually threaten their children with witches, ghosts and demons, or with Kali, the black goddess of destruction – or with pollution by an Untouchable, which is thus equated from infancy with the worst horrors imaginable.
Throughout history a basic fear of pollution has affected many peoples, though none so radically as the Hindus. And, since it is impossible even to try to understand the caste system without taking it into account, I must make the point that Hindu notions of pollution are not bounded by the laws of hygiene. Impurity is naturally associated with physical dirt, but there is much more to it than that – as may be seen from Mary Douglas's comments on the system underlying pollution rules:*
Defilement is never an isolated event. It cannot occur except in view of a systematic ordering of ideas. Hence any piecemeal interpretation of the pollution rules of another culture is bound to fail. For the only way in which pollution ideas make sense is in reference to a total structure of thought whose keystone, boundaries, margins and internal lines are held in relation by rituals of separation.
I have been fascinated to discover that Mrs Douglas uses the Coorgs as a typical example of 'corporate caste dread', despite their own frequent and vigorous affirmations that caste taboos matter less to them than to most Hindus. Perhaps the gentlemen do protest too much...
Hindus agree with Juvenal on the desirability of _mens sana in corpore sano_ , but popular Hindu theories about how to keep a body sound range from the comic to the tragic. There is a widespread belief that semen should be conserved because it is the vital essence of the individual man, which is made in the head, from blood, and sustains both physical and spiritual health while it is stored there. This nonsense must have led to even more tension and domestic unhappiness than the Roman Catholic Church's traditional teachings on sexual morality. It has also helped to lower the status of women, who are supposed to be much more lustful than men and are regarded as an ever-present threat to their husbands' general well-being. Many Hindus believe that sexually unsatisfied women become witches and revenge themselves in the most horrific ways on the whole male population. So it takes a brave as well as a self-controlled man to practise continence; and the birth-rate figures indicate that such men are scarce.
These curious biological misconceptions are also responsible for the obsessional attitudes of orthodox twice-born Hindus towards what and where they eat. Since the blood from which semen is made is itself manufactured out of the food one eats, any pollution reaching the stomach through the mouth will contaminate a man's vital essence.
All this might seem to indicate that 'institutionalised inequality' could be relatively easily abolished by some elementary scientific education. I have, however, mentioned only one of the caste system's many facets, and it is not hard to find Hindu doctors and scientists of repute who are as rigid about certain fundamental taboos as any unlettered peasant. They will not dread their wives turning into witches, but neither will they admit Untouchables into their homes. Also of course there are by now many educated Hindus who in most respects ignore the caste and pollution laws, but they represent only a tiny minority.
This afternoon, when I had soothed Rachel and done my best to soothe a still furiously muttering Subaya, I sat in the sun outside the back door while trimming beans for our supper. Rachel brought her toys out to the compound, in lieu of her Harijan friends coming upstairs, and after some time one of the little boys approached the back door and called to Subaya's small son, asking for a drink of water. This was at once provided, in a brass drinking vessel, and the little caste boy directed the little outcaste boy to pick half a coconut-shell off the dusty ground and hold it out to be filled. When the water had been drunk the Harijan – who is six years old – took the shell to the edge of the compound and carefully threw it into some undergrowth where it could pollute nobody. Clearly these two boys are good friends within the limits imposed by caste – limits which both have recognised and accepted from the age of two or three.
It is when one moves up in the social scale that the contemporary caste situation becomes somewhat confused, because of individuals or families being at various subtly graded stages of 'liberation'. The Machiahs, for instance, after a lifetime in Bombay, are far less pollution-conscious than most stay-at-home Coorgs. They allow their Harijan neighbours to use their well – an enormous concession – and even employ some of them in the house, though not in the kitchen. Yet I found the unpredictability of caste attitudes well illustrated the other day by Mrs Machiah, when she and Rachel and I were walking back from the Ayyappas' house. Ahead of us on the road Rachel saw one of her favourite playmates – an enchanting five-year-old Harijan girl, who admittedly is always filthy – and immediately she ran to her and slipped an arm through hers. Away they went, skipping together in a continuation of some game started that morning, and I turned to Mrs Machiah, about to remark on the little girl's charm. But my companion's expression silenced me. She called Rachel, and I hesitated, caught between the devil of offending our friend's susceptibilities and the deep blue sea of allowing my daughter to be polluted by caste-consciousness. Then, before I had resolved my dilemma, came the final twist to the situation. Suddenly the little girl's mother appeared out of the forest, with a load of firewood on her head, and shrieked angrily at her child not to touch the _mleccha_. Why? Surely even the most uninformed Harijan is aware that _mlecchas_ have no place – do not count, even as outcastes – in the world of caste? (A fact which of itself can give the foreigner in India a strange, underlying feeling of spiritual isolation.)
I longed to ask Mrs Machiah about this but the whole subject of Untouchability is such a delicate one that it has to be approached – if at all – with great tact; and the moment did not seem auspicious. Most educated Indians are now hypersensitive on caste issues, not necessarily because they themselves are ashamed of the institution but because they fancy all foreigners despise it. Often an Indian will – with good reason – accuse a foreigner of over-simplifying and misinterpreting caste, and will then himself add fuel to the fire of misinterpretation by asking defensively 'Don't you have your caste system? But you call it _class_! Where do you send your children to school? Who would you like them to marry? Who do you invite to have meals in your house? What part of your town do you live in?'
At first one is stumped by this, yet the similarity is slight between our constantly changing social classes and the completely segregated units which make up Indian society. The Portuguese saw this at a glance, when they arrived in India in the sixteenth century, and it was they who provided the word _castas_ (derived from the Latin _castus_ ) to describe the intricate network of innumerable _jatis_ (sub-castes) into which Hindu society had evolved by about the sixth century BC.
It is most misleading to refer to 'the four castes'; life in India would be very different if each of its 454 million Hindus belonged to one of only four groups. What really counts is one's _jati_ (the word means 'birth'), which is determined by specialised, hereditary occupation, and it does not at all follow that because two people belong to the same main caste or _varna_ they can marry, or eat together. _Varna_ – the Sanskrit word for caste – literally means 'colour', and even today an ugly, ill-made, fair-skinned Indian will be regarded as incomparably better-looking than someone who is handsome and well-built, but dark-skinned.
There is an obvious parallel between the situation and behaviour of the Aryans, when newly arrived in India, and that of the Europeans in South Africa today. India's Aryan conquerors were divided into three rudimentary, non-hereditary social classes – warriors, priests and common people – and were free of any taboos about intermarriage or eating together. But they were a tiny minority amongst the conquered Dasa, those indigenous, dark-skinned, flat-featured owners and cultivators of the land. (The word _dasa_ later came to mean 'slave', which sufficiently explains the fate of these people.) Therefore, the instinct to preserve racial identity being very powerful, they made rigid laws – almost exactly copied by the white South Africans – forbidding inter-racial marriage and enforcing segregation. Much interbreeding of course took place before the caste system was developed enough to make such a thing psychologically impossible. But those of mixed blood were firmly consigned, with the Dasas, to the fourth caste (the _shudras_ ) who could never take part in Vedic rituals but were left to worship their own primitive, animistic spirits – which they still do, all over India.
## JANUARY 22ND
Today we went by bus to Mercara, to borrow books from the public library, and the twenty-six mile journey took two-and-a-quarter hours. Sitting beside us was a Devangeri neighbour, a slim, trim little man who has recently retired from the civil service and come back to his _Ain Mane_. He told me that oranges are the third most important crop in Coorg, after rice and coffee, and that the sweet, loose-skinned Coorg mandarins are famous throughout South India. But it seems the Coorg farmers – whose traditional rice cultivation methods are so scientific – do not make efficient orange growers. The main season is from December to March and most of the crop is transported by truck to Mysore, Bangalore and other cities. Pepper, he said, is another important sideline; it requires a lot of care, and the picking of the pods is a delicate and laborious business, but because of its value as a dollar earner this crop is being officially encouraged. (Coorg's annual output during the 1960s was about one hundred and twenty tons – a lot of pepper.) Cardamom, too, earns dollars; it grows wild in the evergreen forest along the ghats and government loans are available to farmers who wish to start plantations.
Mercara, when we first saw it, seemed an enchanting little backwater. But this morning, when we arrived fresh from our forest retreat, I felt myself in a bustling metropolis. To our great delight we met a party of elderly Tibetans from Bylekuppa, who had come up on one of their regular trading trips, and we all lunched together at the bus-stand restaurant. I had intended entertaining them, but to my discomfiture the charming old man who seemed to be their leader was adamant that the _ferenghis_ should be his guests.
We returned to Mill Point on the same bus with the same crew and I noticed that as a temporary 'local' I am not being asked to pay for Rachel. This time the journey took three hours because during the threshing season every travelling Coorg is accompanied by sacks of paddy. The rich move it by car or jeep (a distant jeep overloaded with sacks looks strangely like some prehistoric beast lumbering across the landscape), but the less rich move it by bus. And if half a dozen passengers are waiting every few miles with a few sacks each, and if all those sacks have to be carefully secured to the roof, and equally carefully handed down four or five miles farther on – well then naturally it takes three hours to cover twenty-six miles.
## JANUARY 26TH
India's Republic Day – and I think of ten years ago, when I attended the superbly organised triumphal parade in New Delhi, and watched Pandit Nehru and Lord Mountbatten drive down Rajpath four months before the prime minister's death. Today felt very different. All over India the celebrations were either cancelled or drastically curtailed, in deference to the world oil-crisis and the domestic economic crisis, which has led to police killing many food shop looters in states where millions are starving, resentful and violence-prone. On Monday next most Kerala schools and colleges are to be given a holiday because organised mass-opposition to the government's food policy is planned for that day and could lead to further serious rioting – and deaths.
Republic Day has made no impression on Devangeri, apart from the formal ceremony at the local school to which Rachel and I were invited. To my intense alarm I found that I was expected not only to hoist the national flag at the opening of the ceremony but to make a speech. Rachel, however, was thrilled – especially when I at last got hold of the right bit of rope and, as the flag unfurled, she saw a shower of multi-coloured forest blossoms fluttering down to cover my head and shoulders.
I felt quite exhausted after my efforts to communicate with the young teachers, none of whom is fit to teach English. Yet this is one of the three languages which Devangeri schoolchildren have to go through the motions of learning. (The others are Hindi and Kannada.)
India's linguistic problems seem almost as complicated as the caste question and a good deal more controversial. According to the 'Three Language Formula', approved in 1961 by a conference of chief ministers from India's various states, schoolchildren in non-Hindi-speaking areas have to learn Hindi as well as their mother tongue and English. There are over 133 million Hindi-speakers, so more Indians speak this language than any other. Yet in a population of 560 million it cannot be described as the language of the majority, as is frequently pointed out by the 37 million Bengali-speakers, the 30 million Tamil-speakers, the 17 million Malayalam-speakers, the 17 million Kannada-speakers, the 15 million Oriya-speakers, the 10 million Punjabi-speakers – and so on, and on, and on, down to the 142,003 Bhumji-speakers and the 109,401 Parji-speakers.
The 1971 Census showed that since 1951 the literacy rate has gone up from 16.6 per cent to 29.45 per cent. However, with only 39.45 per cent of men and 18.70 per cent of women literate at present, in any language, it would seem rather too soon to attempt to teach Indian schoolchildren three languages, each with a different script.
The nineteen-point official programme for the 'propagation, development and enrichment of Hindi' seems utterly artificial – another, self-imposed, cross for India to bear. South Indians naturally wish the funds and energies now being expended on Hindi could be diverted to providing free primary education in those areas where it is not yet available, or to expanding the well-planned Farmers' Functional Literacy Programme, which has already made some 80,000 adult farmers more accessible to advice on how to increase food production.
The status of the English language provokes a more complex set of arguments, though the two controversies overlap when opponents of Hindi affirm that English – or 'Indish', as Indianised English is often called – is the obvious _lingua franca_ for India. An increasing number of educated Indians long to reclaim their own culture and do not believe this can be done while India's intellectual life is dominated by an English-speaking, English-reading and therefore English- _thinking_ elite. For centuries Indian culture – apart from music and the dance – has been moribund, submerged first by the Mughals and then by that tidal wave of anglicisation which inundated the land as a result of Thomas Babington Macaulay's historic 'Minute' of 2 February 1835.
Macaulay envisaged 'a class of people who can act as intermediaries between us and the millions we govern: English in taste, in opinions, in morals, and in intellect' – and quite soon India had got what Macaulay wanted. The then Governor-General, Lord William Bentinck, had himself referred six years earlier to 'the British language, the key to all improvements'; and on 7 March 1835, with the support of Macaulay and Ram Mohan Roy, leader of the more progressive Bengali intellectuals, he made English the official language of the subcontinent – instead of Persian, the language of the Mughal court.
Since then, speaking English and sending children to English-medium schools has acquired an absurd snob-value. Those who have the means and leisure to practise the arts themselves, or to support creative Indians in practical ways, now too often feel it necessary to despise their own culture. Also, educational aims have become confused, with students attaching greater significance to the English language, as such, than to those subjects they are supposed to be mastering through the medium of English. More important still, the fact that so many of the governing classes live in a cultural world apart means they tend to take an unreal view of India's basic problems.
In 1971 the Simla Congress of Indian Writers declared, 'The inescapable reality is that English continues to be the only expedient language throughout India.' This is very true, but what does seem necessary is an admission that it must remain a minority language – though this would involve switching to Indian languages in the universities. At present eleven million, or 2 per cent of the population, are described as 'English-knowing', but I have been warned that there is a sinister difference between 'English-knowing' and 'English-speaking'. The former applies to those who appear in the statistics as having studied English at school, the latter to the half-million or so who use the language a good deal more fluently and precisely than the average Englishman.
The happiest solution would be if English in India came to have the status of French in England and were regarded as an asset which, though valuable, is not essential to everybody's intellectual well-being. Then the lack of it need breed no inferiority complexes, nor deter creative Indian thinkers and writers from using their own ancient languages – which were expressing sophisticated philosophical concepts while Europeans were still grunting in holes in the ground.
## JANUARY 27TH
Every day I fall more seriously in love with Coorg; it is the only place, outside of my own little corner of Ireland, where I could imagine myself happy to live permanently. Several of our neighbours have wonderingly asked me, 'Don't you get bored, walking so much through the paddy and the forest?' And they look equally delighted and puzzled when I assure them that, far from getting bored, I every day derive more pleasure from their lovely land. Wherever one looks there is beauty, none of it spectacular or wild or dramatic but all of it profoundly satisfying. The light has that exhilarating clarity one expects only at a much higher altitude, the colours glow with magical vitality and the very air tastes good. Then there is the warmth of the Coorg welcome, which makes one feel soaked in contentment as the land itself is soaked in golden sunshine.
Coorg women have traditionally led freer and more active lives than most high-caste Hindu ladies, and the secretary/accountant of Devangeri's Co-operative Society is a competent, elegant young woman named Jagi Chinnappa, who lives about two miles away with her widowed mother, elder brother and nine-year-old sister. This morning, having been invited to spend the day with the Chinnappas, we started out after breakfast and half a mile beyond Mill Point turned into one of those narrow _onis_ that seem like paths to some secret paradise as they wind between high red earth embankments, under the shade of mango, peepul, jack-fruit, nellige and palm trees. When one leaves the motor-road, to approach any of Devangeri's component villages, there is nothing to indicate that one is living in 1974 instead of 1874.
We first paid our respects to Jagi's mother, who speaks no English and has a great sadness behind her eyes; one feels she is still grieving for her husband, who died six years ago when their youngest child was only three. Then Jagi took us to visit four other nearby homesteads, all occupied by her uncles and aunts. As the coffee-picking season has just started only elderly women or very small children were at home and outside every house was spread a carpet of red berries, which must lie for nine or ten days in the sun, to brown before being marketed. Coorg's main crops dovetail most conveniently, the paddy-threshing ending just when the coffee-picking must begin.
Coorg hospitality seems not merely a social duty but part of the people's religion. On each veranda – presided over by innumerable ancestral photographs – we had to partake of coffee, biscuits, savoury scraps with unpronounceable names, papaya knocked from the tree for us, yellow, red and green bananas, supportas, and delicious bull's-hearts, which look exactly like ox-hearts and have sweet, creamy flesh and many large, flat, shiny black seeds. At the end of all this I wondered where I was supposed to fit an Indian lunch for an honoured guest, but when I saw and smelt the meal my appetite revived. There were two sorts of rice – steamed and fried – curried sardines, salted raw shark, omelette with onion and exotic spices, pickled oranges, dahl, dhosies (delicious rice-flour pancakes) and fried cabbage. Jagi's mother hovered anxiously while we ate, obviously on tenterhooks lest her efforts proved unpalatable to the guests, and thus I was compelled, by politeness as well as greed, to overeat grossly. I was in a semi-coma as I panted under the midday sun up the steep slope to catch the Virajpet bus – Jagi having arranged (to my secret dismay) that we should spend the afternoon at the cinema.
The Technicolor Hindi film began in a packed 'Palas' at two o'clock. India has one of the four largest film industries in the world and film-going is by far the most popular form of entertainment for her illiterate 70 per cent. This gives film stars great power; in Bombay – the centre of the film industry – they have on occasions significantly influenced election results. They also raise vast sums through public appeals for flood or famine relief and they have even been known to calm hysterical mobs on the brink of violence.
The three-and-a-half hour film was Rachel's first experience of the cinema and she enjoyed every moment of it. Afterwards I asked Jagi if India's long-standing nationwide debate about kissing on the screen has yet been officially resolved: whereupon she blushed most becomingly, and looked with slightly raised eyebrows at her small sister and Rachel, and said 'No' in a very end-of-the-discussion voice. So evidently she herself is not one of the 'progressives' who favour a change in the law. Some people think it downright hypocritical that in India, where many forms of unnatural vice are graphically depicted in and around places of worship, it is illegal to show an innocent boy-kisses-girl shot on the screen. However, the unsophisticated majority do not find this stylised temple sculpture at all erotic; but as they still think it immodest to sit beside their spouses in a bus they would undoubtedly consider any love-making on the screen offensive. In 1968 the government set up a committee under Mr Justice Khosla to inquire into film censorship, and it recommended that kissing should be allowed on the screen where it could be justified for 'aesthetic or social reasons' – whatever these might be. But the traditionalists would not give in and so far the law remains unchanged.
Jagi had arranged that we should be picked up by a jeep which a cousin of hers is able to borrow – every Coorg cousin has multiple uses – and on the way home we overtook Tim and Sita, being driven to call on the Murphys.
It was good to see them again and, although they returned only yesterday from Madras, I was vastly amused to discover how much they already knew about our habits and customs. They had been told of all our movements since we settled here, down to the last particular – when we had lunched with whom, how long we stayed, what we ate most of, how far we walk, what times of the day I read and write, where we shop in the bazaar, what we buy, how often I do my _dhobi_ -work, when and how we went to Mercara and whom we met there, where my palm-toddy comes from and who has called on us for drinks. What astonishes me is the flawless accuracy of Coorg's bush-telegraph; despite the widespread nature of the gossip we have provoked, not one detail seems to have been distorted or exaggerated. The only thing Tim had been unable to find out was the exact ingredients of an MCC (Murphy's Coorg Cocktail). This blend of Arak, honey and fresh lime juice has deservedly (though I say it myself) become famous throughout the area for its agreeable taste and still more agreeable effects, which Tim and I were both enjoying when Sita broke the party up to get back to Green Hills in time for dinner.
* _Purity and Danger_ : Routledge and Kegan Paul (1966).
CHAPTER FOURTEEN
# _Forest Funeral_
## JANUARY 28TH
Today's social activities took us outside the Coorg community to lunch with a young couple who live about six miles away and spent an evening here last week sampling MCC. The husband – a scientist – studied abroad for eight years and belongs to a rich, fairly orthodox Hindu family from another part of South India, but the wife is a European. When first we met, on the street in Virajpet, she said to me by way of greeting, 'I _hate_ India!' And looking that day at her husband's strained little smile my heart sank, as a whole familiar situation – which never seems any the less tragic for being familiar – was revealed. Against a European background we have handsome, brilliant Indian boy meeting impressionable, naïve European girl whose ignorance of India is complete. They marry in Europe, and perhaps have their first child there, and then return to India where the dashing, exotic Indian bridegroom is reabsorbed into his family and becomes the peremptory Hindu husband. For most such wives, who may be many miles from their nearest fellow-European and have had no adequate preparation before the transplant to India, it is almost impossible to adjust to this country.
Let us call them Ram and Mary. They live in an amply staffed, very comfortable Coorg-built house which Mary thinks no better than a neolithic dwelling because it lacks electricity. Their two sons, aged three and five, are healthy and attractive: but Mary has her own ideas about child-rearing and these, naturally, do not coincide with Ram's. However, when we first spent an evening together at Green Hills, and again when they came to Devangeri last week, they gave a passable imitation of an affectionate young married couple, Western style. It was only today, seeing them in their own home, that I realised how delicately balanced such relationships are – how permanently in danger of being pushed, by a word or a glance, into some lonely chasm of misunderstanding.
Ram is extremely intelligent – already a name to be reckoned with in his own profession – and he is also a dedicated humanist, an outspoken opponent of traditional Hinduism in all its manifestations and an especially fervent crusader against priestly superstition. Yet on the domestic scene he reverts to type in an almost eerie way – one feels he has been taken over by forces too strong for him – and then he orders Mary around as though she were a not very bright child, showing her none of the normal courtesies Western women expect. He is, however, genuinely kind, and I suspect this behaviour may be in part a reaction to Mary's having as her birthright that freedom which he, as a liberal, agnostic young scientist, could have voluntarily conferred on a Hindu girl. He would probably have found it easier to live up to his ideals with a wife of his own kind – a well-educated, intelligent young Hindu whom he could have permitted to lead a liberated life without her ever becoming that challenge to his masculine authority which a European woman inevitably is. Mary is far less intelligent than Ram, but that does not prevent her from voicing strong personal opinions and the situation must be considerably exacerbated by her fatuous criticisms of Indian civilisation.
## JANUARY 29TH
Having Rachel here gives me a close-up view of the profound differences between Indian and Western child-rearing methods; and this in turn helps me to sympathise more easily with people like Ram. Many Indians from orthodox backgrounds who try to grow beyond the static forms of Hinduism find themselves thwarted by childhood attitudes and ideas which have become so firmly entwined with the fibres of their personality that they can never be completely discarded.
This afternoon a neighbour called to present us with a huge basket of plantains, and Rachel, as is her wont, rushed to show him the picture of a crocodile she had just completed. He laughed indulgently and said, 'But crocodiles don't really have such big teeth. And its legs are too long. And the colour is all wrong. Come – lend me your crayons and I'll show you how to draw a crocodile properly.'
Rachel's chin trembled. 'But that's the way I _imagine_ a crocodile,' she said unhappily. 'That's what he looks like in my _mind_ , when I _think_ about him.' And later, after our friend's departure, she asked me plaintively, 'Why do the Indians never like my paintings? You said you liked the crocodile. Don't they know I'm only _five_?'
I tried to explain that in this area Europeans and Indians have very different ideas. When Indian children attempt to exercise an adult skill their efforts are rarely judged as those of small children. Instead, they are irrationally expected to perform up to adult standards and are given no praise simply for _trying_. Their drawing or painting or modelling are seen not as forms of creative play but as failures. No doubt this comes of belonging to a society where economic necessity compels most children to perfect adult skills as soon as possible; but, whatever its cause, it has the indisputable effect of delaying development, withering self-confidence and severely discouraging the experimental, exploratory instinct. A child is unlikely to attempt some new achievement if he knows that failure will be derided and success only acknowledged if it is complete. Amidst a group of European five-year-olds Rachel seems a child of average intelligence: amidst a group of Indian five-year-olds she seems brilliant.
Rachel had just gone to bed this evening when the Chengappas called – father, mother and younger daughter. Mrs Chengappa, too, is a doctor, and yet another of those youthful-looking Coorg mothers with grown-up families who impress one equally by their brains, beauty, poise, humour and sheer strength of character. But she, especially, recalls one of my grandmother's favourite phrases, which I have not heard used for years: 'There is a woman of great presence.'
Halfway through his MCC, Dr Chengappa himself brought up the subject of the local Harijans so I felt free to ask why they have such an aversion to attending school. Since Independence the Indian Government has done everything possible to improve the lot of the 'Scheduled Castes' and Harijan children are issued free uniforms and books, and even hockey sticks, to entice them to school. In some areas both teachers and caste-Hindu parents are strongly opposed to Harijans attending government schools, but I know this is not the case here for I have several times seen teachers trying to convince Harijan parents of the benefits of education.
However, as Dr Chengappa said, the idea of schooling is so novel to this community, and so potentially disruptive to their simple economy, that in Coorg few are influenced by the promise of long-term advantages. They rarely go hungry here, and are accustomed to having children always available to do certain essential jobs while they themselves work to bring in the cash. Moreover, many are probably unable to grasp the magnitude of the change which has officially overtaken their section of the population within the past few decades; and perhaps it is just as well, at this stage of India's development, not to have hordes of unemployed college-educated Harijans added to the millions of young Indians already roaming the cities in search of jobs that do not exist.
## JANUARY 31ST
There is an Irish casualness about Devangeri's social life which naturally appeals to me. When people say 'Call any time' they really mean it: and they do likewise. This morning I was still enjoying my pre-breakfast read – Rachel having not yet been loosed upon the world – when Mr Machiah came bounding up the ladder. (He must be nearly seventy years old but is such a keep-fit enthusiast that he does still bound, even up our ladder.) Rachel of course was thrilled to hear the day's social round beginning so early and came prancing out in the nude, grinning from ear to ear. I made coffee and we discussed the tourist trade in South India, and then Mr Machiah went off to attend to his paddy-business in the compound.
Half an hour later Mrs Ayyappa dropped in for a chat and stayed until eleven, when she had to go home to supervise the cooking of lunch for nine Harijan labourers who are threshing paddy four miles from the house. Every day, for six weeks, nine large lunches of rice and vegetable curry (with trimmings) are wrapped in separate plantain leaves, tied with pepper-vine twine and dispatched in a basket on a servant girl's head to the threshing-ground. Some employers now provide extra money instead of food, but, as Mrs Ayyappa said, 'What use is money to hungry labourers who are seven miles from the nearest eating-house? They would only buy home-made liquor and spend the afternoon asleep instead of working.'
In Coorg, where the only readily available pastimes are reading, card-playing and conversation, one realises the extent to which, in the West, we have grown independent of our neighbours for entertainment. I suppose this is just one more milestone along mankind's road to a completely dehumanised existence. When I stop to think about it – as I did today, while chopping onions after Mrs Ayyappa's departure – it seems to me intensely alarming that so many of us now have to make an effort to 'fit people in' (even close friends) because of the many 'events' that make up the contemporary social rat race. Increasingly, we tend not to regard each other as capable of providing an evening's – or even an hour's – entertainment. The individual is becoming less and less important in comparison with the occasion that brings people together, whether it be a drinks party, a race meeting, going to the theatre, playing golf, attending a concert, skiing in the Alps – or simply watching television. And one wonders what will be the long-term effect of this changed emphasis on the significance of other people in our lives, this habit of regarding them as companionable accessories to the occasion, instead of as original sources of entertainment, worth being with for their own sakes. Most of our Coorg relationships can only be transitory, but already they have a substance they might never have attained against an urban background.
## FEBRUARY 2ND
Yesterday morning, on the bus to Mercara, we found ourselves sitting beside the wife of a first cousin of Dr Chengappa, who invited us to a Coorg wedding at the end of the month. It would not be a very big affair, she explained. Owing to inflation, there were unlikely to be more than 1,000 guests.
Because of the oil-crisis, one occasionally notices on the local buses richly dressed Coorg women who most certainly have never before boarded a bus. They slowly lever themselves in, holding their saris close to their legs while looking comically martyred. Often they are followed by their young, who regard bus journeys as an amusing glimpse of how the other half travels, and if there is no vacant seat the conductor will deferentially make one available – not, of course, because the newcomers are women, but because they are ladies.
Having changed our books at Mercara's library we set off to walk down the very beautiful mountain road, meaning to stop the bus when it came along; but soon we were picked up by two young cousins of the Andanipura Ayyappas who dropped us off at Mill Point. I had walked only a few steps towards home when an infected ant bite on my right heel – which had been throbbing all the previous night – burst rather hideously and it has been making me feel more than a little sorry for myself ever since.
This morning I longed for daughterless peace, after a second restless night, and when Rachel said wistfully that she wished someone could take her to the Machiahs I impulsively suggested – 'Why don't you go on your own? You should know your way round South Coorg by now.' I felt slightly appalled as I listened to my own words – and a good deal more appalled when Rachel's face lit up and she said, 'Oh, _goody_! May I really go on my own?'
'Of course,' I said, busily stiffening the upper lip. 'Why not? There's no traffic here. But don't stay for lunch. Be back at one o'clock. And stay on the path – don't walk in leaves.'
'Goodbye!' called Rachel, disappearing down the ladder to plunge into the depths of a snake-infested forest.
I immediately remembered an article in a recent issue of _The Illustrated Weekly of India_ giving snake-bite death statistics; the annual national average is 3,000. Then I reminded myself that 3,000 is very, very few out of 550 million – and anyway the statistics were probably inaccurate; villagers sometimes poison their enemies and blame snakes. On this consoling thought I settled down to chop cabbage for a salad.
The fact remains, however, that Coorg has more than the national average of snakes per square mile... Having finished the salad I lay down to ease my throbbing leg and sought to lose myself in Fraser's _Account of Coorg and the Coorgs under the Vila Rajas_. But I found Mr Fraser downright off-putting, for he chose on page three to inform me that 'there are seven varieties of poisonous snake common in Coorg'. Next I wrote two rather incoherent letters while drinking my litre of toddy, which came late today. Then I had a chaser of Arak – at 10.30 a.m., I blush to record. After that I re-read the snake article and noted that 62 per cent of India's snakes are non-poisonous. Having made some very strong black coffee I laced it with rum and told myself how lucky I was to have a non-clinging, self-sufficient, outgoing child. Drinking the coffee, I wrote another – even more incoherent – letter which I had just finished when Subaya appeared to inform me that Thimmiah Sahib was planning to call at noon. I leaped to my feet. Rachel dearly loves Tim and would be bitterly disappointed to miss him; so I must hasten to retrieve her, sore foot or not. It is only a slight exaggeration to say that you could not have seen me for dust between here and there.
Rachel was sitting on the veranda, 'helping' Uncle Machiah to chop betel nuts, and she observed my arrival with a perceptible lack of enthusiasm. 'I thought you were going to rest your foot,' she said coldly. 'What are you doing here?'
I explained.
'Oh,' said Rachel, 'I do want to see Uncle Tim. But you go ahead. I'll follow by myself – I know the way.'
As I limped home – painfully aware of my foot, now that the anaesthetic of anxiety had worn off – I could see my excessive fussing about snakes as a cover-up for something rather more complicated. If for five years and three months one has been an essential prop, it comes as a slight blow to the _amour propre_ when that prop is suddenly discarded. But now I feel we are over the worst; I cannot imagine myself ever again getting into such a flap without just cause.
## FEBRUARY 3RD
This being Friday, Dr Chengappa arrived at seven-fifteen to make his weekly offering to the ancestors. While brushing my teeth I could hear in the room below his murmured _mantras_ , and the distinctive, muffled thud of a sharp, heavy knife bisecting hairy coconuts – and then the splash of their milk, which is always followed by the dreamy pungency of incense wafting up the stairs.
The Coorgs' preoccupation with ancestor-veneration, added to their relative independence of the priestly caste, suggests that their religious beliefs have changed less, since the Vedic period, than those of most other Indians. One of the loveliest passages in the _Rig-Veda_ is an address to the spirit of a dead man, made while his body is burning on the funeral pyre, and even before those marvellous hymns were composed the veneration felt by the Indo-Aryans for their ancestors was an ancient tradition. They already possessed a vast treasury of myths when they entered India some 3,500 years ago – terrifying the people of the Indus Valley, who were far more civilised but had never heard of horse-drawn chariots. And these myths have ever since been interacting with that more cerebral religion of the Brahmans which was probably just beginning to burgeon in the Indus Valley at the time of the earliest Aryan invasions. Some of the results of this fusion are wildly irrational – notably the failure to eliminate ancestor-worship, despite the evolution of the doctrines of _karma_ and _samsara_ , and of a hereditary caste system. _Karma_ is not hereditary: one's children are not affected by the consequences of one's deeds in this life; and, according to the doctrine of _samsara_ , a virtuous man can be born into a higher caste in his next life, or a wicked man into a lower caste. Obviously, belief in a heavenly world full of immortal family ghosts cannot be reconciled with _samsara_ by any feat of mental gymnastics – yet for many centuries both beliefs have been held at the same time by millions of Hindus.
This sort of thing drives logical Western minds to the farthest extremes of intellectual discomfort, while leaving Indians apparently quite comfortable, thank you. And such fundamental ambiguities – which are so acceptable a part of Hindu culture that few Indians ever even notice them – contribute quite a lot to the difficulties of Europeans in India. Too often, the mutual understanding one has been working for, and which seems at last within reach, is suddenly swept out of sight by some unexpected, inexplicable eddy that has whirled to the surface of the Indian mind.
## FEBRUARY 5TH
Today we caught the noon bus to Virajpet and found it full of migrant tribal coffee-pickers – filthy, ragged, excessively uncouth in their habits, covered with crude jewellery and open sores, almost black-skinned, very small in stature and laden with babies. (There seemed to be no more than ten months between the countless children in each family: but I dare say this was an optical illusion.) Before circumstances drove them out of their jungles these people lived happy, healthy lives; now, despite all the official benefits and concessions to which they are entitled, many of them have sunk to the lowest level of degradation.
In Virajpet we lunched with a retired teacher who lives in a ramshackle little bungalow halfway up the hill. He had met us a few times around the town and pleadingly invited us to his home; his wife died recently and obviously he is still feeling very lonely.
Like most elderly educated Coorgs, Mr M—–— speaks conspicuously good English – precise without being pedantic – and he greatly deplores the present state of the nation's schools. He is even sceptical – with good reason, I should think – about the apparently improved literacy rate. In his view the Indian government got its priorities wrong at the outset. Thousands of schools and colleges have been built during the past twenty years and these make impressive statistics, if one does not know that most schools are without adequate staff or equipment. Obviously India's future would be much brighter today if the money wasted on buildings had been used to attract a better type of teacher. Nowadays even the most highly qualified and dedicated teachers cannot give of their best to their school duties because to feed their families they must overwork as private tutors. I assured Mr M—— that the quality of education is a problem all over the world, even in developed Western countries. To which he replied, 'Every problem is worse in India than almost anywhere else. And we cannot afford mistakes or vanity or pompous posturing. We have no margin for error. Our government's slips cannot be minor – they lead straight to disaster.'
It is odd how many Indians combine hypersensitivity to criticism from outsiders with an addiction to dwelling on – almost gloating over – their national defects. They seem to take a perverted sort of pride in their proneness to corruption, and a current 'funny story' – I've been told it three times in the past two days – was printed as a news item in the _Deccan Herald_. It concerns a young Bombay university lecturer who last week unsuccessfully attempted suicide because he had become so depressed by the blatant and universal (in cities) adulteration of food. When the contents of his stomach were analysed it was found that he had been sold poison so heavily adulterated it could not have killed a mouse...
## FEBRUARY 7TH
Today we lunched with the Hugheses and while we were waiting for the bus at Mill Point, and chatting to Uncle Machiah (who was going somewhere on _Aruva_ business) Rachel suddenly said, 'I have a very sore eye.'
I glanced at it and remarked in my callous way, 'It doesn't _look_ very sore.' But luckily Uncle Machiah was more compassionate and found a tick embedded in the left upper lid, between the eyelashes.
He is a wonderful person on such occasions – indeed, on every occasion. 'This happens quite often,' he said calmly, 'but it must be removed without delay. What could be more convenient? You are passing Ammathi Hospital on the way to Sidapur. Get off there and Dr Asrani will fix it in ten minutes. All you need is a drop of glycerine or liquid paraffin on the lid – when it has been loosened out it comes with a tweezers – no problem!'
By the time we got to Ammathi the lid had swollen perceptibly and there was a problem, because Dr Asrani had taken a fortnight's leave and his very young Tamil locum proved hair-raisingly incompetent. It was plain that within the ten days since Dr Asrani's departure the whole hospital had nose-dived into the depths of inefficiency, providing a striking example of how completely these small rural establishments depend on the standards of one man.
To begin with Dr P—–— diagnosed a sty instead of a tick, and when I had brusquely put him right – inwardly thanking the Lord for Uncle Machiah – he looked utterly nonplussed until I suggested glycerine or liquid paraffin. A search revealed that neither was available so we settled for Vaseline, applied with cotton wool, and proceeded to the treatment room where Rachel lay obediently on the couch. Then Dr P—–— turned to me and said briskly, 'You must please wait outside. You can come in when I have finished. Parents are never allowed in here.'
'They are, by Dr Asrani,' I retorted, feeling my blood temperature rising by several degrees. 'And I can assure you that I am not leaving this room until my daughter does.'
Dr P—–— looked considerably taken aback. 'You have been here before?' he asked.
'Yes,' I replied, 'I have.'
During this exchange Rachel had been lying calmly on the couch with her hand in mine, knowing quite well I would never desert her and obviously rather enjoying the adults' battle. She now asked, 'When is the doctor going to remove the tick?' and I looked questioningly at Dr P—–—.
In retrospect I can see the funny side of what followed, but at the time it left me shaking with rage. The nurse couldn't find the cotton wool, or tweezers, or any forceps smaller than a jack – and finally a forceps of more practical dimensions was produced by a sweeper who was carrying it in her bare hands. By this stage Dr P—–— was looking thoroughly demoralised. He sulkily obeyed when I ordered him to sterilise the forceps in my presence before putting it near Rachel's eyelid – a delay which may have done good by giving the Vaseline longer to work. When the 'operation' at last began the 'surgeon' made mighty heavy weather of it, though his patient, on maternal instructions, remained more unflinching than I could have believed possible. However, since the tick was extracted intact at the fifth attempt I suppose I should count my blessings and complain no more. As usual, Rachel rapidly recovered from her ordeal – though the eyelid is still very sore – and we arrived at Mylatpur in time for several _iced_ beers (forgotten luxury!) before lunch.
At three-thirty Jane drove us to Ammathi to catch the bus but it had made extra good time from Mercara and left ten minutes early; so we decided to hitch-hike. Often, in Coorg, drivers stop to offer unwanted lifts, but on the whole traffic is very light and this afternoon we saw not even a motor bicycle during our seven-mile walk from Ammathi to Devangeri.
Approaching Vontiangadi, poor Rachel became quite exhausted – she had already walked over three miles this morning – and as I was carrying fifty eggs, bought cheap from a mass-producer at Mylatpur, I was unable to provide a piggyback. But when the air began to cool at six o'clock she suddenly revived and finished the course at a gallop. It was a memorable walk, through the loveliest of this lovely region, and our road climbed high at just the right time to allow an unimpeded view of a vast fiery sunset behind the dark blue splendour of the ghats. Then came an unearthly pink glow, over our whole silent world of forest and paddy-valley, and Rachel was moved to lyricism – 'It looks as if a giant spilled his pink paint over everything!'
## FEBRUARY 8TH
This being Friday, Dr Chengappa arrived at seven-thirty and brought the sad news that last evening our tailor's thirty-six-year-old wife died in Virajpet hospital. The eldest of their three children, a clever girl in her first year at Bangalore University, will now have to give up her studies to look after her brothers, aged nine and thirteen.
We know the tailor, Ponappa, quite well – Rachel often visits his workroom and returns with great bunches of finger-bananas – so we accompanied Dr Chengappa and Uncle Machiah on their visit to the house of mourning. Outside a neat, solid, typically Coorg home half a dozen musicians were playing mournfully – as they had been all night – under the plantain and papaya trees. Many neighbours were chatting quietly in groups, at a little distance from the house, and Ponappa himself stood on the veranda, clad all in white, receiving condolences. When I offered our sympathy he said expressionlessly, 'It is my fate.' There was a certain moving dignity about him: yet those four syllables unconsciously put Indian womanhood in its place. _Her_ death at thirty-six was _his_ fate...
The corpse had been brought from Virajpet during the night and was reclining on a wicker chaise-longue under a canopy of white cloth in the room just off the veranda – robed in a fine sari, with crudely painted scarlet lips. Rachel had been inclined to regard the occasion as a 'treat' and I had had to warn her to suppress her light-hearted interest in corpses; but when she saw the devastated daughter bending weeping over her mother, stroking the dead woman's cheeks, she suddenly clutched my hand very tightly and said, 'I feel sad. I hope you won't die until I'm married.' The two sons were sitting cross-legged on a wall bench opposite their mother, looking completely dazed as they whimpered and moaned and rocked to and fro; and beside the chaise-longue sat the dead woman's elder sister, wielding a fan of sago-palm leaves to deter flies and tending a dish-lamp. When Dr Chengappa entered the room he touched the corpse's chest with the back of his hand and then his own chest with the palm, to indicate that the bereavement has left him feeling heartbroken. But, because dead bodies are regarded as one of the most potent polluting agents, Uncle Machiah had to remain on the veranda, postponing his ritual gesture of grief until later. He was due to meet somebody in Virajpet at ten o'clock, as part of his apparently ceaseless round of _Aruva_ duties, and so he could not return home for the purifying bath and change of clothes that would have been essential had he crossed the threshold of the death-chamber.
As we left, I told Ponappa I would be at the funeral this afternoon and when we were back in the doctor's car Rachel said that she, too, would like to attend. But Uncle Machiah explained that it is not the custom for children – other than close relatives – to witness cremations. Poor Rachel was ravaged by disappointment. 'I wanted,' she wailed, 'to find out if burning humans smelt like cooking meat.'
A few days ago we were invited to accompany Uncle Machiah to this morning's _Aruva_ session – it apparently included some sort of 'brunch' meal – and, as we drove towards Virajpet, I noticed an unprecedented awkwardness in his manner which momentarily baffled me; luckily I recollected our polluted state in time to back out before our unfortunate friend was forced explicitly to cancel the invitation.
We had walked home and I was preparing lunch when one of Dr Chengappa's sisters-in-law (a widow who lives some six miles away, towards Vontiangadi) appeared in the compound to collect her share of this year's paddy. She shouted a greeting to us, and I went to a window and asked her upstairs for coffee or a drink. But she declined. 'I can't come into the house,' she explained, 'I've just been to Ponappa's.'
It is impossible to estimate how seriously each individual takes the pollution taboos, so I made some coffee and took it out to the compound, hoping Mrs Chengappa would drink it there. But no: she would neither eat nor drink until she had performed her purifying ceremonies.
At three o'clock I set off for the cremation with Rachel's instructions ringing in my ears: 'Tell me what it smells like!' In fact I was destined not to discover this, as women have to leave before the pyre is lit – a custom originating in the tendency of women mourners to become so unbalanced by grief (or fear of widowhood) that they impulsively throw themselves on the fire, even if they have not planned to become _satis_. However, this rule is not always enforced strictly enough to protect widows from self-immolation. In Rajasthan, during the past six months, at least four women have voluntarily joined their husband's corpse on the pyre and been burned to death. Moreover, in one case there were some 70,000 witnesses, none of whom felt it necessary to intervene.
Mrs Ponappa's cremation was to take place not far from the Muslim settlement on the way to the Machiahs, under one of those extraordinary 'double trees' often seen in Coorg. It is an ancient local custom to plant two sacred trees together, encourage them to entwine as saplings and then 'marry' them, with much pomp and lavish entertainment, to symbolise the union of Eshwara and his consort Parvathi. This particular Devangeri couple must have been married centuries ago, for each partner has attained a prodigious height and girth and the red and green canopy of their mingled leaves shades an enormous area, including the spot chosen for the cremation.
When I arrived there were only two young village men under the trees, tending the bonfire from which the pyre would be lit, but the usually so silent forest afternoon was throbbing with the slow beat of distant drums, accompanied by the melancholy wailing of Coorg horns, and when I peered through a tangle of scrub I could see, far away, the little funeral procession advancing across the pale gold stubble of a paddy-valley. No more beautiful setting for a poignant ceremony would it be possible to find, with royal blue mountains visible between the slender silver-grey trunks of areca palms, and the high poinsettia hedges around the Muslim settlement forming cascades of colour, and the dense burgundy-red leaves of the incense trees glistening above the countless shades of green in the undergrowth, and the purple-red earth, and the leafless, angular cotton trees bearing their blood-red blossoms like chalices against a cobalt sky.
Many Coorg customs have been abandoned during the past fifty years, or made obsolete by Progress, yet most of those connected with the anthropologists' 'rites of passage' are being maintained. Last night, just as I was falling asleep, I heard two distant gun shots and wondered if Uncle Machiah was still trying to pot that mongoose. But I have since learned that this was the announcement to the village of a bereavement; if those shots had been fired during the day, even at the height of the ploughing or reaping seasons, every Coorg would at once have stopped work and hastened to the house of mourning to offer not only sympathy but practical help. Also their servants would have been sent running to the other homesteads of the _nad_ that were out of earshot, to spread the news and rally support. All the food needed in Ponappa's house for the next eleven days will be provided and cooked by neighbouring women, all his farm work will be done by neighbouring men and all the valuable firewood for the pyre was presented to him today – a little from each village family – as an expression of sympathy and solidarity. On this point, however, discretion must be the better part of generosity; every branch specially cut for a cremation has to be used because, it is believed, the gods would regard any surplus as an invitation to take another life from the family of the deceased.
By four o'clock quite a crowd had gathered in the shade of the double tree, including Uncle Machiah and Colonel Ayyappa, and at last the funeral band appeared through the thick scrub. It was followed by two men bearing a split bamboo stick designed to serve as a holder for half a coconut shell; this had been filled with oil to form a lamp which had to be kept alight throughout the ceremony. Next came the bier – that same wicker chaise-longue – carried by Ponappa and three other male relatives. The chief mourners included about a dozen women, clad in that unrelieved white which is the equivalent of our unrelieved black. One of them, who belonged to the family of the Ponappas' _Aruva_ , was carrying on a section of plantain leaf the _Sameya_ , a mixture of coconut, puffed rice, rice with mutton or egg curry, rice seasoned with turmeric and vegetables fried in oil. This meal has to be provided by a deceased woman's natal family, or by a deceased man's mother's family, and before the ashes are left alone to cool during the night the _Sameya_ is placed beside them, to sustain the spirit on its journey.
When the corpse had been borne three times around the framework for the pyre – a square construction of rough-hewn, leaf-decorated logs – it was laid on the ground nearby, with the head pointing to the south, and Ponappa stripped himself to the waist. The white cotton robe in which he had been clad was now used as a canopy, under which he and his father's brother's wife led the chief mourners three times around the pyre, the elderly women scattering rice and small coins from a flat wicker basket. Next the widower and his daughter and elder son again thrice circled the pyre in single file, each wearing a finger ring of sacred _Kusha_ grass. Ponappa was carrying on his head an earthen vessel of water from which he sprinkled the ground, his daughter was carrying a small brass pot with a spout, a _kindi_ , which would have been carried by her husband had she been married, and the boy was holding a coconut on his head. After the first circuit their family _Aruva_ stepped forward and with the sharp point of his heavy knife punctured Ponappa's vessel so that the water trickled down his face as he continued to walk, symbolising that inexorable flow of time which is every moment bringing each of us closer to death. It might be thought that these elaborate rituals impose an unnecessary strain on a grief-stricken family, but the therapeutic effect of having to concentrate on so much activity and detail is considerable.
Next Ponappa stood at the corpse's head, his son at its feet and his daughter by its right side. Then Ponappa took the pot off his head and twice made as though to break it against the leg of the chair. The third time he did break it, and pushed the pieces under the chair, and then his son cracked the coconut and pushed the two halves under the chair, and his daughter emptied her _kindi_ and pushed it under the chair. Meanwhile the dead woman lay looking quite beautiful and very young, with a small mirror on her folded hands, many fresh forest blossoms tossed on her shroud and an elderly aunt devotedly fanning to keep the flies off.
Next Ponappa put a coin in a tiny bag and tied it to a corner of his wife's sari, which was the signal for everybody present to pay their last respects to the deceased and leave a little money on a nearby plate to help with the funeral expenses. Most people moistened the dead woman's lips with water before touching her breast in a last gesture of grief and farewell. Then the women mourners began to withdraw, as all jewellery, and every garment apart from a flimsy sari, were removed from the corpse. The clothes and the bloodied shroud were given to the Harijan bandsmen, who would not consider them polluting. Finally, a new white cotton sheet was spread over the body, covering even the face, and was smeared by Ponappa with the juice of mango leaves.
Thus far the ceremony had been conducted with great dignity, in a silence broken only by the traditional music. But when the face was covered, by which time the women had all withdrawn to a little distance, the unfortunate daughter suddenly broke down, burst into loud lamentations and shook off her restraining relatives to rush back to the corpse and pull down the sheet that she might look once more upon her mother.
Immediately, as though some lever had been touched, all the women, and quite a number of the men, gave way to their emotion and the ensuing harrowing scene could not possibly be mistaken for a ritual 'funeral display'. However, order was at last restored, the women withdrew again – out of sight, this time – and the macabre business of the day began. For some extraordinary reason custom requires the corpse to recline straight-legged up to this point, when it has to be made to sit cross-legged on the pyre. Almost twenty-four hours after death, this naturally presents a problem. Then the corpse is held in a sitting position while the pyre is built up around it until only the head is visible, at which point the chief male mourner has to come forward to add the final lengths of wood that obscure the head. The eldest son then carries a burning brand from the bonfire, which itself has been lit from the domestic hearth of the deceased, and inserts it into the space left between the bottom of the pyre and the ground. At this moment I, as a woman, had to withdraw, to avoid seriously offending local susceptibilities.
For hours pale blue smoke was visible all over Devangeri, rising through the majestic branches of that double tree, and I knew that at least one representative of each village family was sitting by the pyre to make sure the body was completely burned before the night. Tomorrow, at dawn, the ashes will be removed for immersion in the sacred Cauvery River, and the site of the cremation will be lavishly watered and planted with paddy. If these seeds germinate, it is believed the departed spirit is happy and at peace.
I have always been pro-burial (without a coffin) but this afternoon's ceremony has almost converted me to cremation – if one could arrange to be cremated in a Coorg forest. Aesthetically, being consumed by flames is certainly preferable to being consumed by worms. Fire is so beautiful, and fierce, and final.
CHAPTER FIFTEEN
# _A Naming Ceremony and a Wedding_
## FEBRUARY 7TH
Today we lunched with Aunty Machiah's sister-in-law, whose elder daughter had her first baby three weeks ago in Dr Chengappa's Virajpet maternity home. Like all Hindu brides, Coorg girls return to their parental home, however long the journey may be, for what is regarded as the ordeal of their first confinement – a custom based on the reasonable assumption that a baby will arrive before the bride has had time to settle into an unfamiliar household.
In Coorg, however, the new mother is excessively pampered. She remains with her own family for the sixty days of birth-pollution, following delivery, and during that time is confined to one room with her baby and is not allowed out of bed. Carefully chosen strength-restoring foods are provided and she is given a vigorous daily oil massage and hot bath by specially trained servants – which Uncle assures me has the same effect as normal exercise. But I still feel that such paranoid cosseting must be dreadfully deleterious. We last visited this young mother in hospital, within hours of her confinement, and I thought she looked a lot healthier then than she does today. Yet she seemed perfectly content just to lie there being entertained by her mother, younger sister, servants and a stream of callers. Most of the household's entertaining is now done in the new mother's room, to alleviate her boredom, which means that the baby, throughout each of its waking moments, is being cuddled and fussed over and talked to. In this family the infant's aunt – whose marriage Uncle was arranging today, following her graduation from Madras University with first-class honours in economics and political science – is the Spoiler-in-Chief. She also set about spoiling Rachel and when we were leaving presented her with a magnificent hand-embroidered dress and a silver necklace.
## FEBRUARY 10TH
I woke this morning feeling more than slightly peculiar, having lunched yesterday with a gentleman whose hospitality far outstrips his judgement. Our party began at eleven a.m., with beer, and continued through whisky and Arak to a long afternoon spent on the veranda absorbing small coffees and large (genuine) cognacs. At five p.m., when my host and I could no longer convince even ourselves that it was 'just after lunch', and when an hour remained to sun-downer time, the Murphys got up to go. I therefore deserved no sympathy this morning, nor was any available. Rachel took one look at me when I became perpendicular and asked shrewdly, 'Are you hung-over?'
'Of course not,' I said crossly, groping for the Alka-Seltzer.
'Then why do you look so ghastly and dopey?' challenged Rachel – a combination of adjectives which so took my fancy that I was at once restored to cheerfulness. Daughters have their uses.
My restoration needed to be pretty rapid this morning as we were invited to a naming ceremony at Byrambada, about six miles away, quite close to the scene of yesterday's debauchery.
About one hundred guests had already assembled when we arrived at nine-thirty – seventy or so women within the house, and twenty-five or thirty men on the outer veranda. Naming ceremonies are not normally attended by many males, apart from close relatives, and only women participate in the _Ganga Puja_ (water worshipping). Formerly children were named and cradled twelve days after birth, at the end of the first stage of the birth-pollution period, during which family members are debarred from taking part in village festivals or _pujas_. Now, however, it is more usual to combine the naming ceremony with the _Ganga Puja_ , which takes place sixty days after a birth to mark the mother's resumption of normal life. Having bathed, she dresses as a bride, and the enormous vessel in which her bath water has been heated for the past two months is removed from the wash-room and filled with cold water by a woman who intones, 'May your stomach be cool like this copper pot.'
Our first duty, privilege and pleasure was to admire the cause of today's excitement – a dainty baby girl who, since she had not yet been cradled, lay asleep on a double bed under a muslin net in a wicker basket. She cared nothing for the procession of proudly beaming female relatives, ranging in age from two to eighty-eight, who were passing through the room. Under the cradle I glimpsed the knife that had cut the umbilical cord, a formidable weapon on which all Coorg babies sleep until they have been named. Soon after our arrival the child had to be roused, but she retained her oriental calm even when Rachel helped to change her nappy with more zeal than skill. (The nappy was of course dry, since nicely brought-up Indian babies, however young, seem to perform only on their pots.)
The brief naming and cradling ceremony – attended only by women – took place in the main room of the house. Her paternal grandmother held the infant over a vessel of burning incense while Aunty Machiah, acting on behalf of her dead maternal grandmother, tied black threads around her wrists and ankles. (Had she been a boy, a thread would also have been tied round the waist.) Then, before cradling her, Aunty and two other women three times placed a grinding stone in the cradle and lifted it out again while chanting, 'Live long like a stone!' – for the first time addressing the child by name. This little girl was simply named Cauvery, after Coorg's most sacred river. But many Coorg names are more colourful: Belliappa (Silver Father), Ponappa (Gold Father), Maiddanna (Brother of the Village Green), Puvakka (Flower Sister), Muttakka (Pearl Sister), Chinnava (Gold Mother) – and so on in this rather ornate vein.
Next the paternal grandmother called, 'Cauvery, get up and eat rice mixed with milk!' And, to Cauvery's very evident distaste, a minute particle of curds, rice and honey was forcibly fed to her off the edge of a gold coin. She at once spat this mixture out with the well-known decisiveness of Coorg females, yet she did not disgrace her warrior ancestors by crying or even whimpering.
When the men had joined us everybody formally saluted Cauvery and dropped an envelope containing a few rupees into the cradle. Then, to drink her health, the women were given glasses of extremely potent home-made wine and every woman emptied her glass in one, as is the custom here. I noticed, too, that not all were averse to a refill, though in most regions a high-caste Hindu woman would as soon go out naked as drink alcohol.
At noon, for the _Ganga Puja_ , Chinnava – the baby's mother – appeared in a shimmering, pale pink, gold-spangled sari, wearing glittering gold and silver ornaments. She beckoned me to follow her to the well, where Aunty again had a central role to play, she and the paternal grandmother handing Chinnava the ritual coconut, three betel leaves, three pieces of areca nut and some rice. First Chinnava offered prayers while breaking the coconut over the well and throwing it into the water, followed by the leaves and nuts. Then she drew a vessel of water and drank three gulps out of the palm of her hand before filling two small, antique silver pitchers. These she placed one above the other on her head, and meanwhile Aunty had filled two other pitchers which were carried by a couple of Chinnava's nieces, aged six and ten. Very slowly, in an atmosphere of joyful solemnity, the little procession moved back to the house through a garden brilliant with saris and flowers – yellow, scarlet, deep blue, white, pale pink. When the water had been left in the kitchen Chinnava went to the central hall, where the sacred wall-lamp had been lit, and quietly offered prayers while sprinkling rice on the flame. Finally, she turned to take the blessings of the older women, bowing low before them and touching their feet three times while they gently laid their hands on her glossy raven hair. And an old lady beside me exclaimed – 'What a wonderful girl! Did you know she is one of India's best nuclear scientists?' Of such shocks is life in modern Coorg compounded.
The banquet was served in the garden, under a temporary roof of freshly cut branches, on long trestle tables draped with snowy lengths of cotton. Chinnava's immediate family waited on us, bearing great cauldrons of delicious food: steamed rice, fried rice, curried mutton, chicken and pork, fluffy _idlis_ , soft rice flour pancakes, fresh coconut chutney, _sambhar_ deliciously tangy with tamarind, fresh curds, spiced cabbage with grated coconut, curried potatoes and beans with hard-boiled eggs. For pudding there were large tumblers of a delectable liquid made from ground rice, jaggery and milk, flavoured with fragrant cardamom and laced with crunchy cashew-nuts; and for dessert there were bananas, oranges, grapes and fresh pineapple chunks. At last we all rose, washed our hands and moved slowly indoors to chew pan and betel-nuts while a swarm of servants descended on the tables to lay them with fresh plantain leaves for the men.
Betel-leaves and areca-nuts are believed by the Coorgs to be very auspicious and the mixture certainly aids digestion. At all important religious ceremonies and social functions chewing is considered essential and it is so closely associated with happiness and contentment that abstinence from betel is required during mourning periods. The ceremonial giving of a betel-leaf is accepted as an adequate receipt for money or goods, and an exchange of betel leaves, in the course of an agreement involving mutual trust, is regarded as more binding than any signed and witnessed legal document. Obviously this is a relic of the days when most Coorgs, whose own language has no script, were illiterate.
At four-thirty the party began to break up and, after a prolonged hunt, I found Rachel in the nearby forest with about twenty other junior guests who had been prompted by my daughter to indulge in nefarious activities which did their party clothes no good. On the way home I asked Rachel what game they had been playing: 'Oh,' she said unconcernedly, 'we threw a coconut into the well and fished it up again'; which reply I found not a little unnerving, as many wells are over eighty feet deep.
Incidentally, Aunty wordlessly registered disapproval today when she saw Rachel dressed for the occasion in that Madrassi outfit made for her by the Ittamozhi tailor's apprentice. This baffled me, until I realised that the outfit is typical of what little Harijan and low-caste girls wear, not only in Tamil Nadu but here in Coorg. Little high-caste girls, before they graduate to saris at puberty, wear European-style clothes, usually beautifully tailored by mother, aunt or grandmother but modelled exactly on Marks and Spencer's children's garments. So poor Rachel's glad rags – of which she is so proud, and in which she looks so attractive – were today a _faux pas_ of the first order.
## FEBRUARY 18TH
In every Coorg home, from the grandest to the humblest, one notices a photograph or oleograph of Tala Cauvery – the source of Coorg's sacred river – and Coorgs treat these pictures with as much reverence as though they were statues of a god. So I was very pleased today when invited to visit Tala Cauvery with Tim and Sita.
Inevitably I felt restless during the twenty-mile drive, which took us almost to the top of a steep, forested mountain, but when we got out of the car our journey seemed well worthwhile. From this lonely height we were overlooking the whole of South Coorg, stretching away in three directions.
Unhappily, Tala Cauvery itself is well on the way to being modernised. Crude concrete walls surround the ancient, sacred stone tank beside the even more sacred spring, surmounted by a small shrine, which is the source of Mother Cauvery. Another very old and beautiful shrine, not far away, has been enclosed in a corrugated-iron-roofed cube that looks like a temporary public lavatory hastily erected on an earthquake site. (This is the first piece of corrugated iron I have seen in Coorg.) Beside the temple another 'lavatory' is in the process of construction, as are various larger buildings of indeterminate purpose and shocking ugliness; and nothing can be done to halt this despoiling process. As Tim said,
In the old days you had thousands of penniless pilgrims walking from all over South and Central India to Tala Cauvery. Now you also have black marketeers and venal government officials sweeping up the new road in their illegally imported Mercedes to try to save their rotten souls by paying lakhs of rupees to the Brahmans. Which is how the temple authorities can afford to ruin the place with all this nonsense.'
Soon after our arrival an elderly priest, stripped to the waist, came panting up the hill, having been summoned by Tim's ringing of the handsome bronze temple bell. Unlike most temple priests, he was not obese – possibly because of these frequent sprints up a steep slope. However, had he known who was there this morning he might not have bothered to hurry himself because Tim, following in the footsteps of his ancestors, holds strong views on the part money should play in religious ceremonies. He is a man who in his time has given lavishly to schools and hospitals, but today he only spent five rupees on his _puja_.
The fact that Tim goes to Tala Cauvery as a simple pilgrim made our visit memorable for me. While Sita wandered around nearby, taking photographs, Rachel and I stood beside the little shrine over the spring, watching the pilgrim and the priest. And, as we watched, all the confusion that Hinduism creates in Western minds suddenly cleared away, like our morning mists at Devangeri when the sun has climbed above the palms. A good man was worshipping, with faith. I looked down into the clear, fresh water of the spring-well, where rose petals and coconut shells and red powder and mango leaves floated on the surface, and it all seemed wonderfully simple. Then, as though he could sense my mood, Tim quickly looked up and signed that if I wished I might join him. So Rachel and I received some of the purifying well-water from the priest, drank it, held our hands over the sacred camphor flame of the dish-lamp, and thrice followed Tim as he walked clockwise round the little shrine. And I knew he knew I was not doing this _puja_ to be polite, or for a stunt, any more than I was affecting to be a Hindu.
We took another road back to Green Hills – a narrow track, inches deep in red dust, which switchbacked through miles of forest before coming to a vast coffee estate surrounding Tim's _Ain Mane_. This magnificent house was built towards the end of the eighteenth century and is the most impressive of the many _Ain Manes_ I have seen; its wood carvings are of a fantastic delicacy and intricacy. Three young men greeted us: all were comparatively poor relations who have been enabled to get started on good careers (law, army, university lecturer) because Tim uses some of the income from this estate to support a whole tribe of relatives. The rest goes on maintaining the structure of the _Ain Mane_ , which is at present being discreetly modernised.
Although our arrival was completely unexpected, Coorg law forbade us to leave without partaking of food and drink; so while the womenfolk put their emergency plans into operation we walked down a long _oni_ , under the shade of gigantic ebony and sandalwood trees, to gaze respectfully at the elaborate tombs of some of Tim's more illustrious eighteenth-century ancestors. Sita explained that not all Coorgs are cremated: burial is also quite common and children and young unmarried people are always buried, usually on the family estate.
Here the veranda wall was – as usual – covered in family photographs, some obviously contemporaneous with the invention of photography, and as we enjoyed our thick squares of sweet omelette I found my eye being repeatedly drawn to an enlarged and surprisingly clear portrait of Tim's grandmother. This splendid but evidently formidable old lady was successfully organising girls' schools here when Suffragettes were a novelty in Britain. She is largely responsible for the fact that about 73 per cent of Coorg women are literate and have been for a few generations, though the all-India women's average is 18 per cent – rising to 54 per cent in Kerala and falling to 8 per cent in the densely populated states of UP and Bihar.
Tomorrow we must be at the Machiahs' by eight a.m., when I will be robed in a Coorg sari before we all set off together for the _Kodava_ _Samaj_ – a large, rather dreary edifice on the outskirts of Virajpet. It was specially built some years ago for the holding of marriage ceremonies-cum-wedding parties and has already acquired that shoddy look which marks most newish Indian public buildings. To have such a building available for the complicated and lavish entertaining of one thousand or more guests is obviously labour-saving, but the older generation complain that the abandoning of private homes for the occasion has meant regrettable changes to the traditional rituals.
In the arranging of marriages a very important role is played by the family _Aruvas_. When both sets of parents have come to an informal agreement the girl's _Aruva_ asks for the boy's horoscope – or, if there is none, both _Aruvas_ , accompanied by members of both families, go to the temple to ask for God's blessing on the union. An idol is decorated with white and red flowers, and if a white flower falls during the ceremony this is considered most auspicious, especially if it falls from the idol's right side. But if a red flower falls some families, even today, will abandon a match simply on the strength of this inauspicious indication. Other families consult an astrologer instead of doing the temple _puja_ and are greatly influenced by his findings; and an astrologer is in every case consulted, during the betrothal party at the girl's home, to determine the most auspicious date and time for the _Muhurtham_ (marriage). During betrothal parties the _Aruvas_ play leading parts, the girl's _Aruva_ guaranteeing to keep her safe until the wedding day and receiving from the boy's _Aruva_ a jewel to mark the betrothal. On the day before the wedding the _Aruvas_ complete all the arrangements for the _Muhurtham_ , supervise dress rehearsals of the ceremony (which rehearsals are part of the ritual), and organise feasts for the neighbouring villagers.
On several points, Coorg marriage laws and traditions diverge from those of most Hindus. Divorce has always been easy to obtain if loss of caste, incompatibility of temperament or a wife's unfaithfulness could be proved before the village _panchayat_ ; but of course a wife can take no action because of her husband's unfaithfulness, nor can she leave him without his consent. A divorced wife may not keep any of her children over the age of three, and babies or toddlers who accompany her when she leaves home must normally be returned to their father on their third birthday. Should the mother in an exceptional case be able to obtain permanent custody, the children's links with their father are formally severed and they forfeit their right to any share of his family property. Divorce, however, has always been rare amongst Coorgs, as has polygamy, though a man without a son by his first wife is free to take a second. Alternatively, he can adopt his eldest daughter's husband (as was also the custom in Tibet), if the young man is willing to forfeit his share of his own family property.
Child-marriages were never customary here and widows and divorced women have always been permitted to remarry – the former one year after their husband's death, the latter six months after their divorce. In pre-British days, polyandry was sometimes practised: but the strangest of the six forms of marriage available to a Coorg woman is the _Pachchadak Nadapad_. This is a temporary marriage, now uncommon though still occasionally resorted to when for some reason no suitable husband can be found to wed an heiress. The young man's only duty is to beget a child so he retains his right to his own family property, receives no share of his wife's – apart from food and clothing while he remains with her – and is free to marry another girl whenever he chooses. The children of such marriages can claim maternal property only. Another odd form of 'marriage' is the _Paithandek Alepa Mangala_ , a special ceremony to honour a woman who has borne ten healthy children. (Formerly Coorgs considered five sons and five daughters the ideal family: now one of each is the aim.)
Many university-educated Coorg women continue to work after marriage, if they have already been leading independent professional lives, and many others return to work as teachers, doctors – or whatever – when their children go away to school. Moreover, the women of less well-off families are often on their local _panchayat_ committee, where they take a vigorous part in debates on every aspect of rural development.
## FEBRUARY 19TH
We arrived at the _Kodava Samaj_ in a hired jeep at nine-thirty, Rachel wearing a smartly tailored skirt and blouse, specially made for her by Aunty, and myself gorgeously attired in borrowed plumes and laden with borrowed jewellery. The bridegroom was not due until ten-fifteen, so we had time to study the scene before the crowd gathered.
The open space in front of the _Kodava Samaj_ had been covered by an awning of bamboo mats and dried plantain fronds, under which five hundred metal folding chairs awaited the male guests; within the building, another five hundred awaited the female guests. At the far end of the long main hall, on the right as one entered by the central door, was a small carpeted platform under a canopy of white and red cloth, supported by four tall plantain stumps decorated with coconuts, mango garlands, jasmine and various other richly scented cream-coloured blossoms. In the centre of the platform stood two low, three-legged teak stools with a large, shallow, circular wicker basket beside each, and to the left of these stools, as one faced the hall, was a rosewood and brass pedestal lamp, three feet high, which would soon be lit with a flame from the sacred wall-lamp in the bridegroom's _Ain Mane_. Near the platform was a door leading to a small room, simply furnished with two single beds and two chairs, where the bridegroom and his closest friends could lunch in private and rest during the afternoon; and at the far end of the hall was a similar room for the bride and her attendants. Opposite the main entrance another door led to the dining hall, which seats four hundred, and behind that we found the enormous kitchen shed where, at ten o'clock, mountains of chopped vegetables and raw meat loomed in every direction, and rows of colossal cauldrons, attended by battalions of servants, were simmering on gigantic mud stoves.
'It's like the witches brewing in my book!' exclaimed Rachel, goggle-eyed. 'Are the bride and bridegroom very rich?'
I had wondered the same thing, but in fact neither family is particularly well off, the bride's father being a retired army major and the bridegroom's a retired secondary school teacher. For this reason, no alcohol was served: a most sensible decision since drinks for 1,000 guests could have run these families into lifelong debt. And those who wished to have a self-supplied drink before lunch were free to do so without giving offence.
Coming back from the kitchen we stood in the doorway and looked around the huge hall, brilliantly lit by clear golden sunshine. I have already described the simple splendour of the _Kupya_ – the Coorg man's costume – but we had not previously seen a gathering of women in all their traditional glory and this was such an overwhelming vision that even Rachel remained speechless for half a minute. Here were hundreds of glossy raven heads and golden-skinned arms and faces, and shimmering gowns and fluttering veils, and glittering, gleaming, glowing gold and silver ornaments – studded with rubies, emeralds or diamonds – and, standing in that doorway, I was mesmerised by the ever-changing pattern of saris and jewels, blending and contrasting, as little groups strolled up and down the hall, or stood animatedly chatting. There were so many rich materials, their colours and shades beyond counting – pale blue, rosy pink, old gold, turquoise, silver-grey, lime green, primrose yellow, sapphire, crimson, smoky blue, russet, dove-grey, flame red, deep purple – and here and there the pure white of a widow's sari, adding an effective touch of elegant austerity.
I failed to recognise several elderly neighbours who were wearing the Coorg veil, now no longer in everyday use. This is a large kerchief, of which one end encircles the forehead with those two corners tied at the nape of the neck, so that the rest gracefully drapes the shoulders. The fine features with which Providence – or Mother Cauvery – has endowed most Coorgs are thus emphasised, and one wonders why such a simple aid to beauty has fallen out of fashion.
At ten-fifteen a distant throbbing of drums announced the imminent arrival of Ponnappa, the bridegroom. (Here Ponnappas are as thick on the ground as Murphys in Ireland.) I hurried out to watch the procession and found that Rachel, quite beside herself with excitement, had joined a group of Ponnappa's small nieces and was enthusiastically dancing in the middle of the road, to the huge amusement of the watching crowd. And indeed the bridegroom presented a spectacle romantic enough to make any Irish girl lose her head. He wore a dazzling white _Kupya_ , a broad crimson silk sash, a flat-topped white and gold turban, a short ivory-handled dagger in a silver and gold ornamental scabbard, a heavy golden-sheathed sword, a solid gold bangle and a necklace of alternate gold and coral beads. In his right hand he carried a long staff of intricately carved rosewood, decorated with silver rings and bells and known as the _Gejje Thandu_. Formerly, if the bridegroom fell ill at the eleventh hour, this staff was accepted as his substitute and the ceremony was performed without him. To complete the picture, as Ponnappa walked slowly up the road his best man held a crimson-and-gold-tasselled white umbrella over his head.
A chair draped with crimson cloth had been placed in the centre of the road – weddings take precedence over traffic – and along the verge a dozen four-foot-high plantain stumps, each decorated with a flower, had been embedded in the ground. When the bridegroom had seated himself, and been surrounded by merrily playing musicians, his _Aruva_ offered clear water from a pitcher, and a betel-nut, to a small group of relatives and close friends who in times past would have brought with them meat, rice, plantains, and their own drummers and trumpeters. Then the _Aruva_ handed the bridegroom's sword to one of this group, who was supposed to cut each plantain stump with a single stroke while praying to the village god. (He succeeded in cleanly cutting only four; obviously Coorgs are not what they were.) This custom is said to be of _Kshatria_ origin and to symbolise the winning of a bride through superior physical strength, skill and courage.
When we returned to the hall for the _Dampathi Muhurtham_ the pedestal lamp and several dish-lamps had been lit on the platform and a large basket of rice stood ready near the stools for the giving of blessings. First the groom was led to the right-hand stool and then Nalini, the bride, who had arrived by a side entrance while we were watching the plantain cutting, took her place beside him. Dressed all in red, she looked, poor girl, very pale and tense. It was now time for each guest to ascend the platform individually, sprinkle rice on the couple, bless them, and drop a few rupees into one of the baskets. This part of the ceremony is initiated by the bride's mother. Standing before the groom, she tosses a handful of auspicious rice over his head and shoulders while invoking the blessings of God, gives him milk to drink from a spouted silver vessel and presents him with the _Pombana_ – a gold coin which, being a mother's gift, is considered most precious and treasured throughout the couple's life. The women guests ascend the platform first and then, when the men form their long queue – the only orderly queue I have ever seen in India – the women move into the dining hall for lunch.
I was advised to eat with the first sitting lest I might miss the _Sambanda Kodupa_ ritual, which follows immediately after the _Dampathi Muhurtham_. From my seat near the door I watched many members of the bride's family moving up and down the long lines of white-draped trestle tables, serving food with an unhurried air that belied their speed and efficiency. When each guest had a heaped leaf-platter before her someone called out, ' _Ungana_?' (Shall we eat?) and the feast began; it is considered very bad form to eat before everybody has been served. As always at a Coorg banquet, the main dish was curried pork, accompanied today by a lavish variety of irresistibly delicious foods.
It is also considered bad form to get up before everybody has finished but an exception was made for me when Uncle Machiah beckoned from the door, calling that the _Dampathi Muhurtham_ was almost over. As I hurried back to the hall the headman of the bridegroom's party – always the last to ascend the platform – was giving his blessings and gifts. The groom then stood up to be led three times around the sacred lamp by his best man, who next presented him to the still-sitting bride. Having sprinkled Nalini with rice, Ponnappa gave her a gold coin which she received in both hands and then, holding it in her left hand, she put her right hand in the outstretched right hand of the groom and stood up. Next her bridesmaid tied the coin presented by the groom into the corner of her sari, and the young couple stepped off the platform for the _Sambanda Kodupa_ ritual.
This ceremony might be described as the legally binding part of the marriage – according to traditional law – since it involves the formal transference of the bride to the groom's family and the granting to her of all that family's rights and responsibilities. During the _Sambanda_ the young couple stand at a little distance from the _Muhurtham_ platform, with the bride's _Aruva_ and two of her kinsmen beside the groom, and the groom's _Aruva_ and two of his kinsmen beside the bride, while relatives and friends of both families gather nearby to listen. According to a translation I obtained later in the afternoon, the main part of the _Aruvas_ ' dialogue goes as follows:
Bride's _Aruva_ : The people of both _nads_ , men of the houses, relatives and family friends, are they standing in rows?
Groom's _Aruva_ : Yes, they are standing.
Bride's _Aruva_ : Will you give to our child Nalini of Ponnappa family, whom we are about to give in marriage to your child Ponnappa of Subbiah family, the _Sambanda_ of the groom's _Okka_? (Paddy-valleys.) Will you give her rights in the ten plots of pasture, in the cattle stand, in the ten pairs of bullocks, in the house, in the garden, in the ten milch cows, in the bamboo receptacle used for milking, in the cattle shed, in the manure heaps, in the axes, swords and knives, in the paddy in the granary, in the bellmetal dish leaning against the wall, in the wall-lamp, in the stock of salt in the kitchen store, in the buried treasure, in the stock of threads and needles and in all from one to hundreds of things?
Groom's _Aruva_ : We give.
Bride's _Aruva_ : On the marriage of our child into your family, our servants will carry on their heads goods and valuable things and cash in a box. If this is lost who is to be held responsible for the loss?
Groom's _Aruva_ : I am.
Bride's _Aruva_ : Then take these twelve pieces of gold (in fact eleven small pebbles are handed to the groom's _Aruva_ at this point).
Groom's _Aruva_ : I have received the pieces of gold. If your innocent child, who is given in marriage to our boy, complains at the groom's house that the cooked rice is too hot, the curry too pungent, the father-in-law too abusive, the mother-in-law mean, the husband incompetent and that she is not willing to stay with him, or complains that his people are too poor and goes back to her natal family and sits there, who is the person to be held responsible to advise her properly and send her back to us providing servants for company and torches to light the way?
Bride's _Aruva_ : I am.
Groom's _Aruva_ : Then take this witness money [he hands over a token coin].
Bride's _Aruva_ : If our child were to suffer unforeseen misfortune [by this is meant the loss of her husband before she has conceived], who is responsible for sending her to her natal family with servants for company and torches for the road?
Groom's _Aruva_ : I am.
Bride's _Aruva_ : Then take this witness money [and he hands over a token coin].
So ends the _Sambanda_ ritual, and when I enquired about the rather mystifying presentation of eleven pebbles I was told that twelve pebbles (representing pieces of gold) symbolise the sum total of an individual's rights within a joint family; and so when the bride's _Aruva_ gives eleven to the groom's _Aruva_ this signifies that the girl has forfeited most of her rights in her natal family, in exchange for those granted by her conjugal family. But one pebble is retained because she has a right to return to her natal family if divorced or prematurely widowed.
By this time it was two-thirty and most people were departing, leaving only one hundred or so relatives to attend the _Ganga Puja_ and subsequent 'dance ordeal' at four-thirty. Nalini and Ponnappa, both looking utterly exhausted, had retired to their rooms and I assumed their doors would remain firmly closed all afternoon. But when I got back to the hall after a shopping trip into Virajpet – where my appearance in a Coorg sari occasioned much delighted comment – I saw people constantly trooping in and out of both rooms and was warmly invited to do likewise. From the door of Ponnappa's room I observed the poor fellow lying full length on a bed under a heap of tumbling small children – one of whom, need I say, had fair hair... In an effort slightly to alleviate his torment I urged Rachel to come with me to admire the bride's ancient ornaments, but my daughter merely abated her gymnastics for long enough to say – 'I prefer the bridegroom.' Tactful prevarications have never been her forte.
In Nalini's room, the money collected during the _Dampathi Muhurtham_ was being carefully counted by the bride's brother, tied in bundles and packed in a tin trunk. It looked a lot but most of the notes represented only a rupee or two and the total would scarcely cover one-quarter the cost of the banquet. Nalini was talking to three Indian nuns from Ammathi Convent School – one of them was the only Coorg ever to have become a Christian – and I sat on the bed beside her to study the bridal ornaments. I particularly liked her silver _Kausara_ – a ring on each finger connected by silver chains over the back of the hand to a heavy silver wrist bracelet. No less beautiful was her _Kasara_ – a similar ornament of toe rings, connected to an ankle bracelet. Most Coorg married women habitually wear a silver ring – a _Kamoira_ – on the second toe of their left foot, as well as a plain solid gold wedding ring on the third finger of the left hand. Loveliest of all, however, was her _Kakkethathi_ , a necklace of golden beads from which hung a large, crescent-shaped golden pendant, studded with rubies and edged with many small pearls.
The next ceremony – the _Ganga Puja_ – took place soon after four-thirty at the well behind the _Kodava Samaj_. For this Nalini was attended by two maidens (her first cousins) and a little group of older relatives. On the wall of the well were laid out a towel, a coconut, a hand of plantains, a bowl of rice, a lime, betel-leaves and nuts, _vibhuthi_ (a coloured powder for anointing the forehead) and the bridegroom's ornamental knife. Having washed her face, hands and feet, and prayed while anointing her forehead, the bride thrice sprinkled auspicious rice into the well as a salute to Ganga, the goddess of water. Then she placed three pieces of areca-nut on three betel-leaves and dropped them carefully into the water, so that they would not overturn. Next she half peeled the bananas and left them on the well wall while she cracked the coconut with her husband's _peechekathi_ and spilled all its water into the well. She chewed betel – an indulgence not permitted to unmarried women – while filling two brass pitchers with water and placing them one above the other on her head: and then her ordeal began.
The ordeal called _Battethadpa_ (obstructing the path) is another of those Coorg marriage customs said to be of _Kshatria_ origin. When the bride, followed by her attendants, leaves the well to carry the pitchers around the house and into the kitchen, she finds her way blocked by energetically dancing menfolk of the groom's family. This gambol sometimes continues all night and a four- or five-hour session is common. Obviously it imposes a severe strain on the already exhausted bride, who is being closely studied by scores of her new relatives as she stands immobile, balancing two heavy pitchers of water on her head and only occasionally being allowed to move a few steps forward. Perhaps it is appropriate that a martial race should thus treat its young women, testing their fitness as mothers of the next generation of warriors, but I did feel very sorry for Nalini this afternoon.
The moment the bandsmen began to play dance music Rachel came bounding along from I don't know where, and seizing Major Ponnappa's hand (they seemed by now to be intimate friends) proceeded to execute a most complicated _pas de deux_ with him. At its conclusion she continued to dance in front of the bride, without ceasing, for an hour and forty minutes; and, though only males are supposed to take part in the _Battethadpa_ , she was constantly egged on by her fellow dancers.
The Coorgs are a strange and delightful mixture of traditionalist and what you might call 'unconventionalist'. They seem always ready to make allowances for the customs, whims and eccentricities of others and, much as they value their own ancient ceremonies, they are not fanatically rigid about detail if for any reason it seems desirable to improvise or permit modifications.
When we left the _Kodava Samaj_ at six-thirty, as the bride was entering the kitchen, I had misgivings about Rachel's ability to walk three miles after so vigorous a dancing session; but she went leaping ahead of me, over-excitedly recalling the day's highlights. These included being allowed to play with the bridegroom's sword – which brought me out in a cold sweat, as Coorg swords are kept in good working order.
On our way home the sunset seemed like an echo of those saris in the _Kodava Samaj_. At first the western sky was spread with pinkish-gold clouds, against which the ever-present ghats were sharply outlined, their shadows a delicate mauve, while beyond a burnished paddy-valley stood the dark silhouettes of palm and plantain fronds, and all the noble trees of the forest. But soon the clouds deepened to crimson, as the clear sky above changed from pale blue to blue-green – and then to that incomparable royal blue of dusk in the tropics. Now the clouds were a rare, pink-tinged brown, above purple mountains, and moments later the first stars – chips of gold – were glinting overhead, and jungle bats bigger than crows came swooping and squeaking from the trees, and in the distance a jackal began his forlorn, eerie solo.
CHAPTER SIXTEEN
# _Praying and Dancing_
## FEBRUARY 20TH
Today six _banjaras_ – known to generations of British as 'brinjarries' – arrived in Devangeri with three covered wagons and set up shop on the maidan behind this house. These traders criss-cross South India with huge covered wagons drawn by pairs of magnificent Mysore whites, which, according to Hydar Ali, are 'to all other bullocks as the horses of Arabia are to all other horses'. (In Coorg, where there are no representatives of the equine species, one begins to develop an eye for a good bullock.) Most brinjarries look exceedingly wild, ragged and unkempt but are cheerful, friendly and scrupulously honest. They spend five or six days in each village, exchanging the produce of their land near Mysore for surplus paddy which is eventually transported to areas where it is scarce and dear. When I asked why the Coorgs do not keep their surplus grain, and sell it themselves later on, I was told the cost of arranging transport for small quantities would make the profits not worthwhile. It is more economic to barter it now for a supply of potatoes, onions and pulses, which will rocket in price during the monsoon.
It does one good to see such institutions still flourishing in 1974. This afternoon I bartered our surplus rice – Tim had presented us with enough to feed twenty Irish people – for potatoes and onions, which have recently become very expensive in the bazaar; and as I watched my little bag being carefully weighed on an antique scales, I remembered a letter written to Bombay by Arthur Wellesley before the Battle of Assaye:
The brinjarries are a species of dealers who attend the army with grain and other supplies which they sell in the bazaars. In general, they seek for these supplies which are sold for the cheapest rate and they bring them on their bullocks to the armies... Captain Barclay wrote by my orders to the brinjarry _gomashta_ [agent]... to inform him that all the brinjarries of the Carnatic, Mysore and the ceded districts would be immediately wanted and that they were to load and join the army.
That was in 1803 and already the brinjarries had become the mainspring of Britain's military campaigns throughout South and Central India. There was then no issue of army rations and no army service corps; the Maratha and French troops simply lived off the land, looting their way through various regions and naturally not endearing themselves to the inhabitants. So when the British bought their supplies from the brinjarries at current market rates they made a good impression which has lasted to this day in South India.
This evening, as I was reading Rachel's bedtime story, Ponappa the tailor called – he whose wife died a few weeks ago. I did not at once realise that the poor man had been on the batter and an MCC reduced him to an hour and a half of maudlin lamentations. His main obsession was the humiliating fact that the drugs given to his wife during her last illness had darkened her skin, previously 'as fair as a European's', so that I never saw her 'looking beautiful like a flowering jasmine'. He anxiously asked if I believed him, and repeatedly asserted that he could never have married a girl 'with so much darkness on her'. Having given him three mugs of strong black coffee I at last succeeded in gently but firmly guiding him down the ladder – no easy task, by candlelight – and setting him on his homeward path. But I suspect he will have stumbled back to our 'local' as soon as my back was turned.
As I write, a group of men and boys are making merry in the courtyard by torchlight: dancing, leaping, singing, shouting, drumming, fluting, horn-blowing – and exhaling such powerful Arak fumes that I shall scarcely need another MCC this evening. They are celebrating, as I suppose Ponappa was, an annual Hindu festival which, being very light-hearted, particularly appeals to Coorgs. The Lord Krishna is supposed to be fast asleep tonight, so petty thieving is allowed by tradition and householders are meant to admit these roving bands who may help themselves to food, drink and small coins. They also play practical jokes on the community, such as throwing something unpalatable (but not polluting) down public wells, felling trees to block roads and filling with water the petrol tanks of buses or motor cars. Subaya very properly says they must not be admitted to this house because the owners are absent, but I suppose I had better go down now to tip them before they waken Rachel. They certainly make a cheerful scene, by the wavering light of unsteadily held plantain-stump torches, but their musicians are rather too far gone to be melodious.
## FEBRUARY 24TH
Today we were invited to a farewell lunch with the Chengappas in Virajpet and, it being Sunday, I decided to attend Mass in the Roman Catholic church. The large building was packed, mostly with women and children, and everyone sang hymns lustily if untunefully. By far the best feature of the interior was a simple Face-the-People altar of polished teak.
As we left the church we were stopped by a skinny, frail-looking little man of perhaps thirty-five, who had collected the offerings. He asked Rachel her name and then exclaimed, 'Rachel! That is nice bit of chance! This minute my daughter is to be christened Rachel also, so you must come to watch how she gets her name!'
Turning to follow the proud father into the church, I marvelled that such a fragile creature should have begotten a child. Then we took our place beside the font, where a forty-day-old infant was being held by an elderly woman whom I assumed to be a godmother of granny's generation. By now most of the congregation had left, though I noticed that one long pew near the font was full of schoolchildren of mixed ages who seemed to be taking a lively interest in the proceedings.
At the end of the twenty-minute ceremony, Rachel II's father turned to the elderly 'godmother' and introduced her as his wife; then he turned to the pewful and introduced it collectively as 'my other children'.
'How many?' I asked weakly, feeling too pole-axed to do my own counting.
'Thirteen, with Rachel,' said the skinny little man happily. 'So now we quickly have another, because thirteen is a bad and misfortunate number.' He beamed at his haggard wife. 'Perhaps we shall have the full score, the round twenty – my wife is aged only thirty-four – there is time.' At the Chengappas Rachel for once said the right thing by remarking that she would like to live here always; and I can quite see why. There is never any fuss about the dangers of motor-traffic, or about getting too hot, too cold or too wet – she can run naked all day through the forest and over the paddy-valleys and in and out of as many streams and ponds as come her way. This morning she was out with friends from eight o'clock until ten-thirty and returned mud to the ears, having obviously had a whale of a time in some buffalo hole. I had to take her to the well and pour several buckets of water over her before she was fit to go out to lunch.
During the meal we discussed the problems of recruiting well-educated Indian girls to the nursing profession, which because of pollution complications is still regarded as fit only for the lowest caste. Mrs Chengappa explained that until living conditions for the student nurses are improved there is little hope of the situation changing. The younger Chengappa daughter's ambition to be a nurse is supported in theory by her parents; but in practice they feel bound to discourage it because student nurses are not allowed to rent flats and conditions in the hospital hostels would prove intolerable for such a girl. Yet nursing will only become socially acceptable _after_ a pioneering corps of high-caste girls has led the way, so here India has yet another vicious circle.
## FEBRUARY 25TH
On the third of March we leave Coorg for North India, so we have only six more nights in Devangeri. Coincidentally, on our last evening a torchlight display of Coorg folk-dancing is being staged on the maidan here, as part of the annual Mercara-Darien (Connecticut) get-together, and those jollifications may perhaps lighten that gloom which has already settled on me at the thought of leaving Devangeri. We have been invited to spend the night of the second at the Machiahs, and next morning we catch the Bangalore bus.
Now the midday hours are noticeably hotter – though never uncomfortable, as there is an increasing amount of cloud and breeze. Soon the heavy 'blossom showers' of March will come; how I wish we could have stayed to see the plantations being transformed into white oceans of heavily scented blossom, and the grey-brown maidans turning green! These March showers are vitally important for next year's coffee; if they are inadequate the crop is ruined, however good the later monsoon rains may be. And it is not always easy to get the ripe berries harvested before the showers, which would destroy them, so during the past week we have observed tremendous activity in the plantations.
Rachel had just gone to sleep this evening when an unfamiliar car appeared in the compound and I saw emerging from it one of our Virajpet merchant friends, coming with his wife and two small sons to say goodbye and present us with farewell gifts of sandalwood and expensive Cadbury's chocolate. Mr Kusum's father wrote a history of Coorg in Kannada, and in addition to his flourishing general store in Virajpet he owns a printing press in Mercara and is therefore, by Indian reckoning, a publisher.
When I first asked Mr Kusum, 'To which community do you belong?' he proudly replied, 'I am of Indira Gandhi's community – a Kashmiri Brahman.' But the family moved from Goa to Coorg eighty years ago and it is many generations since they left Kashmir. They remain, however, strict vegetarians, teetotallers and non-smokers – not easy people to entertain chez Murphy.
Mr Kusum's account of the status of Indian authors made my hair stand on end. He assured me that an author can hope to make no more than fifteen or twenty pounds sterling on a book that sells 2,000 or 3,000 copies. Moreover, reviewers are paid nothing by the newspapers – the free review copy is their fee – and are therefore open to bribes from authors or the enemies of authors. Probably – added Mr Kusum – the enemies, because by the time the author has paid for the printing of his book, and the paper on which it is printed, he is unlikely to be able to afford a bribe. My professional blood ran cold as the Indian literary scene was thus revealed in all its ghastly detail. No wonder Indians are incredulous when their persistent questioning reveals that I am (a) a writer and (b) not given a grant to travel by the Irish Government, a university, a business firm or anyone else. They simply cannot imagine a lowly _writer_ being able to afford to travel abroad.
## FEBRUARY 26TH
At last week's wedding the Good Shepherd nuns who were our fellow-guests invited us to their Ammathi school to meet its ancient English founder. This school has over three hundred pupils, between the ages of four and thirteen, and it was built and is being run without the government support that was hoped for – which lack of support is interpreted by some as a symptom of official anti-Christian bias. However, the Good Shepherd Order is extremely wealthy in India, where it has been established for over one hundred and thirty years, and the Coorg families for whom the school caters are well able to pay high fees. The tiny minority of non-fee-paying pupils are 'deserving cases' from poor Ammathi families and are presumably admitted as a token gesture, since the Order was founded not to educate the rich but to tend the poor – and especially to reclaim the souls of unmarried mothers and prostitutes.
After touring the well-equipped classrooms I was taken to meet Mother Christine, the seventy-nine-year-old English woman who founded the school. Sixty years ago she became a Roman Catholic, to the horror of her peppery old colonel father, and a year later she joined the Good Shepherd Order in Bangalore. Her forefathers had been soldiers in India for almost two centuries and I enjoyed her account of coming to Ammathi at seventy years old, with only one seventy-three-year-old companion, and briskly building a new school of which the local Indian authorities did not really approve. It is beautifully ironical that this archaic flare-up of British Imperialism was in a cause which Mother Christine's forebears would have abhorred.
By any standards Mother Christine is a memorable personality: a tiny wisp of a woman, hardly up to my shoulder, but still vibrant with energy, intelligence, good humour and determination – and having, at the core of all this, great gentleness, sympathy and wisdom. As we sat drinking endless cups of tea, in a small, sunlit, freshly painted parlour, I again became aware of the difference between Roman Catholic and Protestant missionary attitudes to non-Christians. In theory the Roman Catholic Church is one of the most inflexible: in practice the majority of its representatives are conspicuously tolerant and considerate in their relationships with non-Christians.
At noon, when we stood up to leave Mother Christine, she accompanied us on to the balcony, looked at the children erupting from their classrooms and suddenly exclaimed, 'I love India!' Then she turned to me and said, 'Perhaps the hippies are right – perhaps in the future mankind's spiritual salvation will flow from here. Have you ever thought that this is the most prayerful country in the world?'
## FEBRUARY 27TH
In the forest near Jagi's village is an ancient temple to which, for certain festivals, pilgrims come from all over South West India. I find its special character most attractive; so discreetly does it merge into the landscape that one could walk by without noticing it, but for a massive black Nandi facing the entrance. The oblong structure is crudely built of dark grey stone blocks, unskilfully dressed, and the façade has only a few clumsy carvings of mythological figures, almost erased by time. Such a temple could well be 1,000 years old, or more; no one has the least idea when it was erected, though all agree that it is of extraordinary antiquity. The door is kept locked and only the local Brahman priest, who lives nearby, may actually enter the shrine, but yesterday Jagi suggested that I should attend this morning's _puja_ and then have a farewell breakfast at her house; she added that I would most likely find myself alone with the Brahman, Coorg villagers not being great temple-goers.
We set out early this morning, before the sun had lifted the night mist from the face of Coorg, and walked enchanted through a world all silver and green and filled with bird song – until suddenly, as we approached Jagi's house, a warm golden light came sliding through the trees to catch the richly blooming poinsettias that line this _oni_.
I left Rachel with Jagi and continued alone, removing my shoes at the little opening in the low stone wall around the grassy temple compound. As the priest had not yet arrived, Nandi and I were on our own in the shade of giant nellige, peepul, jack-fruit, mango and palm trees. The sky above those lofty, mingling branches was a clear, fresh, morning blue, criss-crossed by the emerald flashes of parakeets, and the peace of that place was immense.
Then the Brahman appeared: a tall, thin, stooping elderly man, wearing only a _lunghi_ and a forbidding expression. Probably he disapproves of _mlecchas_ within the temple compound – but this, I must stress, is sheer conjecture. Nothing was said or done to make me feel unwelcome. Indeed, so completely was I ignored that at the end of an hour I had begun to doubt the reality of my own existence. Yet I could sympathise with his attitude: in a remote, impersonal way I even found him congenial. Plainly he was a devout man of the gods.
Amidst the hubbub of a big temple, or even of a small temple in a town, all is bewilderment and confusion for the uninitiated, and one cannot quite grasp what is going on. But this morning, alone with the Brahman in the stillness of the forest, I could observe every detail from the moment the sacrificial fire was roused in the little stone hut beside the temple. As I stood by the open door, watching the small flames jumping and lengthening in the half-darkness, I saw them – not too fancifully – as links with the _garhapatya_ fires of the earliest Aryans in India, who had no temples or holy precincts of any kind but lit their sacred fires on some level grassy spot and worshipped joyously under the sky.
All the time murmuring Sanskrit verses – for in the beginning was the Word – the priest took his brass pitcher to the well near Nandi, and fetched water in which to cook his sacrificial rice. While it was simmering he stripped a coconut, half-peeled a few plantains, prepared his camphor dish-lamp and incense-burner, strung a few aromatic garlands of forest flowers, and ground antimony between two stones to make a red paste – symbol of happiness – with which to anoint Shiva, Ganesh, Nandi and the _lingam_ stone that stands under a sacred tree behind the temple.
When he approached the hut door with his laden brass tray I stepped aside, and then followed him to the temple door, which he had opened on his way to the well. Two ancient images loomed within, close to the entrance – the four-armed Shiva, dancing on the prostrate body of the demon of delusion, and Rachel's beloved elephant-headed, pot-bellied Ganesh, who is Shiva's son by his consort Parvati, the mountain goddess. Standing at the foot of the half-dozen worn stone steps that led up to the shrine, I was hardly six feet away from the Brahman as he sat cross-legged before his gods and began to perform those rituals that already were old when Christ was born.
Occasionally, in India, the sheer weight of tradition overwhelms and our Western concept of time becomes meaningless – a disturbing and yet exhilarating experience, offering a glimpse of possibilities discounted by logic and modern science, but not by the immemorial intuitions of mankind. And so it was this morning, as I watched the Brahman making his oblations, ringing his bell, wafting incense, presenting garlands, cupping his hands over the flame of the dish-lamp and gravely reciting Sanskrit formulas the exact words of which he may or may not have understood.
I despair of conveying, to those who have never seen it, the eloquent gracefulness of a Hindu priest's hand-movements as he worships. All his oblations and recitations are accompanied by these intricate, stylised, flowing gestures which symbolically unite him to the object of his worship and are of surpassing beauty. At the end of this morning's _puja_ , as the Brahman withdrew from the temple – moving past the _mleccha_ with downcast eyes – I could not at once emerge from the state of exaltation into which he had unwittingly drawn me.
## MARCH 2ND
The Ayyappas had nobly offered to entertain Rachel today, while I got on with sorting and packing and cleaning, but early in the afternoon I heard at the foot of the ladder that choked kind of sobbing which means a child is deeply upset. During a romp with her Harijan friends she had fallen on to a pile of broken stones off a five-foot wall and she is lucky only to have minor cuts on her left upper arm and what looks like a badly sprained right wrist. When I had washed her cuts and read three chapters of _Alice_ as an anaesthetic she said chirpily, 'Aunty Ayyappa has asked us both to tea so I think we'd better go now.' Which we did, and she skipped ahead of me like a spring lamb. But by the time Dr Chengappa and his family arrived at six o'clock, to supervise the final arrangements for the dance display, her right forearm was perceptibly swollen and the doctor said she should wear a sling.
By sunset all Devangeri had assembled on the maidan. A row of chairs stood ready for the dozen or so Darien guests, who were being driven down from Mercara, and Tim beckoned me to sit beside him; predictably, he is president of the Mercara-Darien Association. He told me that Devangeri is among the few villages in which women's dancing is being revived. During the pre-Lingayat era Coorg women participated in all community events, dancing at village festivals and joining their menfolk in those lengthy songs which form an important part of the ceremonies at funerals, weddings and _Huthri_ celebrations.
In the centre of the maidan stood the _Kuthimbolicha_ – a tall brass pedestal lamp, around which the dancers circle – and by seven-fifteen the guests had arrived, the lamp had been lit and Rachel was well established on the lap of the most famous of all Coorgs, General K. M. Cariappa, retired commander-in-chief of the Indian Army. Clearly they had fallen in love at first sight, which then astonished me; later I discovered that the General is famous on three continents as a child-magnet.
There were three groups of dancers and the programme was opened by a score of slim, shy, graceful schoolgirls who performed with great assurance and skill. Next came the women, who have several times been invited to participate in New Delhi's annual Republic Day celebrations. They dance to the music of a cymbal, chanting gravely as they circle around the flaring lamp – bending, swaying, twisting – and rhythmically they raise and lower their arms while their ornaments tinkle and flash and their silken saris ripple in the torchlight like cascades of colour.
Then appeared the turbanned, barefooted men in their immaculate _Kupyas_ , each armed with his shining sword, ready to dance the renowned and exhausting _Balakata_ – a Coorg war-dance of incalculable antiquity. I was stirred to the depths by these handsome sons of warriors who invoked the war gods while running and pirouetting and flourishing their swords as though about to behead the next man. As the dance progressed everyone became increasingly caught up in the emotion it generated and the circle whirled faster and faster, while swords were flourished more and more boldly, and the dust rose from proudly stamping feet, and dark eyes gleamed beneath gilded turbans. Then the excitement spread and, with typical Coorg spontaneity, many of the crowd surged on to the maidan to give their own performances – including General Cariappa and Rachel, who went stamping and leaping through clouds of dust, hand in hand, beaming at each other and waving gaily in response to the cheers of the delighted crowd. I shall not quickly forget the tall, slim, military figure of the General, contrasting with the small, sturdy, suntanned figure of my daughter as they cavorted improbably together by the light of mighty plantain-stump torches – held high, with rosy sparks streaming off them in the night breeze, by a dozen laughing youths on the periphery of the crowd.
An hour later, as we walked with the Machiahs through the silver and black silence of a brilliantly moonlit forest, we could hear behind us the chanting, cheering and cymbal-clashing of the Devangeri villagers who had settled down to an impromptu dancing session that was unlikely to end before dawn.
# _Epilogue_
Our train journey from Bangalore to Delhi took forty-nine hours. Luckily, however, a kind attendant – who never looked for a tip, much less a bribe – went to a lot of trouble and was eventually able to provide us with sleeping-berths. (These were narrow slatted wooden shelves and during the heat of the day they were too close to the roof for comfort; but we both had good nights.) Only when travelling by rail is it an unqualified advantage to be a woman in India; the third-class ladies' coaches are usually less crowded and filthy than the rest, although men accompanying women relatives also use them.
We changed trains at Madras, where I had only forty minutes to find our reserved seats. The anxiously hurrying crowds were so dense I had to use force to make progress and Rachel understandably found the scene a little frightening. As she was in some danger of being injured by the mob I bundled her into a convenient ladies' coach and left her guarding our kit, sitting beside an amiable European nun for company. Then I resumed my search, but because of the startling metamorphosis that had overtaken the name MURPHY at the pen of some railway clerk it was too late to move Rachel by the time I had found the right coach.
The nun was an Italian who had spent twenty years in India as a medical missionary. She mentioned that she now practises as a gynaecologist in Kerala and this reminded me of a name given me in London by Jill Buxton, before we left for Bombay.
'Do you know a Sister Dr Alberoni?' I asked. 'She works in the Nirmala Hospital near Caldicot.'
The nun looked at me strangely for a moment and then said, ' _I_ am Sister Alberoni!'
One long, unbroken rail journey is an almost essential ingredient of travel in India, for it enables the traveller to _feel_ that country's vastness. North of Madras city we passed through mile after endless mile of flat, desiccated, unpeopled landscape, where one remembered that India is not at all overpopulated in relation to her area. The earth was cracked and grey and worn, and the grey-brown, dusty, ragged leaves, dangling from stunted trees in the still heat, looked like the grey-brown, dusty, ragged garments of the peasants who crowded every station, staring impassively at the train. Although many outsiders, including myself, may romanticise about the beautiful simplicity of life in rural India, there is nothing either beautiful or simple about life as it is now lived by the majority in Maharashtra, Gujerat, UP or Bihar.
The very poor are rarely met on a train, for obvious reasons – though my ticket from Bangalore to Delhi cost only Rs.62 – but near Wardha one conscience-smiting family did get aboard for a few hours. It consisted of a mother and five small children and they had their lunch wrapped in a leaf: two thin chapattis and a little chilli sauce at the bottom of a tin mug. They sat opposite us in a row, like an Oxfam advertisement, and when the two chapattis had been divided between six each had only two or three mouthfuls. It was plain that never in their lives had they eaten a full meal and this is the fate of hundreds of millions of Indians – the grim reality which we had evaded in Coorg. When I handed a banana to each of them they stared at me for a moment with a dreadful incomprehension, then hastily peeled the fruit and stuffed it into their mouths as though afraid I might change my mind and take it back. There was no attempt at a smile or nod of thanks; these people are so unused even to the minimal generosity involved that they received it with incredulity rather than gratitude.
Several attempts were made to board our train by 'ticketless persons', who are always suspect though they may genuinely only want a free ride. One nasty incident involved a youngish, ragged man with a tangled beard and a not unpleasant expression. He tried to jump on as we were moving out of a small station and I happened to be sitting by an open window beside the locked door with which he was struggling. Then a guard came along and, instead of merely forcing him to drop off, opened the door, dragged him on board and beat him up so savagely with a truncheon that he fell unconscious outside the lavatory door – and lay there for three hours, with a bleeding head. He had not long come to when the train stopped in the middle of nowhere (as it not infrequently did, for reasons of its own) and the guard again unlocked the door and thrust the man out into a hot, barren, rocky wilderness.
In Delhi we were invited to spend the night at Crystal Rogers' Animals' Shelter. This institution consists of an enormous, dusty compound, containing many comfortable enclosures for animals and one acutely uncomfortable bungalow for humans – or at least that is the theory. In practice the bungalow might belong to Dr Dolittle; it is so full of dogs, cats, guinea-pigs, rabbits, monkeys, mice, parrots and mynahs that we had to sleep in the compound on charpoys. Rachel was ecstatic to find herself having supper in a room where two tame monkeys were playing ball and within moments of our arrival a pack of puppies had eaten through three of the most vital straps on my rucksack. Half an hour later, as I straightened up after trying to wash myself with a quart of water in a hip bath, I almost split my skull on the sharp end of a cage that hung over the bath and contained two foul-mouthed parrots. At meal times ravening cats attempted to intercept one's food between plate and mouth, and in the compound were countless other cats and dogs, and several injured bulls, bullocks and horses lying around looking contented. Spacious wired-in enclosures are provided for badly maimed or seriously ill large animals, whose eyes would otherwise be picked out by carrion crows. Some patients have to be put down every week, but any with a chance of recovery are given the best treatment. Moreover, each animal, from a colossal white humped bull to a diminutive white mouse is loved individually and reacts accordingly; and the whole of this extraordinary institution is run on funds raised through Miss Rogers' own efforts.
On March 13th, a few hours before we were due to catch our train to Bombay, I discovered that our return air tickets were missing: perhaps a monkey or a mouse had devoured them. This looked like being a major disaster, since our cheap-rate concession expired on March 15th. Most appropriately, however, we were rescued by a Coorg – P. M. Ayyappa, one of the Machiahs' three sons, who is an Air India pilot and was then living in Bombay. His parents had arranged for us to spend our last Indian night in his flat and when he drove us to the airport, to catch a plane for which we had no tickets, he took enormous trouble to contact London and use his influence to get confirmation of our right to board the 9.30 a.m. British Airways flight from Bombay.
As we took off I glanced at Rachel, who was peering down at the 'shattered' environs of Bombay, and it struck me that five-year-olds are scarcely less enigmatic than Hindus. What had the past months meant to her? I only knew that from my point of view she had been the best of travelling companions – interested, adaptable and uncomplaining. Then suddenly she turned to me and said sorrowfully, 'I don't really like leaving India!' And with that comment I was content.
# _Select Bibliography_
_Beast and Man in India_. Kipling, J. G. (Macmillan 1891)
_Mother India_. Mayo, Katherine (Cape 1927)
_Father India_. Ranga Jyer, C. S. (Selwyn & Blount 1927)
_An Indian Journey_. Bonsels, Waldemar (Allen & Unwin 1929)
_The Myth of the Mystic East_. Elliot, R. H. (Blackwoods 1934)
_The Legacy of India_. Garratt, G. T. (OUP 1937)
_India of the Princes_. Forbes, Rosita (The Book Club 1939)
_The Discovery of India_. Nehru, Jawaharlal (London 1946)
_Religion and Society among the Coorgs of South India_. Srinivas, M. N. (OUP 1952)
_The Other Mind: A Study of Dance in South India_. de Zoete, Beryl (Gollancz 1953)
_Just Half a World Away_. Lyon, Jean (Hutchinson 1955)
_A History of South India_. Sastri, Nilakanta (OUP 1955)
_India_. Biardeau, Madeleine (Vista Books 1960)
_Hinduism_. Sen, K. M. (Penguin Books 1961)
_Caste in India_. Hutton, J. H. (OUP 1963)
_Marriage and Family in India_. Kapadia, K. M. (OUP 1963)
_India_. Zinkin, Taya (Thames & Hudson 1965)
_The Continent of Circe_. Chaudhuri, N. C. (Chatto & Windus 1965)
_The Crisis of India_. Segal, Ronald (Cape 1965)
_Purity and Danger_. Douglas, Mary (Routledge & Kegan Paul 1966)
_A History of India_ (2 vols.). Thapar, Romila and Spear, Percival (Pelican Books 1966)
_The Kodavas_. Ganapathy, B. D. (Privately published, Mangalore 1967)
_A Special India_. Halliday, James (Chatto & Windus 1968)
_India from Curzon to Nehru and After_. Das, Durga (Collins 1969)
_The British Image of India_. Greenberger, Allen (OUP 1969)
_Life without Birth_. Johnson, Stanley (Heinemann 1970)
_Basic Writings of S. Radhakrishnan_ (E. P. Dutton 1970)
_Portrait of India_. Mehta, Ved (Weidenfeld & Nicolson 1970)
_The Speaking Tree_. Lannoy, Richard (OUP 1971)
_Delusions and Discoveries_. Parry, Benita (Allen Lane 1972)
_Witness to an Era_. Moraes, Frank (Weidenfeld & Nicolson 1973)
_Journey to Gorakhpur_. Moffit, John (Sheldon Press 1973)
_Into India_. Keay, John (John Murray 1973)
_India 1973_. (Published by Ministry of Information, Government of India)
_Murray's Handbook to India, Pakistan, Burma, Ceylon_. (21st Edition)
_The Penguin Bhagavad Gita_. Trans by Juan Mascaro
# _About the Author_
Dervla Murphy was born in Co. Waterford in 1931, of Dublin-born parents. Her grandfather and most of his family were involved in the Irish Republican movement. Dervla was educated at the Ursuline Convent in Waterford until she was fourteen, after which she kept house for her parents and nursed her invalid mother for sixteen years – with occasional breaks bicycling on the Continent. On her mother's death she was free to go further afield and in 1963 she set off for India by bike.
Her description of that journey – _Full Tilt: From Ireland to India with a Bicycle_ – was published in 1965 and has been a critical and popular favourite ever since. She went on to explore the culture and mountain valleys of the Himalayas and then Ethiopia. Her fifth book, _On a Shoestring to Coorg_ , introduced Dervla's young daughter Rachel, as a doughty travelling companion. These early works were crowned by the publication of _Wheels within Wheels_ , a funny, touching, beautifully written autobiography charting her richly unconventional first thirty years.
Since then, fifteen increasingly political investigations led to a journey to Cuba in the company of Rachel and her three granddaughters, in _The Island that Dared_. Her most recent book, A _Month by the Sea: Encounters in Gaza_ , was published in 2013.
61 Exmouth Market, London EC1R 4QL
Email: info@travelbooks.co.uk
Eland was started in 1982 to revive great travel books which had fallen out of print. Although the list soon diversified into biography and fiction, all the titles are chosen for their interest in spirit of place.
One of our readers explained that for him reading an Eland was like listening to an experienced anthropologist at the bar – she's let her hair down and is telling all the stories that were just too good to go into the textbook. These are books for travellers, and for those who are content to travel in their own minds. They open out our understanding of other cultures, interpret the unknown and reveal different environments as well as celebrating the humour and occasional horrors of travel. We take immense trouble to select only the most readable books and many readers collect the entire series.
Extracts from each and every one of our books can be read on our website, at www.travelbooks.co.uk. If you would like a free copy of our catalogue, please order it from the website, email us or send a postcard.
# Copyright
First published in Great Britain by John Murray Ltd in 1976
First published by Eland Publishing Limited
61 Exmouth Market, London EC1R 4QL in 2014
This ebook edition first published in 2014
All rights reserved
Copyright © Dervla Murphy 1976
The right of Dervla Murphy to be identified as author of this work has been asserted in accordance with the Copyright, Designs and Patents Act 1988
This ebook is copyright material and must not be copied, reproduced, transferred, distributed, leased, licensed or publicly performed or used in any way except as specifically permitted in writing by the publishers, as allowed under the terms and conditions under which it was purchased or as strictly permitted by applicable copyright law. Any unauthorised distribution or use of this text may be a direct infringement of the author's and publisher's rights, and those responsible may be liable in law accordingly
ISBN 978–1–78060–049–9
Cover Image: _A Kuruba boy during the begging festival_ © John Isaac
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Note: I now offer specific treatment for Osgood-Schlatter's Disease.
Osgood-Schlatter's disease is the most common overuse injury among childhood athletes. It is a condition of the knee, where pain is felt below the kneecap at the bony bump at the top of the shin. It is likely caused by growth spurts, where the muscles of the thigh do not keep up with growth of the femur (the long bone of the upper leg), combined with overuse in sports or other activities.
The quadriceps muscle group, on the front of the thigh, goes over and attaches just below the kneecap. Osgood-Schlatter's disease is present when the muscle tendon at the attachment point gets partially torn. This causes pain when running, jumping and kicking. It's important to allow recovery to avoid an outright fracture of the kneecap and/or complications into adulthood. Historically, using conventional treatment, an average of 21 months is needed for recovery.
One study demonstrated that with this approach, a full pain-free wall squat was achieved by all 25 of the study's patients in an average of 20 days and no longer than 50 days. At that point, the patients were discharged and could return to their sports. Three weeks is a LOT faster than 21 months! Patients who continued to stretch as advised were still healthy 1-5 years after the first treatment period.
Myofascial release massage (MRM, also known as MFR) is one of my favorite techniques because it is so effective for a variety of pain conditions. When a child (and parent) come in for this treatment, I demonstrate how to do MFR on his/her thigh(s), as well as teach a parent how to do MFR at home.
I then give an appropriate stretch for the quadriceps, to be undertaken as soon as pain-free flexion of the knee is achieved by the massage. It is important not to stretch too early or the problem can be worsened.
To prevent this condition, active kids should be checked for flexibility in the quadriceps and hamstrings. I offer range-of-motion testing (part of my Orthopedic Massage training). Those who lack flexibility are at risk of developing Osgood-Schlatter's disease. Daily stretches should be followed. However, I recommend avoiding stretching cold muscles. Research shows that stretching is not an effective way to warm muscles. Walking for 5-10 minutes is best to warm up and stretching should follow.
Please let me know if I can help with this condition. Feel free to read about the treatment I offer, call for a consultation or schedule an appointment online (60 minutes).
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Q: Download file from server using Swift Hi I have a whole bunch of .mp3 files I want to use with NSFileManager and store in the documents folder. Is there a way I can download the .mp3 files online and then have it save to the documents folder? This is what I'm using for a local file.
let filemanager = NSFileManager.defaultManager()
let documentsPath : AnyObject = NSSearchPathForDirectoriesInDomains(.DocumentDirectory,.UserDomainMask,true)[0]
let destinationPath:NSString = documentsPath.stringByAppendingString("/Attention.mp3")
if (!filemanager.fileExistsAtPath(destinationPath)) {
var theError: NSError?
let fileForCopy = NSBundle.mainBundle().pathForResource("Attention",ofType:"mp3")
filemanager.copyItemAtPath(fileForCopy!,toPath:destinationPath, error: &theError)
if (theError == nil) {
println("The music files has been saved.")
} else {
println("Error")
}
} else {
println("The files already exist")
}
A: edit/update: Xcode 11.5 • Swift 5.2
import UIKit
import AVFoundation
class ViewController: UIViewController {
var player: AVPlayer!
override func viewDidLoad() {
super.viewDidLoad()
let alarm = URL(string: "https://www.ringtonemobi.com/storage/upload/user_id_1/iphone-5-alarm-2016-08-21-01-49-25.mp3")!
do {
try alarm.download(to: .documentDirectory) { url, error in
guard let url = url else { return }
self.player = AVPlayer(url: url)
self.player.play()
}
} catch {
print(error)
}
}
}
import Foundation
extension URL {
func download(to directory: FileManager.SearchPathDirectory, using fileName: String? = nil, overwrite: Bool = false, completion: @escaping (URL?, Error?) -> Void) throws {
let directory = try FileManager.default.url(for: directory, in: .userDomainMask, appropriateFor: nil, create: true)
let destination: URL
if let fileName = fileName {
destination = directory
.appendingPathComponent(fileName)
.appendingPathExtension(self.pathExtension)
} else {
destination = directory
.appendingPathComponent(lastPathComponent)
}
if !overwrite, FileManager.default.fileExists(atPath: destination.path) {
completion(destination, nil)
return
}
URLSession.shared.downloadTask(with: self) { location, _, error in
guard let location = location else {
completion(nil, error)
return
}
do {
if overwrite, FileManager.default.fileExists(atPath: destination.path) {
try FileManager.default.removeItem(at: destination)
}
try FileManager.default.moveItem(at: location, to: destination)
completion(destination, nil)
} catch {
print(error)
}
}.resume()
}
}
Original answer
Xcode 8.3.2 • Swift 3.1
if let audioUrl = URL(string: "http://freetone.org/ring/stan/iPhone_5-Alarm.mp3") {
// create your document folder url
let documentsUrl = try! FileManager.default.url(for: .documentDirectory, in: .userDomainMask, appropriateFor: nil, create: true)
// your destination file url
let destination = documentsUrl.appendingPathComponent(audioUrl.lastPathComponent)
print(destination)
// check if it exists before downloading it
if FileManager.default.fileExists(atPath: destination.path) {
print("The file already exists at path")
} else {
// if the file doesn't exist
// just download the data from your url
URLSession.shared.downloadTask(with: audioUrl, completionHandler: { (location, response, error) in
// after downloading your data you need to save it to your destination url
guard
let httpURLResponse = response as? HTTPURLResponse, httpURLResponse.statusCode == 200,
let mimeType = response?.mimeType, mimeType.hasPrefix("audio"),
let location = location, error == nil
else { return }
do {
try FileManager.default.moveItem(at: location, to: destination)
print("file saved")
} catch {
print(error)
}
}).resume()
}
}
A: Xcode 10.1, Swift 4
I used the example above from @leo-dabus but broke up the code a bit into two functions. One flaw I found in that approach was that it did not handle the case where the file is already downloaded.
This example will remove any previous file that was already downloaded and write the latest version.
/// Downloads a file asynchronously
func loadFileAsync(url: URL, completion: @escaping (Bool) -> Void) {
// create your document folder url
let documentsUrl = try! FileManager.default.url(for: .documentDirectory, in: .userDomainMask, appropriateFor: nil, create: true)
// your destination file url
let destination = documentsUrl.appendingPathComponent(url.lastPathComponent)
log.info(m: "downloading file from URL: \(url.absoluteString)")
if FileManager().fileExists(atPath: destination.path) {
print("The file already exists at path, deleting and replacing with latest")
if FileManager().isDeletableFile(atPath: destination.path){
do{
try FileManager().removeItem(at: destination)
print("previous file deleted")
self.saveFile(url: url, destination: destination) { (complete) in
if complete{
completion(true)
}else{
completion(false)
}
}
}catch{
print("current file could not be deleted")
}
}
// download the data from your url
}else{
self.saveFile(url: url, destination: destination) { (complete) in
if complete{
completion(true)
}else{
completion(false)
}
}
}
}
func saveFile(url: URL, destination: URL, completion: @escaping (Bool) -> Void){
URLSession.shared.downloadTask(with: url, completionHandler: { (location, response, error) in
// after downloading your data you need to save it to your destination url
guard
let httpURLResponse = response as? HTTPURLResponse, httpURLResponse.statusCode == 200,
let location = location, error == nil
else { print("error with the url response"); completion(false); return}
do {
try FileManager.default.moveItem(at: location, to: destination)
print("new file saved")
completion(true)
} catch {
print("file could not be saved: \(error)")
completion(false)
}
}).resume()
}
A: I found the @leo-dabus worked straight away, but had to make two minor changes for my needs. This might be helpful for others.
Change #1: Handle filenames that come included with a path-extension
if let fileName = fileName {
if fileName.hasSuffix(self.pathExtension) {
destination = directory
.appendingPathComponent(fileName)
} else {
destination = directory
.appendingPathComponent(fileName)
.appendingPathExtension(self.pathExtension)
}
} else {
destination = directory
.appendingPathComponent(lastPathComponent)
}
Change #2: If the destination file exists, generate a unique name
E.g. generate File (2).txt to avoid overwriting File.txt, like a web browser would.
if !overwrite {
let pathExtension = destination.pathExtension
let lastComponent = destination.deletingPathExtension().lastPathComponent
var copyNumber = 2
var attemptedURL = destination
while FileManager.default.fileExists(atPath: attemptedURL.path) {
attemptedURL = destination
.deletingPathExtension()
.deletingLastPathComponent()
.appendingPathComponent("\(lastComponent) (\(copyNumber))")
.appendingPathExtension(pathExtension)
copyNumber += 1
}
destination = attemptedURL
}
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 50
|
Opinion Columnists 09 Jan 2022 Saeed Naqvi | Wasn&r ...
Opinion, Columnists
Saeed Naqvi
The writer is a senior journalist and commentator based in New Delhi
Saeed Naqvi | Wasn't world a better place in middle of the Cold War?
My memory of the events three decades ago is of a personal nature as I was the only journalist who interviewed Mikhail Gorbachev
Mikhail Gorbachev (Twitter)
When he wrote The End of History, Francis Fukuyama hoped the West would not waste the possibilities which had opened up with the collapse of the Soviet Union 30 years ago. But the West made the fatal mistake: it mistook rampaging capitalism for democracy. In 2009, with the collapse of Lehman Brothers, its decline accelerated.
My memory of the events three decades ago is of a personal nature as I was the only journalist who interviewed Mikhail Gorbachev, the man who, on a high wire act of historic reforms, lost control. India's foreign secretary Romesh Bhandari wouldn't obstruct my interview but he promised the media accompanying Prime Minister Rajiv Gandhi to Moscow that "they would all stand around an arena while I did the interview".
The choreography dictated the set. A circular boxing arena was created, ropes et al, in which four chairs were placed. Two for Gorbachev and his interpreter, one for the interviewer, but the fourth? As Romesh Bhandari didn't wish to be unpopular with the media accompanying the PM by allowing one journalist to steal a scoop, he awarded the third chair to a notional representative for the rest of the media. Who could this be but the inimitable Russi Karanjia, the colourful editor of Blitz?
What Romesh didn't realise is exactly what Andrei Gromyko, USSR's longest serving foreign minister who stayed on for Gorbachev's first year in office, immediately did. He peeped into the hall where the "rope-ring" had been set up. After concluding his talks with Rajiv Gandhi, Gorbachev would walk towards this arena.
Imagine the scene. Two interviewers looking at two empty chairs in the ring, and 30 journalists, craning their necks into the arena, clearing their throats and waiting for Gorbachev to take his seat. Gromyko, the old fox, wasn't going to allow the new CPSU general secretary, in his very first outing with the media, to be exposed to a free-for-all press conference, a "tamasha". Gromyko called it off.
My disappointment couldn't be measured and for that reason I persisted. I returned to Moscow the next year to interview Gorbachev, but that is another story. Before I close the Gorbachev segment for this column, a word on what Gorby's eventual vision for Soviet Russia was? "Something like the Scandinavian welfare state." This was before neo-con excesses during the fleeting unipolar moment and a rushed Murdochisation of the media had disfigured much of the world, including Scandinavia.
The second image is of South Block, with the external affairs ministry split down the middle on the goings-on in Moscow. Arundhati (Chuku) Ghosh, that heavy-smoking, clean-hearted Brahmo, joint secretary for Africa, was in a state of anxiety. She was following events in Moscow -- the coup, a tense moment for her. She isn't clear what she wants, but her DNA demands a "liberal" system, not the Soviet Union. To her it didn't matter if Boris Yeltsin replaces Gorbachev.
Round the corner from Chuku, in his room at the far end of the corridor, foreign secretary Muchkund Dubey, a homespun Bihari intellectual, culturally as distinct from Chuku as chalk is from cheez, is on the line to his ambassador in Moscow, Alfred Gonsalves. The two are classical status quoists. Having spent a lifetime writing position papers mindful of the two blocs, the imminent collapse of the Soviet Union is, for them, like having to walk on one leg.
This brings me to the third question: Was the Indian Establishment ever emotionally embedded with the Soviet Union?
On one hand C. Rajeswara Rao, CPI's longest-serving general secretary, is shaking with rage at a reporter who asked him if the Soviet Union was collapsing.
"Sir (loaded with satire), not a pin in this world moves without the Soviet Union being involved."
This touching faith in the Soviet Union was all-pervasive among progressive writers and Urdu poets carted to Mumbai by an earlier CPI general secretary, P.C. Joshi.
"Kremlin ke minar jaage hue kharey hain." (The minarets of the Kremlin beckon us).
This was Javed Akhar's father Jaan Nisar Akhtar, ecstatic about the Kremlin's minarets. A fine ghazal writer like Majrooh Sultanpuri could not resist the pressure of his peers.
"Meri nigah mein hai arze Moscow, Majrooh/ Woh sarzameen ki sitarey jise salaam karein." (My eyes are set on Moscow, that blessed place where stars come down from heaven to shower their salutations).
Poets, writers, painters, actors, film producers, college campuses and coffee house regulars — this entire lot was marginal to the pro-West establishment, big industrialists whose "proximity" to Gandhiji gave them an all-pervasive influence.
Before V. Shankar, ICS, could join Deputy PM Sardar Vallabhbhai Patel's office, he had to be interviewed by Ghanshyam Das Birla, the leading industrialist in whose house Gandhiji died.
Marwari-owned newspapers which Indira Gandhi dubbed the "jute press" never posted a correspondent to Moscow even in the days when the Indian ambassador had direct access to the central committee. Instead, correspondents were posted to London and Washington where they had no access.
The only Indian journalist in Moscow was the towering figure of Masood Ali Khan, a Pathan to boot, representing the CPI organ New Age. He had phenomenal access to the otherwise impenetrable Soviet system. He was a mandatory fixture for all visiting Indian journalists, diplomats and progressive writers. When the Soviet Union collapsed, Masood fell into abject penury. His salary which the Soviet system had arranged through the Red Cross was stopped. He died on the box-sofa of his one-room tenement near a metro station. Beneath the cushion on the sofa were lined hundreds of 78 rpm records of Western classical music that he had collected during his better days at the BBC in London.
Tags: cold war era
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|
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"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 8,892
|
Tekutina je společný název pro kapaliny a plyny (patrně i pro plazma a kvark gluonové plazma), jejichž významnou společnou vlastností je tekutost, neboli neschopnost udržet svůj stálý tvar díky snadnému vzájemnému pohybu částic. K tekutinám se většinou řadí také sypké látky, které jsou sice pevného skupenství, ale splňují kritérium tekutosti.
Tekutiny se liší od pevných látek především velkou pohyblivostí svých částic, nemají vlastní tvar a snadno se dělí. Protože tekutiny kladou malý odpor vůči silám působícím ve směru vnější normály plochy, která tekutinu omezuje, nemluvíme u tekutin o tlaku, ale o napětí.
Odpor tekutin proti změně tvaru nazýváme viskozitou, která se projevuje jen pokud není tekutina v klidu. Viskózní síla má snahu zmenšit vzájemný rozdíl rychlostí v proudící tekutině a je tudíž analogií k třecí síle, která je součástí mechaniky pevných látek.
Tekutinu, u které se neprojevují viskózní síly, nazýváme dokonalou. Jak je z názvu zřejmé, taková tekutina je pouze myšlenkový konstrukt, který nemá v reálném světě oporu. V praxi se ovšem setkáme s některými tekutinami, které mají tak malou viskozitu, že je dokonalá tekutina jejich dobrou aproximací.
Tekutiny dělíme na kapaliny a plyny. Vzájemně se liší především stlačitelností a rozpínavostí. Plyny jsou rozpínavé, kdežto kapaliny vytvářejí volnou hladinu. Kapaliny jsou stlačitelné jen nepatrně, kdežto plyny jsou stlačitelné velmi jednoduše.
Tekutiny se dělí na
newtonské (např. voda)
nenewtonské (např. barvy, škrobové roztoky, mléko)
podle toho, zda splňují Newtonův zákon viskozity, který říká, že odpor způsobený vnitřním třením v tekutině je přímo úměrný rychlosti toku. Studiem vlastností tekutin se zabývá rheologie.
Ideální tekutina
Ideální (dokonalá) tekutina je taková tekutina, v níž jsou všechna smyková napětí nulová, a tenzor napětí lze vyjádřit ve tvaru
,
kde . V každém bodě ideální tekutiny (tedy na všech rovinách proložených tímto bodem) je napětí čistým tlakem o velikosti . Modul pružnosti ve smyku ideální tekutiny je nulový, tzn. . Nepřítomnost smykového napětí znamená, že v ideální tekutině nepůsobí vnitřní tření.
Ideální tekutina se nebrání změně tvaru, tzn. je dokonale tekutá.
Zvláštním případem ideální tekutiny je:
ideální kapalina
ideální plyn
Základní rovnice rovnováhy tekutin
Základní rovnice rovnováhy tekutin je fyzikální rovnice popisující rovnovážný stav v tekutině. Běžný její zápis je .
Následuje její postup odvození.
Postup odvození
Předpokládejme, že se ideální tekutina pohybuje tak, že jedna vrstva molekul pomalu
klouže po druhé vrstvě.
Vyjděme z rovnice rovnováhy elastického kontinua
(rovnice 1)
, kde jsou složky síly a jsou složky tenzoru napětí, pro které platí .
Dokonalá tekutina neodporuje změnám tvaru a proto jsou tečná napětí nulová, tedy
Rovnici (2) tedy můžeme považovat za definiční rovnici tekutiny v rovnováze. Protože tato rovnice platí pro libovolnou kartézskou soustavu souřadnic, jsou její osy hlavními osami tenzoru napětí a tenzorová plocha je v tomto případě kulová. Proto jsou si normálová napětí rovna
Položíme-li , kde p je tlak, pak musí platit .
Po dosazení (2) do (1) dostaneme základní hydrostatickou rovnici nebo vektorově
Poslední rovnice je nutná a postačující podmínka rovnováhy tekutiny. Úplný diferenciál tlaku p, který je funkcí souřadnic xi, vychází ze základní hydrostatické rovnice
U stlačitelných tekutin závisí hustota ρ na stavu kontinua, nevztahujeme proto vnější síly na jednotku objemu, nýbrž na jednotku hmotnosti. Objemovou sílu vztaženou na jednotku hmotnosti budeme značit G, její složky Gi, tedy .
Rovnici rovnováhy tekutin můžeme přepsat takto nebo vektorově
Poznámka
U tekutin, které jsou v rovnováze, se neuplatňují viskózní síly. Takže zde uvedené rovnice se vztahují jak na ideální tak na viskózní tekutiny.
Reference
Literatura
Miroslav Brdička, Ladislav Samek a Bruno Sopko: Mechanika kontinua,Academia, 2000
Miroslav Brdička, Arnošt Hladík: Teoretická mechanika, Academia, 1988,
Související články
Mechanika tekutin
Mechanika kontinua
Tekoucí písek
Externí odkazy
Mechanika tekutin
Hmota
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| 1,090
|
Q: How can I obfuscate database authentication info during open-source development? I'm working on an open-source web application that will retrieve and display data from a database whose authentication info I would like to keep under wraps, but at the same time, I would like anyone to be able to view and contribute to the source code. The idea is that we don't want the database to be used for profit.
Is there a way to make the database schema public, but only have a few rows of each table actually visible outside of the production server? I'm using ASP.NET MVC 4 in Visual Studio 2012, hosting the code on git, and publishing to Windows Azure. I'm also using a pre-existing Microsoft Access 2007 database.
A: You could encrypt the connectionStrings section of the Web.config file.
How you do that is described here. The connectionStrings section would not be decryptable on any machine except the server. It would be rather inconvenient for other developers though. You could set up so that this connection string is only used when the web site is published using transforms.
|
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| 6,832
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RUST BELT RISING ALMANAC, Vol. 1 reviewed by Ariel Diliberto
Cleaver Magazine Posted on July 23, 2013 by thwack October 9, 2014
click to return to reviews index
RUST BELT RISING ALMANAC, Vol. 1
The Head & The Hand Press, 168 pages
reviewed by Ariel Diliberto
Rust Belt Rising Almanac presents a pastiche of short stories, poems, photographs and artwork. Collectively they form a fairly complete image of the post-industrial cities that comprise the toponymous "belt" (in the case of this publication, namely Philadelphia, Cleveland, Detroit, and Pittsburgh). Collectively being the operative word. For individually, some of the stories are flashes in the (rusting) pan. However, together these ethereal dispatches evoke the negative space inside an abandoned factory building, and upon reaching page 168, readers can step back and see it for what it is.
So what is it? The triumph of Rust Belt is its ability to dispel the false narrative about America's trajectory from industrial to post-industrial, in which the peak of our society was the peak of the industrial era, and it's been downhill ever since. Put another way, the idea that when factories were pumping in the hearts of these cities, it was the "good old days," and now that they've shut down or relocated, despair ensues. Rust Belt demonstrates that a) the "good old days" weren't always all that good, as Kim Geralds illustrates in the opening poem "Trademarks":
Hands mashed, two fingertips lost
Stamp fenders of galvanized steel, in
2.4 minutes, rushed down the line
And Sarah Grey elaborates upon in "Under This Cloud: Life and death in the shadow of a coal-fired power plant": "your sign of home and life and prosperity is also a sign of death… the people you love, and indeed you yourself, have always been dependent on an industry that sees the lives of you and everyone who raised you as collateral damage."
And b) things aren't always so bad right now, depending on who you are. Many of the authors invoke the thrills of being a young person in these Rusties: riding bikes through abandoned streets at night, renting cheap art studios in former factories, gardening in urban soils, roadtripping. Fear not, other authors look beyond the rehabbed warehouses, to the open-air drug markets and prostitute drags just out of sight, and the people whose lives are trapped in them. In Liz Moore's interviews with prostitutes working along Philadelphia's Kensington Avenue, a woman named Tanya describes her failed attempt to enter normative pathways of society: "I was clean for five months. Those five months, when I was clean, I couldn't get a job at all. I went so many places, so many places, like K-Mart, Pathmark. Anything you can think of, I went to…None of them are hiring."
At first, I was dubious of the "almanac" epithet. An almanac is traditionally a collection of statistics and information upon which hobbyists or farmers base their decisions. But ultimately, I would say Rust Belt is an almanac: an arsenal of documentation about "what is," that feeds the imaginative of "what could be" for America's post-industrial cities.
Make no mistake, Rust Belt doesn't seem to imply that the ideal version of "what could be" is accomplished by more small businesses and artists' studios. Those edifices are the horizon the book constructs that we must look beyond.
Looking beyond is essential in an era of urban revitalization where the dominant paradigm is Richard Florida's regrettable "creative class" approach—a theory that Florida himself admits provides little trickle-down benefit for cities' lower-income inhabitants. I'm someone who hopes that these rusted old cities can someday thrive in ways other than merely serving as a concentration of "creative" capital.
In Marissa Johnson-Valenzuela's piece "Trumbullplex," the protagonist contemplates "how a city might be after people stopped using it the way it was built to be used." I can only hope cities will someday be used to foster residents' pursuit of a vocation as Alexander Barton defines it in "Cleveland is a Vocation":"[the word's] roots are the Latin words for 'a call' or 'a summons.' The underlying belief is that everyone, through their upbringing, passions, experiences, and education, is searching for an honest expression of how they see the world." Everyone, including Tanya on Kensington Ave.
Ariel Diliberto is Block Programs Coordinator at New Kensington Community Development Corporation. She is also a contributor to Hidden City Philadelphia and sits on the central committee of the Philly Socialists. Ariel received a B.A. in Urban Ecology from Vassar College in 2011. For more information, visit her website.
RUST BELT RISING ALMANAC, Vol. 1 reviewed by Ariel Diliberto Published on July 23, 2013 in reviews (Click for permalink.)
|
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| 9,574
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– One very important element to consider in buying a Bengal cat is its actual price. Well, if you want a Bengal in your home, you should very well know it's a rare breed. With rarity comes the high price, so you should expect that a Bengal cat may price from 500 USD to approximately 5,000 USD, depending on what Bengal quality you would like.
As you know, there are three main types of Bengals-pet quality, breeder quality, and display quality. Pet quality Bengals price 500-1,000 USD while a breeder or show quality Bengal could cost from 1,500-5,000 USD (reveal Bengals could be expensive depending on the breeder).
The cost of the breeder cat food changes from time to time, based on the price of raw materials. You need to keep yourself updated with all the cost variations in the community grocery store.
Vet care and vaccines should be regarded as well. This may also include potential emergency care, hospitalization, nutritional supplements, and other medications. This is a very important factor in determining how far a Bengal could cost. Vaccinations price 50-70 USD, whilst flea and de-worming drugs cost 20 USD.
Insuring your Bengal cat might really help you from the entire medical cost to getting you reunited with your Bengal (if you misplaced it). Including this in your Bengal budget is crucial. Bengal cat insurance can cost 30 USD monthly.
The amount of money needed in obtaining a Bengal cat also depends upon where you're likely to receive your Bengal. If you decide to get your cat from a reputable breeder, then you ought to be preparing a bigger amount. But if you are going to receive your Bengal cat from a rescue centre, it is only going to cost you a lot less because you will be adopting the cat. Nevertheless, you still need to consider the costs in keeping your Bengal cat.
Find out the most recent images of The Truth About Bengal Cat Breeders On Long Island Is About To Be Revealed | Bengal Cat Breeders On Long Island here, and also you can get the image here simply image posted uploaded by Teman Saya that saved in our collection.
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{
"redpajama_set_name": "RedPajamaC4"
}
| 4,843
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This trampoline ladder calculator only works if your measurement is accurate.
To measure the height of your trampoline, you just need a metric tape measure.
Measure from the base of the trampoline (the ground) to the top of the frame, as shown in the image below.
Using this Ladder Calculator will help eliminate guesswork.
Approximating or guessing will distort the outcome!
|
{
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}
| 6,369
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Q: Numpy functions clobber my inherited datatype Say I have a class ndarray_plus that inherits from numpy.ndarray and adds some extra functionality. Sometimes I pass it to numpy functions like np.sum and get back an object of type ndarray_plus, as expected.
Other times, numpy functions that I pass my enhanced object to return an numpy.ndarray object, destroying the information in the extra ndarray_plus attributes. This happens usually when the numpy function in question does a np.asarray instead of np.asanyarray.
Is there a way to prevent this from happening? I can't go into the numpy codebase and change all instances of np.asarray to np.asanyarray. Is there a Pythonic way to pre-emptively protect my inherited object?
A: The defined and guaranteed behaviour of asarray is to convert your subclass instance back to base class
help on function asarray in numpy:
numpy.asarray = asarray(a, dtype=None, order=None)
Convert the input to an array.
Parameters
----------
a : array_like
Input data, in any form that can be converted to an array. This
includes lists, lists of tuples, tuples, tuples of tuples, tuples
of lists and ndarrays.
dtype : data-type, optional
By default, the data-type is inferred from the input data.
order : {'C', 'F'}, optional
Whether to use row-major (C-style) or
column-major (Fortran-style) memory representation.
Defaults to 'C'.
Returns
-------
out : ndarray
Array interpretation of `a`. No copy is performed if the input
is already an ndarray. If `a` is a subclass of ndarray, a base
class ndarray is returned.
See Also
--------
asanyarray : Similar function which passes through subclasses.
< - snip - >
You could try and monkeypatch:
>>> import numpy as np
>>> import mpt
>>>
>>> s = np.matrix(3)
>>> mpt.aa(s)
array([[3]])
>>> np.asarray = np.asanyarray
>>> mpt.aa(s)
matrix([[3]])
file mpt.py
import numpy as np
def aa(x):
return np.asarray(x)
Sadly, this doesn't always work.
alternative mpt.py
from numpy import asarray
def aa(x):
return asarray(x)
here you'd be out of luck.
|
{
"redpajama_set_name": "RedPajamaStackExchange"
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| 1,851
|
Ion Exchange Materials Properties and Applications
This book PDF is perfect for those who love Science genre, written by Andrei A. Zagorodni and published by Elsevier which was released on 02 November 2006 with total hardcover pages 496. You could read this book directly on your devices with pdf, epub and kindle format, check detail and related Ion Exchange Materials Properties and Applications books below.
Author : Andrei A. Zagorodni
Publisher : Elsevier
Release Date : 02 November 2006
Ion Exchange Materials Properties and Applications by Andrei A. Zagorodni Book PDF Summary
Ion Exchange Materials: Properties and Applications fills a "two-dimensional" gap in books currently available on the subject. Firstly, there is a lack of modern comprehensive publications on the chemistry of ion exchange materials and on the relationships between their properties and practical applications. Secondly, there are few books on ion exchange chemistry that are targeted to industrial R&D specialists and research students who (i) do not work with ion exchange on a daily basis, (ii) need to develop competence in this area, and (iii) find it difficult to start studying the subject from primary scientific publications. The book bridges these gaps by describing classical and modern theoretical concepts, as well as practical approaches for using ion exchange materials. Ion exchange materials combine properties of homogeneous and heterogeneous materials. Besides being an interesting subject for investigation, they are essential in a wide variety of industrial technologies: in the chemical and biochemical industries, pharmacy, medicine, microelectronics, the nuclear industry, food production, waste treatment, and many other areas. Ion exchange is a powerful tool in chemical analysis and scientific research. The main focus in this book is on ion exchange polymers: ion exchange resins, chelating resins, imprinted (templated), and other functional polymers. It provides an in-depth study of ion exchange materials, suitable for postgraduate students and R&D industrial specialists in chemistry, chemical and biochemical technology. Comprehensively covers the subject Provides links between theoretical concepts, material properties, practical applications, and technical solutions Easy to understand - requires only ground knowledge of university-level chemistry and can be read without an in-depth knowledge of mathematics Supported with an interactive website
Ion Exchange Materials Properties and Applications by Andrei A. Zagorodni
Ion Exchange Materials: Properties and Applications fills a "two-dimensional" gap in books currently available on the subject. Firstly, there is a lack of modern comprehensive publications on the chemistry of ion exchange materials and on the relationships between their properties and practical applications. Secondly, there are few books on ion
Ion Exchange Technology I by Inamuddin Dr.,Mohammad Luqman
Ion-exchange Technology I: Theory and Materials describes the theoretical principles of ion-exchange processes. More specifically, this volume focuses on the synthesis, characterization, and modelling of ion-exchange materials and their associated kinetics and equilibria. This title is a highly valuable source not only to postgraduate students and researchers but also to
Ion Exchange by C E Harland
Ion Exchange, 2nd Edition is a totally revised and updated version of the highly popular Monograph for Teachers, first published by The Royal Society of Chemistry in 1975. It covers the practical application of ion exchange and the synthesis of organic ion exchange resins, which have spanned nearly 60 years of development
Ion Exchangers Properties and Applications by Konrad Dorfner
Download or read online Ion Exchangers Properties and Applications written by Konrad Dorfner, published by Unknown which was released on 1972. Get Ion Exchangers Properties and Applications Books now! Available in PDF, ePub and Kindle.
Applications of Ion Exchange Materials in Biomedical Industries by Inamuddin
This book presents the applications of ion-exchange materials in the biomedical industries. It includes topics related to the application of ion exchange chromatography in determination, extraction and separation of various compounds such as amino acids, morphine, antibiotics, nucleotides, penicillin and many more. This title is a highly valuable source of
Ion Exchange by Clive E. Harland
Annotation Extensively revised and updated from the popular 1975 guide for college teachers. Explains the theory, history, methods, and industrial applications of ion-exchange materials. Includes 22 experiments that require inexpensive equipment and demonstrate the principles being described. Annotation c. by Book News, Inc., Portland, Or.
Applications of Ion Exchange Materials in the Environment by Inamuddin,Mohd Imran Ahamed,Abdullah M. Asiri
This book presents the applications of ion-exchange materials in the area of environmental analysis and treatment. It includes chapters on applications of organic, inorganic and composite ion exchange materials and hexacyanoferrates in various fields such as chemical and biochemical separations, water purification, removal of harmful impurities, dyes and cationic and
Inorganic Ion Exchange Materials by Clearfield
This book extends the frontiers of the ion exchange technologist and highlights new materials for the future.
The Devil S Chessboard
Godot From Zero To Proficiency Beginner
Classical and Modern Direction-of-Arrival Estimation
Handbook of Modern Pharmaceutical Analysis
Implementing Analytics
Operative Techniques: Spine Surgery
Advanced Power Generation Systems
The Devil in the White Cit
Guilty Minds
Cardiovascular Thrombus
Laboratory Assessment of Vitamin Status
The Sentences On The Incarnation Of The Word
Multimedia Information Retrieval
Central Banking 101
Data-Centric Safety
Cognitive Electrophysiology of Attention
100 Ideas For Secondary Teachers Stretch And Challenge
Protein Bioinformatics
Fredric Jameson and The Wolf of Wall Street
Airborne Radioactive Contamination in Inhabited Areas
Space Exploration in the United States
Self-assembling Biomaterials
Existentialism Is A Humanism
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 6,920
|
Q: Crear un for para consultar valores de un data Tengo un data con varias variables y quiero usar un for para que recorra varias variables y consulte los valores.
El data table datos contiene las variables V1, V2... V15. Lo que quiero es crear una variable Stotal que sea la suma de los valores SI que hay en las variables V1 a V15.
for (i in 1:nrow(datos)){
for (j in 1:15){
(if(sprintf("V%d",j)[i])=="SI"){
aux<-1
Stotal[i]<-1+aux
}
}
El codigo no funciona, entre otras cosas, porque la función sprintf pega el texto pero no saca el valor de la variable en la posicion que le pido.
Editado:
Un ejemplo con menos columnas podría ser:
V1 <- c("Si","No","Si")
V2 <- c("Si","No","No")
V3<-c("Si","Si","Si")
datos <- data.frame(V1,V2,V3)
datos
V1 V2 V3
1 Si Si Si
2 No No Si
3 Si No Si
En este caso la salida esperada sería: 3 1 2
A: Puede utilisar una dataframe :
Sval<-0
# Creo tres vectores of misma tamano. Utiliso tres vectores para simplicidad
V1 <- c(5,9,3)
V2 <- c(10,11,12)
V3<-c(13,14,15)
X <- data.frame(V1,V2,V3)
rownames(X) <- c("SI","b","c")
datos <- X
print(datos)
Que da :
V1 V2 V3
SI 5 10 13
b 9 11 14
c 3 12 15
Y para calcular las valores del attributo SI :
for (val in datos["SI",]){
Stotal=Stotal + val
}
print(Stotal)
Que da
[1] 28
A: Más allá que lo puedas resolver mediante un loop R tiene mecanismos más efectivos y performantes. Por ejemplo:
V1 <- c("Si","No","Si")
V2 <- c("Si","No","No")
V3<-c("Si","Si","Si")
datos <- data.frame(V1,V2,V3)
datos
apply(datos, MARGIN = 1, function(x) sum(ifelse(x=="Si", 1, 0)))
La Salida:
V1 V2 V3
1 Si Si Si
2 No No Si
3 Si No Si
V1 V2 V3
2 1 3
*
*Aplicamos apply() la función sum a datos por filaMARGIN = 1
*Pero solo sumamos 1 si el valor es Si (ifelse(x=="Si", 1, 0))
O incluso mucho más fácil:
rowSums(datos[,]=="Si")
*
*Aplicamos rowSums para sumar por fila, únicamente los valores que sean Si (datos[,]=="Si")
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 9,384
|
VTV (Vaša televízia) byla v letech 1995 až 2000 televizní stanicí na Slovensku. Vysílala přes satelit a kabel.
Začátky
Televize začala vysílat 22. dubna 1995. Vysílání bylo uvedeno americkým filmem Tah jezdcem.
Finanční problémy a pád VTV
K VTV přibyla konkurenční soukromá televizní stanice Markíza. TV Markíza se zahraničním kapitálem a know-how vytlačila VTV na okraj diváckého zájmu. V dobách kdy dluh VTV vůči Všeobecné úvěrové bance stoupal k 300 milionům Sk, dostala televize v roce 1998 první velkou finanční injekci – po prodeji 51% podílu společnosti VTV Cable TV spol s r. o. společnosti TV Plus Vladimíra Poóra. V záři se uskutečnil ve VTV relaunching, televize byla posilněna balíkem TV filmů a německých TV seriálů. Paralelně se objevila outdoorová kampaň televize. Televize však postupně začala opět programově stagnovat. Po dalších majetkových přísunech se dostala k televizi bývalá programová ředitelka TV Markíza Tatiana Heldová, která se pokusila zlepšit situaci upravením programové struktury. VTV ukončila vysílání v únoru 2000 po téměř pěti letech vysílání.
Pořady VTV
Aj múdry schybí
Osmička
Dvanástka (česky Dvanáctka)
Receptárium
Motomagazín
Hitparáda K.O
Kokteil (česky Koktejl)
Tenisky
Magická záhrada (česky Magická zahrada)
Bez dresu
Tourclub
Hitparáda SC TOP 10
Denník VTV (česky Deník VTV)
Ententičky (česky Ententičky)
Klub 22
2+2
TeenAge
Vo fraku (česky Ve fraku)
Pošepky (česky Posypky)
Level majstrov (česky Level mistrů)
Zaniklé slovenské televizní stanice
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 3,912
|
\section{Introduction}
Gaussian processes (GPs) are a widely-used class of models for learning an unknown function within a Bayesian framework.
They are particularly attractive for use within decision-making systems, e.g. in Bayesian optimization \cite{snoek2012} and reinforcement learning \cite{deisenroth11, deisenroth13}, where well-calibrated uncertainty is crucial for enabling the system to balance trade-offs, such as exploration and exploitation.
A GP is specified through its mean and covariance kernel.
The Mat\'{e}rn family is a widely-used class of kernels, often favored in Bayesian optimization due to its ability to specify smoothness of the GP by controlling differentiability of its sample paths.
Throughout this work, we view the widely-used squared exponential kernel as a Mat\'{e}rn kernel with infinite smoothness.
Motivated by applications areas such as robotics \cite{jaquier19,calinon20} and climate science \cite{camps2016}, recent work has sought to generalize a number of machine learning algorithms from the vector space to the manifold setting.
This allows one to work with data that lives on spheres, cylinders, and tori, for example.
To define such a GP, one needs to define a positive semi-definite kernel on those spaces.
In the Riemannian setting, as a simple candidate generalization for the Mat\'{e}rn or squared exponential kernel, one can consider replacing Euclidean distance in the formula with the Riemannian geodesic distance.
Unfortunately, this approach leads to ill-defined kernels in many cases of interest \cite{feragen15}.
An alternative approach was recently proposed by \textcite{lindgren11}, who adopt a perspective introduced in the pioneering work of \textcite{whittle63} and define a Mat\'{e}rn GP to be the solution of a certain stochastic partial differential equation (SPDE) driven by white noise.
This approach generalizes naturally to the Riemannian setting, but is cumbersome to work with in practice because it entails solving the SPDE numerically.
In particular, setting up an accurate finite element solver can become an involved process, especially for certain smoothness values \cite{bolin17, bolin19}.
This also prevents one from easily incorporating recent advances in scalable GPs, such as sparse inducing point methods \cite{titsias09a, hensman13}, into the framework.
This in turn impedes one from easily employing mini-batch training, online training, non-Gaussian likelihoods, or incorporating GPs as differentiable components within larger models.
In this work, we extend Mat\'{e}rn GPs to the Riemannian setting in a fully constructive manner, by introducing Riemannian analogues of the standard technical tools one uses when working with GPs in Euclidean spaces.
To achieve this, we first study the special case of the $d$-dimensional torus $\bb{T}^d$.
Using ideas from abstract harmonic analysis, we view GPs on the torus as periodic GPs on $\R^d$, and derive expressions for the kernel and spectral measure of a Mat\'{e}rn GP in this case.
Building on this intuition, we generalize the preceding ideas to general compact Riemannian manifolds without boundary.
Using insights from harmonic analysis induced by the Laplace--Beltrami operator, we develop techniques for computing the kernel and generalized spectral measure of a Mat\'{e}rn GP in this setting.
These expressions enable computations via standard GP approaches, such as Fourier feature or sparse variational methods, thereby allowing practitioners to easily deploy familiar techniques in the Riemannian setting.
We conclude by showcasing how to employ the proposed techniques through a set of examples.
\section{Gaussian processes}
Let $X$ be a set, and let $f: X \-> \R$ be a random function.
We say that $f \~[GP](\mu, k)$ if, for any~$n$ and any finite set of points $\v{x} \in X^n$, the random vector $\v{f} = f(\v{x})$ is multivariate Gaussian with prior mean vector $\v\mu = \mu(\v{x})$ and covariance matrix $\m{K}_{\v{x}\v{x}} = k(\v{x},\v{x})$.
We henceforth, without loss of generality, set the mean function to be zero.
Given a set of training observations $(x_i, y_i)$, we let $y_i = f(x_i) + \eps_i$ with $\eps_i \~[N](0,\sigma^2)$.
Under the prior $f \~[GP](0,k)$ the posterior distribution $f\given\v{y}$ is another GP, with mean and covariance
\<
\E(f\given\v{y}) &= \m{K}_{(\cdot)\v{x}} (\m{K}_{\v{x}\v{x}} + \sigma^2\m{I})^{-1}\v{y}
&
\Cov(f\given\v{y}) &= \m{K}_{(\cdot,\cdot)} - \m{K}_{(\cdot)\v{x}} (\m{K}_{\v{x}\v{x}} + \sigma^2\m{I})^{-1} \m{K}_{\v{x}(\cdot)}
\>
where $(\cdot)$ denotes an arbitrary set of test locations. The posterior can also be written
\[
\label{eqn:pathwise}
(f\given\v{y})(\cdot) = f(\cdot) + \m{K}_{(\cdot)\v{x}} (\m{K}_{\v{x}\v{x}} + \sigma^2\m{I})^{-1} (\v{y} - f({\v{x}}) - \v\eps)
\]
where equality holds in distribution \cite{wilson20}.
This expression allows one to sample from the posterior by first sampling from the prior, and transforming the resulting draws into posterior samples.
On $X = \R^d$, one popular choice of kernel is the \emph{Mat\'{e}rn} family with parameters $\sigma^2,\kappa,\nu$, defined as
\[
\label{eqn:matern-kernel-eucl}
k_{\nu}(x,x') = \sigma^2 \frac{2^{1-\nu}}{\Gamma(\nu)} \del{\sqrt{2\nu} \frac{\norm{x-x'}}{\kappa}}^\nu K_\nu \del{\sqrt{2\nu} \frac{\norm{x-x'}}{\kappa}}
\]
where $K_\nu$ is the modified Bessel function of the second kind \cite{gradshteyn14}.
The parameters of this kernel have a natural interpretation: $\sigma^2$ directly controls variability of the GP, $\kappa$ directly controls the degree of dependence between nearby data points, and $\nu$ directly controls mean-square differentiability of the GP \cite{rasmussen06}.
As $\nu\->\infty$, the Mat\'{e}rn kernel converges to the widely-used squared exponential kernel
\[
\label{eqn:rbf-kernel-eucl}
k_{\infty}(x,x') = \sigma^2 \exp\del[3]{-\frac{\norm{x-x'}^2}{2 \kappa^2}}
\]
which induces an infinitely mean-square differentiable GP.
For a bivariate function $k:X\x X\->\R$ to be a kernel, it must be \emph{positive semi-definite}, in the sense that for any $n$ and any $\v{x}\in X^n$, the kernel matrix $\m{K}_{\v{x}\v{x}}$ is positive semi-definite.
For $X = \R^d$, a translation-invariant kernel $k(x,x') = k(x - x')$ is called \emph{stationary}, and can be characterized via Bochner's Theorem.
This result states that a translation-invariant bivariate function is positive definite if and only if it is the Fourier transform of a finite non-negative measure $\rho$, termed the \emph{spectral measure}.
This measure is an important technical tool for constructing kernels \cite{rasmussen06}, and for practical approximations such as \emph{Fourier feature} basis expansions \cite{rahimi08,hensman17}.
\subsection{A no-go theorem for kernels on manifolds}
We are interested in generalizing the Mat\'{e}rn family from the vector space setting to a compact Riemannian manifold $(M,g)$
such as the sphere or torus.
One might hope to achieve this by replacing Euclidean norms with the geodesic distances in \eqref{eqn:matern-kernel-eucl} and \eqref{eqn:rbf-kernel-eucl}.
In the latter case, this amounts to defining
\[
\label{eqn:rbf-geodesic}
k(x,x') = \sigma^2 \exp\del{-\frac{d_g(x,x')^2}{2 \kappa^2}}
\]
where $d_g$ is the geodesic distance with respect to $g$ on $M$.
Unfortunately, one can prove this is not generally a well-defined kernel.
\begin{theorem}
\label{thm:no-go}
Let $(M,g)$ be a complete, smooth Riemannian manifold without boundary, with associated geodesic distance $d_g$. If the geodesic squared exponential kernel \eqref{eqn:rbf-geodesic} is positive semi-definite for all $\kappa > 0$, then $M$ is isometric to a Euclidean space.
\end{theorem}
\begin{proof}
\textcite[Theorem 2]{feragen15}.
\end{proof}
Since Euclidean space is not compact, this immediately implies that \eqref{eqn:rbf-geodesic} is not a well-defined kernel on any compact Riemannian manifold without boundary.
We therefore call \eqref{eqn:rbf-geodesic} and its finite-smoothness analogues the \emph{na\"{i}ve generalization}.
In spite of this issue, the na\"{i}ve generalization is usually still positive semi-definite for some $\kappa$, and it has been used in a number of applied areas \cite{jaquier19}.
\textcite{feragen16} proposed a number of open problems arising from these issues.
In Section \ref{sec:torus}, we show that, on the torus, the na\"{i}ve generalization is \emph{locally correct} in a sense made precise in the sequel.
We now turn to an alternative approach, which gives well-defined kernels in the general case.
\subsection{Stochastic partial differential equations} \label{sec:spde}
\begin{figure}
\begin{subfigure}{.33\textwidth}
\centering
\includegraphics[height=2.5cm]{Figures/circle_kernel.pdf}
\label{fig:circle-kernel}
\end{subfigure}
\begin{subfigure}{.33\textwidth}
\centering
\includegraphics[height=2.5cm, trim=100 75 100 75, clip]{Figures/sphere_kernel.pdf}
\label{fig:sphere-kernel}
\end{subfigure}
\begin{subfigure}{.33\textwidth}
\centering
\includegraphics[height=2.5cm, trim=0 30 0 30, clip]{Figures/dragon_kernel.pdf}
\label{fig:dragon-kernel}
\end{subfigure}
\caption{The Mat\'{e}rn kernel $k_{1/2}(x, \cdot)$, defined on a circle, sphere and dragon. The point $x$ is marked with a red dot.
The height of the solid line and color, respectively, give the value of the kernel.
}
\label{fig:kernels}
\end{figure}
\textcite{whittle63} has shown that Mat\'{e}rn GPs on $X = \R^d$ satisfy the stochastic partial differential equation
\[
\label{eqn:spde-matern}
\del{\frac{2 \nu}{\kappa^2} - \lap}^{\frac{\nu}{2} + \frac{d}{4}}f = \c{W}
\]
for $\nu < \infty$, where $\lap$ is the Laplacian and $\c{W}$ is Gaussian white noise re-normalized by a certain constant.
One can show using the same argument that the limiting squared exponential GP satisfies
\[
\label{eqn:spde-rbf}
e^{-\frac{\kappa^2}{4} \Delta} f = \c{W}
\]
where $e^{-\frac{\kappa^2}{4} \Delta}$ is the (rescaled) heat semigroup \cite{evans10, grigoryan2009}.
This viewpoint on GPs has recently been reintroduced in the statistics literature by \textcite{lindgren11}, and a number of authors, including \textcite{simpson12, sarkka13b}, have used it to develop computational techniques, notably in the popular \textsc{inla} package \cite{rue09}.
One advantage of the SPDE definition is that generalizing it to the Riemannian setting is straightforward: one simply replaces $\lap$ with the Beltrami Laplacian and $\c{W}$ with the canonical white noise process with respect to the Riemannian volume measure.
The kernels of these GPs, computed in the sequel, are illustrated in Figure \ref{fig:kernels}.
Unfortunately, the SPDE definition is somewhat non-constructive: it is not immediately clear how to compute the kernel, and even less clear how to generalize familiar tools to this setting.
In practice, this restricts one to working with PDE-theoretic discretization techniques, such as Galerkin finite element methods, the efficiency of which depend heavily on the smoothness of $f$, and which can require significant hand-tuning to ensure accuracy.
It also precludes one from working in non-conjugate settings, such as classification, or from using recently-proposed techniques for scalable GPs via sparse inducing point methods \cite{titsias09a, hensman13, hensman17}, as they require one to either be able to compute the kernel point-wise, or compute the spectral measure, or both.
\subsection{State of affairs and contribution}
In this work, our aim is to generalize the standard theoretical tools available for GPs on $\R^d$ to the Riemannian setting.
Our strategy is to first study the problem for the special case of a $d$-dimensional torus.
Here, we provide expressions for the kernel of a Mat\'{e}rn GP in the sense of \textcite{whittle63} via \emph{periodic summation}, which yields a series whose first term is the na\"{i}ve generalization.
Building on this intuition, we develop a framework using Laplace--Beltrami eigenfunctions that allows us to provide expressions for the kernel and generalized spectral measure of a Mat\'{e}rn GP on a general compact Riemannian manifold without boundary.
The framework is fully constructive and compatible with sparse GP techniques for scalable training.
A number of closely related ideas, beyond those described in the preceding sections, have been considered in various literatures.
\textcite{solin2020} used ideas based on spectral theory of the Laplace--Beltrami operator to approximate stationary covariance functions on bounded domains of Euclidean spaces.
These ideas were applied, for instance, to model ambient magnetic fields using Gaussian processes by \textcite{solin2018}.
A truncated analog of the expression we provide in equation \eqref{eqn:mani-matern-formula} for the Riemannian Mat\'{e}rn kernel was previously proposed as a practical GP model by \textcite{coveney2020}---in this work, we \emph{derive} said expression from the SPDE formulation of Mat\'{e}rn GPs.
Finally, the Riemannian squared exponential kernel, also sometimes called the heat or diffusion kernel, has been studied by \textcite{gao2019}.
We connect these ideas with stochastic partial differential equations.
In this work, we concentrate on Gaussian processes $f : M \-> \R$ whose \emph{domain} is a Riemannian manifold.
We do not study models $f : \R \-> M$ where the \emph{range} is a Riemannian manifold---this setting is explored by \textcite{mallasto2018}.
\section{A first example: the $d$-dimensional torus} \label{sec:torus}
\begin{figure}
\<
&\mathclap{
\begin{tikzpicture}[baseline={([yshift=-.5ex]current bounding box.center)}]
\node at (-0.05,-0.1) {};
\node at (0,1) {};
\draw[thick] (0,0) node[circle, fill, inner sep=1] {} to[out=0, in=270] (0.5,0.5) node[circle, fill, inner sep=1] {} ;
\end{tikzpicture}
}
&
&\mathclap{
\begin{tikzpicture}[baseline={([yshift=-.5ex]current bounding box.center)}]
\draw[thick] (0,0) node[circle, fill, inner sep=1] {} to[out=180, in=270] (-0.5,0.5) to[out=90, in=180] (0,1) to[out=0, in=90] (0.5, 0.5) node[circle, fill, inner sep=1] {};
\end{tikzpicture}
}
&
&\mathclap{
\begin{tikzpicture}[baseline={([yshift=-.5ex]current bounding box.center)}]
\draw[thick] (0,0) node[circle, fill, inner sep=1] {} to[out=0, in=270] (0.5,0.5) to[out=90, in=0] (0,1.05) to[out=180, in=90] (-0.55,0.5) to[out=270, in=180] (0, -0.1) to[out=0, in=270] (0.6, 0.5) node[circle, fill, inner sep=1] {};
\end{tikzpicture}
}
&
&\mathclap{
\begin{tikzpicture}[baseline={([yshift=-.5ex]current bounding box.center)}]
\draw[thick] (0,0) node[circle, fill, inner sep=1] {} to[out=180, in=270] (-0.5,0.5) to[out=90, in=180] (0,1) to[out=0, in=90] (0.5, 0.45) to[out=270,in=0] (0,-0.1) to[out=180, in=270] (-0.6,0.5) to[out=90, in=180] (0,1.1) to[out=0, in=90] (0.6,0.5) node[circle, fill, inner sep=1] {};
\end{tikzpicture}
}
&
&\mathclap{
\begin{tikzpicture}[baseline={([yshift=-.5ex]current bounding box.center)}]
\draw[thick] (0,0)
node[circle, fill, inner sep=1] {}
to[out=0, in=270] (0.5,0.5)
to[out=90, in=0] (0,1.05)
to[out=180, in=90] (-0.55,0.5)
to[out=270, in=180] (0, -0.1)
to[out=0, in=270] (0.6, 0.5)
to[out=90, in=0] (0,1.15)
to[out=180, in=90] (-0.65,0.5)
to[out=270, in=180] (0, -0.2)
to[out=0, in=270] (0.7, 0.5)
node[circle, fill, inner sep=1] {};
\end{tikzpicture}
}
\nonumber
\\
&\mathclap{\norm{x - x'}}
&
&\mathclap{\norm{x - x' - 1}}
&
&\mathclap{\norm{x - x' + 1}}
&
&\mathclap{\norm{x - x' - 2}}
&
&\mathclap{\norm{x - x' + 2}}
\nonumber
\>
\caption{
The distances being considered in definitions \eqref{eqn:matern-torus} and \eqref{eqn:rbf-torus}.
}
\label{fig:dist-torus}
\end{figure}
To begin our analysis and build intuition, we study the $d$-dimensional torus $\bb{T}^d$, which is defined as the product manifold $\bb{T}^d = \bb{S}^1 \x ... \x \bb{S}^1$ where $\bb{S}^1$ denotes a unit circle\footnote{Note that $\bb{T}^2 = \bb{S}^1 \times \bb{S}^1$ is diffeomorphic but \emph{not} isometric to the usual donut-shaped torus whose metric is induced by embedding in $\R^3$. This is important, because it is the Riemannian metric structure that gives rise to the Laplace--Beltrami operator and hence to the generalized Mat\'{e}rn and squared exponential kernels. Diffeomorphisms do not necessarily preserve metric structure, so they may not preserve kernels.}.
Since functions on a circle can be thought of as periodic functions on $\R$, and similarly for $\bb{T}^d$ and $\R^d$, defining a kernel on a torus is equivalent to defining a periodic kernel.
For a general function $f : \R^d \-> \R$, one can transform it into a function $g : \bb{T}^d \-> \R$ by \emph{periodic summation}
\[ \label{eqn:periodic-summation}
g(x_1,...,x_d) = \sum_{n\in\Z^d} f(x_1 + n_1,...,x_d + n_d)
\]
where $x_j \in [0, 1)$ is identified with the angle $2\pi x_j$ and the point $\exp(2 \pi i x_j) \in \bb{S}^1$.
Define addition of two points in $\bb{S}^1$ by the addition of said numbers modulo $1$, and define addition in $\bb{T}^d$ component-wise.
Periodic summation preserves positive-definiteness, since it preserves positivity of the Fourier transform, which by Bochner's theorem is equivalent to positive-definiteness---see \textcite[Section 4.4.4]{scholkopf2002} for a formal proof.
This gives an easy way to construct positive-definite kernels on~$\bb{T}^d$.
In particular, we can generalize Mat\'{e}rn and squared exponential GPs from $\R^d$ to $\bb{T}^d$ by defining
\[
\label{eqn:matern-torus}
k_{\nu}(x,x')
=
\sum_{n\in\Z^d}
\frac{\sigma^22^{1-\nu}}{C'_\nu\Gamma(\nu)}
\del{
\sqrt{2\nu}
\frac{\norm{x-x' + n}}{\kappa}
}^\nu
K_\nu \del{
\sqrt{2\nu}
\frac{\norm{x-x' + n}}{\kappa}
}
\]
where $C'_{(\cdot)}$ is a constant given in Appendix \ref{apdx:examples} to ensure $k_{(\cdot)}(x,x) = \sigma^2$, and
\[
\label{eqn:rbf-torus}
k_{\infty}(x,x')
=
\sum_{n\in\Z^d}
\frac{\sigma^2}{C'_\infty}
\exp\del{
-
\frac{\norm{x-x' + n}^2}{2 \kappa^2}
}
\]
respectively.
We prove that these are the covariance kernels of the SPDEs introduced previously.
\begin{proposition}
\label{prop:matern-and-se-torus}
The Mat\'{e}rn (squared exponential) kernel $k$ in \eqref{eqn:matern-torus} (resp. \eqref{eqn:rbf-torus}) is the covariance kernel of the Mat\'{e}rn (resp. squared exponential) Gaussian process in the sense of \textcite{whittle63}.
\end{proposition}
\begin{proof}
Appendix \ref{apdx:torus-proof}.
\end{proof}
This result offers an intuitive explanation for \emph{why} the na\"{i}ve generalization based on the geodesic distance might fail to be positive semi-definite on non-Euclidean spaces for all length scales, yet work well for smaller length scales: on $\bb{T}^d$, it is \emph{locally correct} in the sense that it is equal to the first term in the periodic summation \eqref{eqn:matern-torus}.
To obtain the full generalization, one needs to take into account not just geodesic paths, but geodesic-like paths which include loops around the space---a Mat\'{e}rn GP incorporates global topological structure of its domain.
For the circle, these are visualized in Figure \ref{fig:dist-torus}.
For spaces where this structure is even more elaborate, definitions based purely on geodesic distances may not suffice to ensure positive semi-definiteness or good numerical behavior.
We conclude by presenting a number of practical formulas for Mat\'{e}rn kernels on the circle.
\begin{example}[Circle]
Take $M = \bb{S}^1$. For $\nu = \infty$, the kernel and spectral measure are
\<
k_{\infty}(x, x^\prime)
&=
\frac{\sigma^2}{C_\infty} \vartheta_3(\pi(x - x'), \exp(-2 \pi^2 \kappa^2))
&
\rho_{\infty}(n)
&=
\frac{\sigma^2}{C_\infty} \exp(-2 \pi^2 \kappa^2 n^2)
\>
where $n \in \Z$, $\vartheta_3(\cdot, \cdot)$ is the third Jacobi theta function \cite[equation 16.27.3]{abramowitz1972}, and $C_\infty = \vartheta_3(0, \exp(-2 \pi^2 \kappa^2))$.
This kernel is normalized to have variance $\sigma^2$.
\end{example}
\begin{example}[Circle]
Take $M = \bb{S}^1$. For $\nu = 1/2$, the kernel and spectral measure are
\<
k_{1/2}(x, x^\prime)
&=
\frac{\sigma^2}{C_{1/2}}
\cosh \del{\frac{\abs{x-x'} - 1/2}{\kappa}}
&
\rho_{1/2}(n)
&=
\frac{
2\sigma^2
\sinh\del{\nicefrac{1}{2 \kappa}}
}
{
C_{1/2} \kappa
}
\del{\frac{1}{\kappa^2} + 4\pi^2 n^2 }^{-1}
\!\!\!\!\!
\>
where $C_{1/2} = \cosh\del{\nicefrac{1}{2 \kappa} }$.
This kernel is normalized to have variance $\sigma^2$.
\end{example}
A derivation and more general formula, valid for $\nu = 1/2 + n$, $n \in \N$, can be found in Appendix \ref{apdx:examples}.
Note that these spectral measures are \emph{discrete}, as the Laplace--Beltrami operator has discrete spectrum.
Finally, we give the Fourier feature approximation \cite{rahimi08,hensman17} of the GP prior on $\bb{T}^1 = \bb{S}^1$,~which~is
\<
f(x)
&\approx
\sum_{n=-N}^{N}
\sqrt{\rho_{\nu}(n)}
\del[1]{
w_{n, 1} \cos(2 \pi n x)
+
w_{n, 2} \sin(2 \pi n x)
}
&
w_{n,j} &\~[N](0,1)
.
\>
We have defined Mat\'{e}rn and squared exponential GPs on $\bb{T}^d$ and given expressions for the kernel, spectral measure, and Fourier features on $\bb{T}^1$.
With sharpened intuition, we now study the general~case.
\section{Compact Riemannian manifolds} \label{sec:comp_man}
The arguments used in the preceding section are, at their core, based on ideas from abstract harmonic analysis connecting $\R^d$, $\bb{T}^d$, and $\Z^d$ as topological groups.
This connection relies on the algebraic structure of groups, which does not exist on a general Riemannian manifold.
As a result, different notions are needed to establish a suitable framework.
Let $(M,g)$ be a compact Riemannian manifold without boundary, and let $\lap_g$ be the Laplace--Beltrami operator.
Our aim is to compute the covariance kernel of the Gaussian processes solving the SPDEs \eqref{eqn:spde-matern} and \eqref{eqn:spde-rbf} in this setting.
Mathematically, this amounts to introducing an appropriate formalism so that one can calculate the desired expressions using spectral theory.
We do this in a fully rigorous manner in Appendix \ref{apdx:theory}, while here we present the main ideas and results.
First, we discuss how the operators on the left-hand side of SPDEs \eqref{eqn:spde-matern} and \eqref{eqn:spde-rbf} are defined.
By compactness of $M$, $-\lap_g$ admits a countable number of eigenvalues, which are non-negative and can be ordered to form a non-decreasing sequence with $\lambda_n\->\infty$ for $n\->\infty$.
Moveover, the corresponding eigenfunctions form an orthonormal basis $\{f_n\}_{n\in\Z_+}$ of $L^2(M)$, and $-\lap_g$ admits the representation
\[ \label{eqn:lap_spec}
-\lap_g f = \sum_{n=0}^\infty \lambda_n \innerprod{f}{f_n} f_n
\]
which is termed the \emph{Sturm--Liouville decomposition} \cite{chavel1984,canzani13}.
This allows one to define the operators $\Phi(-\lap_g)$ for a function $\Phi: [0, \infty) \to \R$, by replacing $\lambda_n$ with $\Phi(\lambda_n)$ in \eqref{eqn:lap_spec}, and specifying appropriate function spaces as domain and range to ensure convergence of the series in a suitable sense.
This idea is called \emph{functional calculus} for the operator $-\lap_g$.
Using it, we define
\< \label{eqn:operator_definitions}
\del{\frac{2 \nu}{\kappa^2} - \lap_g}^{\frac{\nu}{2}+\frac{d}{4}} f
&=
\sum_{n=0}^\infty \del{\frac{2 \nu}{\kappa^2} + \lambda_n}^{\frac{\nu}{2}+\frac{d}{4}} \innerprod{f}{f_n} f_n
\\
e^{-\frac{\kappa^2}{4} \lap_g} f
&=
\sum_{n=0}^\infty e^{\frac{\kappa^2 \lambda_n}{4}} \innerprod{f}{f_n} f_n
.
\>
Figure \ref{fig:eigenfuntions} illustrates the eigenfunctions $f_n$.
Note that when $M = \bb{T}^d$, the orthonormal basis $\{f_n\}_{n\in\Z_+}$ consists of sines and cosines, and thus the corresponding functional calculus is defined in terms of standard Fourier series.
This also agrees with the usual way of defining such operators in the Euclidean case using the Fourier transform.
\begin{figure}
\centering
\includegraphics[height=1.875cm, trim=0 0 20 0, clip]{Figures/circle_eigfs.pdf}
\includegraphics[height=1.875cm, trim=10 10 0 10, clip]{Figures/sphere_eigfs.pdf}
\includegraphics[height=1.875cm, trim=0 20 0 20, clip]{Figures/dragon_eigfs.pdf}
\caption{Examples of eigenfunctions of Laplace--Beltrami operator on a circle, sphere, and dragon. For the circle, the value of the eigenfunction is given by the (signed) distance between the solid line and dashed unit circle.
For the sphere and dragon, the value of the eigenfunction is given by the color.
}
\label{fig:eigenfuntions}
\end{figure}
Next, we proceed to define the remaining parts of the SPDEs.
The theory of stochastic elliptic equations described in \textcite{lototsky17} gives an appropriate notion of white noise $\c{W}$ for our setting, as well as a way to uniquely solve SPDEs of the form $\c{L} f = \c{W}$, where $\c{L}$ is a bounded linear bijection between a pair of Hilbert spaces.
We show that the operators
\<
\del{\frac{2 \nu}{\kappa^2} - \lap_g}^{\frac{\nu}{2}+\frac{d}{4}} &: H^{\nu + \frac{d}{2}}(M) \to L^2(M)
&
e^{\frac{\kappa^2}{4} \lap_g} &: \c{H}^{\frac{\kappa^2}{2}}(M) \to L^2(M)
\>
are bounded and invertible, where $H^s(M)$ are appropriately defined Sobolev spaces on the manifold, and $\c{H}^s(M)$ are the \emph{diffusion spaces} studied by \textcite{devito19}.
We prove that the solutions of our SPDEs in the sense of \textcite{lototsky17} are Gaussian processes with kernels equal to the reproducing kernels of the spaces $H^{\nu + d/2}(M)$ and $\c{H}^{\kappa^2/2}(M)$, which are given by \textcite{devito19}.
Summarizing, we get the following.
\begin{theorem}
Let $\lambda_n$ be eigenvalues of $-\lap_g$, and let $f_n$ be their respective eigenfunctions.
The kernels of the Mat\'{e}rn and squared exponential GPs on $M$ in the sense of \textcite{whittle63} are given by
\<
\label{eqn:mani-matern-formula}
k_{\nu}(x, x') &= \frac{\sigma^2}{C_\nu}\sum_{n=0}^\infty \del{\frac{2 \nu}{\kappa^2} + \lambda_n}^{-\nu-\frac{d}{2}} f_n(x)f_n(x')
\\
\label{eqn:mani-rbf-formula}
k_{\infty}(x, x') &= \frac{\sigma^2}{C_\infty}\sum_{n=0}^\infty e^{-\frac{\kappa^2}{2} \lambda_n} f_n(x)f_n(x')
\>
where $C_{(\cdot)}$ are normalizing constants chosen so that the average variance\footnote{The marginal variance $k_{(\cdot)}(x, x)$ can depend on $x$, thus we normalize the kernel by the average variance.}
over the manifold satisfies $\vol_g(M)^{-1} \int_X k_{(\cdot)}(x, x) \d x = \sigma^2$.
\end{theorem}
\begin{proof}
Appendix \ref{apdx:theory}.
\end{proof}
Our attention now turns to the spectral measure.
In the Euclidean case, the spectral measure, assuming sufficient regularity, is absolutely continuous---its Lebesgue density is given by the Fourier transform of the kernel.
In the case of $\bb{T}^d$, the spectral measure is discrete---its density with respect to the counting measure is given by the Fourier coefficients of the kernel.
Like in the case of the torus, for a compact Riemannian manifold the spectral measure is discrete---its density with respect to the counting measure is given by the generalized Fourier coefficients of the kernel with respect to the orthonormal basis $f_n(x)f_{n'}(x')$ on $L^2(M\x M)$.
For Mat\'{e}rn and square exponential GPs, these are
\<
\label{eqn:matern-spectral-manifold}
\rho_{\nu}(n) &= \frac{\sigma^2}{C_\nu} \del{\frac{2 \nu}{\kappa^2} + \lambda_n}^{-\nu-\frac{d}{2}}
&
\rho_{\infty}(n) &= \frac{\sigma^2}{C_\infty} \exp\del{-\frac{\kappa^2}{2} \lambda_n}
&
n &\in \N
.
\>
This allows one to recover most tools used in spectral theory of GPs.
In particular, one can construct a regular Fourier feature approximation of the GPs by taking the top-$N$ eigenvalues, and writing
\< \label{eqn:ff_approx}
f(x)
&\approx
\sum\limits_{n=0}^{N-1}
\sqrt{\rho(n)}
w_n
f_n(x)
&
w_n &\~[N](0,1)
.
\>
Other kinds of Fourier feature approximations, such as random Fourier features, are also possible.
We now illustrate an example in which these expressions simplify.
\begin{example}[Sphere]
Take $M = \bb{S}^d$ to be the $d$-dimensional sphere.
Then we have
\[
k_\nu(x,x') = \sum_{n=0}^\infty c_{n,d}\,\rho_\nu(n)\, \c{C}^{(d-1)/2}_n \del[2]{\cos\del[1]{d_g(x,x')}}
\]
where $c_{n,d}$ are constants given in Appendix \ref{apdx:examples}, $\c{C}_n^{(\cdot)}$ are the Gegenbauer polynomials, $d_g$ is the geodesic distance, and $\rho_\nu(n)$ can be expressed explicitly in terms of $\lambda_n = n(n+d-1)$ using \eqref{eqn:matern-spectral-manifold}.
See Appendix \ref{apdx:examples} for details on the corresponding Fourier feature approximation.
\end{example}
A derivation with further details can be found in Appendix \ref{apdx:examples}.
Similar expressions are available for many other manifolds, where the Laplace--Beltrami eigenvalues and eigenfunctions are known.
\subsection{Summary}
We conclude by summarizing the presented method of computing the kernel of Riemannian Mat\'{e}rn Gaussian processes defined by SPDEs.
The key steps are as follows.
\1 Obtain the Laplace--Beltrami eigenpairs for the given manifold, either analytically or numerically.
This step needs to be performed once in advance.
\2 Approximate the kernel using a finite truncation of the infinite sums \eqref{eqn:mani-matern-formula} or \eqref{eqn:mani-rbf-formula}.
\0
This kernel approximation can be evaluated pointwise at any locations, fits straightforwardly into modern automatic differentiation frameworks, and is simple to work with.
The resulting truncation error will depend on the smoothness parameter $\nu$, dimension $d$, and eigenvalue growth rate, which is quantified by Weyl's law \cite{zelditch2017}.
For $\nu < \infty$ convergence will be polynomial, and for $\nu = \infty$ it will be exponential.
If $\sigma^2$ is trainable, the constant $C_\nu$ which normalizes the kernel by its average variance can generally be disregarded.
If Fourier feature approximations of the prior are needed, for instance, to apply the pathwise sampling technique of \textcite{wilson20}, they are given by \eqref{eqn:ff_approx}.
\section{Illustrated Examples} \label{sec:examples}
Here we showcase two examples to illustrate the theory: dynamical system prediction and sample path visualization.
We focus on simplified settings to present ideas in an easy-to-understand manner.
\subsection{Dynamical system prediction}
\begin{figure}
\begin{center}
\begin{subfigure}{.26\linewidth}
\centering
\includegraphics[trim=50 45 50 50,clip]{Figures/pendulum_ground_truth}
\caption{Ground truth}
\label{fig:cylinder-ground-truth}
\end{subfigure}
\begin{subfigure}{.26\linewidth}
\centering
\includegraphics[trim=50 45 50 50,clip]{Figures/pendulum_learned_trajectories}
\caption{Posterior 95\% intervals}
\label{fig:cylinder-learned-trajectories}
\end{subfigure}
\begin{subfigure}{.44\linewidth}
\centering
\includegraphics[scale=0.75,trim=0 4 0 12,clip]{Figures/pendulum_predictive_intervals}
\caption{Posterior samples for one trajectory}
\label{fig:cylinder-single-trajectory}
\end{subfigure}
\end{center}
\caption{Visualization of the dynamical system's learned phase diagram.
Middle: we simulate 40 trajectories starting at the red dots, integrate the learned Hamilton's equations forward and backward in time until they approximately intersect other trajectories, and plot 95\% intervals in phase space.
Right: we simulate the trajectory beginning from the yellow dot, and plot mean and 95\% intervals.
}
\label{fig:cylinder}
\end{figure}
We illustrate how Riemannian squared exponential GPs can be used for predicting dynamical systems while respecting the underlying geometry of the configuration space the system is defined on.
This is an important task in robotics, where GPs are often trained within a model-based reinforcement learning framework \cite{deisenroth11,deisenroth13}.
Here, we consider a purely supervised setup, mimicking the model learning inner loop of said framework.
For a prototype physical system, consider an ideal pendulum, whose configuration space is the circle $\bb{S}^1$, and whose phase space is the cotangent bundle $T^*\bb{S}^1$, which is isometric to the cylinder $\bb{S}^1 \x \R$ equipped with the product metric.
The equations of motion are given by Hamilton's equations, which are parameterized by the Hamiltonian $H : T^*\bb{S}^1 \-> \R$.
To learn the equations of motion from observed data, we place a GP prior on the Hamiltonian, with covariance given by a squared exponential kernel on the cylinder, defined as a product kernel of squared exponential kernels on the circle and real line.
Following \textcite{hensman13}, training proceeds using mini-batch stochastic variational inference with automatic relevance determination.
The full setup is given in Appendix \ref{apdx:experiments}.
To generate trajectories from the learned equations of motion, following \textcite{wilson20}, we approximate the prior GP using Fourier features, and employ \eqref{eqn:pathwise} to transform prior sample paths into posterior sample paths.
We then generate trajectories by solving the learned Hamilton's equations numerically for each sample, which is straightforward because the approximate posterior is a basis function approximation and therefore easily differentiated in the ordinary deterministic manner.
Results can be seen in Figure \ref{fig:cylinder}.
From these, we see that our GP learns the correct qualitative behavior of the equations of motion, mirroring the results of \textcite{deisenroth11}.
\subsection{Sample path visualization}
To understand how complicated geometry affects posterior uncertainty estimates and illustrate the techniques on a general Riemannian manifold, we consider a posterior sample path visualization task.
We take $M$ to be the \emph{dragon} manifold from the Stanford 3D scanning repository, modified slightly to remove components not connected to the outer surface.
We represent the manifold using a $202490$-triangle mesh and obtain 500 Laplace--Beltrami eigenpairs numerically using the \emph{Firedrake} package \cite{rathgeber16}.
For training data, we introduce a ground truth function by fixing a distinguished point at the end of the dragon's snout, and compute the sine of the geodesic distance from that point.
We then observe this function at $52$ points on the manifold chosen from the mesh's nodes, and train a Mat\'{e}rn GP regression model with smoothness $\nu = 3/2$ by maximizing the marginal likelihood with respect to the remaining kernel hyperparameters.
By using the path-wise sampling expression \eqref{eqn:pathwise}, we obtain posterior samples defined on the entire mesh.
Results can be seen in Figure \ref{fig:dragon}.
Here, we see that posterior mean and uncertainty estimates match the manifold's shape seamlessly, decaying roughly in proportion with the geodesic distance in most regions.
In particular, we see that the two sides of the dragon's snout have very different uncertainty values, despite close Euclidean proximity.
This mimics the well-known \emph{swiss roll} example of manifold learning \cite[Section 6.1.1]{lee2007}, and highlights the value of using a model which incorporates geometry.
\begin{figure}
\begin{minipage}{0.01\textwidth}
\begin{subfigure}{\linewidth}
\centering
\includegraphics[width=\linewidth]{Figures/plasma.pdf}
\caption*{}
\label{fig:dragon-colorbar}
\end{subfigure}
\end{minipage}
\begin{minipage}{.95\textwidth}
\begin{subfigure}{.24\linewidth}
\centering
\includegraphics[width=\linewidth, trim=0 0 0 0, clip]{Figures/dragon/1_ground_thruth.pdf}
\caption{Ground truth}
\label{fig:dragon-ground-truth}
\end{subfigure}
\begin{subfigure}{.24\linewidth}
\centering
\includegraphics[width=\linewidth, trim=0 0 0 0, clip]{Figures/dragon/1_mean.pdf}
\caption{Mean}
\label{fig:dragon-mean}
\end{subfigure}
\begin{subfigure}{.24\linewidth}
\centering
\includegraphics[width=\linewidth, trim=0 0 0 0, clip]{Figures/dragon/1_standard_deviation.pdf}
\caption{Standard deviation}
\label{fig:dragon-sample-0}
\end{subfigure}
\begin{subfigure}{.24\linewidth}
\centering
\includegraphics[width=\linewidth, trim=0 0 0 0, clip]{Figures/dragon/1_sample_1.pdf}
\caption{One posterior sample}
\label{fig:dragon-sample-1}
\end{subfigure}
\end{minipage}
\begin{minipage}{0.01\textwidth}
\begin{subfigure}{\linewidth}
\centering
\includegraphics[width=\linewidth]{Figures/viridis.pdf}
\caption*{}
\label{fig:dragon-colorbar-right}
\end{subfigure}
\end{minipage}
\caption{Visualization of a Mat\'{e}rn Gaussian process posterior on the dragon.
We plot the true function values, posterior mean, marginal posterior variance, and one posterior sample evaluated on the entire mesh.
Here, black dots denote training locations, and color represents value of the corresponding functions.
Additional posterior samples can be seen in Appendix \ref{apdx:experiments}.
}
\label{fig:dragon}
\end{figure}
\section{Conclusion}
In this work, we developed techniques for computing the kernel, spectral measure, and Fourier feature approximation of Mat\'{e}rn and squared exponential Gaussian processes on compact Riemannian manifolds, thereby constructively generalizing standard Gaussian process techniques to this setting.
This was done by viewing the Gaussian processes as solutions of stochastic partial differential equations, and expressing the objects of interest in terms of Laplace--Beltrami eigenvalues and eigenfunctions.
The theory was demonstrated on a set of simple examples: learning the equations of motion of an ideal pendulum, and sample path visualization for a Gaussian process defined on a dragon.
This illustrates the theory in settings both where Laplace--Beltrami eigenfunctions have a known analytic form, and where they need to be calculated numerically using a differential equation or graphics processing framework.
Our work removes limitations of previous approaches, allowing Mat\'{e}rn and squared exponential Gaussian processes to be deployed in mini-batch, online, and non-conjugate settings using variational inference.
We hope these contributions enable practitioners in robotics and other physical sciences to more easily incorporate geometry into their models.
\section*{Broader Impact}
This is a purely theoretical paper.
We develop technical tools that make Mat\'{e}rn Gaussian processes easier to work with in the Riemannian setting.
This enables practitioners who are not experts in stochastic partial differential equations to model data that lives on spaces such as spheres and tori.
We envision the impact of this work to be concentrated in the physical sciences, where spaces of this type occur naturally.
Since the state spaces of most robotic arms are Riemannian manifolds, we expect these ideas to improve performance of model-based reinforcement learning by making it easier to incorporate geometric prior information into models.
Since climate science is concerned with studying the globe, we also expect that our ideas can be used to model environmental phenomena, such as sea surface temperatures.
By employing Gaussian processes for data assimilation and building them into larger frameworks, this could facilitate more accurate climate models compared to current methods.
These impacts carry forward to potential generalizations of our work.
We encourage practitioners to consider impacts on their respective disciplines that arise from incorporating geometry into models.
\section*{Acknowledgments and Disclosure of Funding}
VB was supported by the St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences and by the Ministry of Science and Higher Education of the Russian Federation, agreement N\textsuperscript{\underline{o}} 075-15-2019-1620.
PM was supported by the Ministry of Science and Higher Education of the Russian Federation, agreement N\textsuperscript{\underline{o}} 075-15-2019-1619.
VB and PM were supported by "Native towns", a social investment program of PJSC Gazprom Neft, and by the Department of Mathematics and Computer Science of St. Petersburg State University.
AT was supported by the Department of Mathematics at Imperial College London.
\printbibliography
\newpage
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 9,259
|
I'd Rather Be Your Fool Song Lyrics and Chords
I'd Rather Be Your Fool Song Lyrics and Chords by Johnny Paycheck
I'd Rather Be Your Fool
Written and Recorded by Johnny Paycheck
Everybody says I'm a fool t
o love you
I'd rather be th
e judge of tha
You may have a heart that's filled wit
h hate instead of love
I'd rather b
e your fool than anyone I kno
time friends say I must be blind
I wish they'd stop and think
can set the wine on the table
But the
man don't have to drink
Yes I'm satisfied and I've got my pride
still possess your love
Who sang the the song I'd Rather Be Your Fool?
- The song I'd Rather Be Your Fool was sang by Johnny Paycheck.
Who is Johnny Paycheck?
- Johnny Paycheck (born Donald Eugene Lytle May 31, 1938 - February 19, 2003) was an American country music singer-songwriter, multi-instrumentalist, and Grand Ole Opry member notable for recording the David Allan Coe song "Take This Job and Shove It". He achieved his greatest success in the 1970s as a force in country music's "outlaw movement" popularized by artists Hank Williams Jr., Waylon Jennings, Willie Nelson, Billy Joe Shaver, and Merle Haggard. In the 1980s, his music career slowed due to drug, alcohol and legal problems. He served a prison sentence in the early 1990s and his declining health effectively ended his career in early 2000. In 1980, Paycheck appeared on the PBS music program Austin City Limits (season 5).
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 335
|
Hublersburg es un lugar designado por el censo ubicado en el condado de Centre en el estado estadounidense de Pensilvania. En el Censo de 2010 tenía una población de 104 habitantes y una densidad poblacional de 403,89 personas por km².
Geografía
Hublersburg se encuentra ubicado en las coordenadas . Según la Oficina del Censo de los Estados Unidos, Hublersburg tiene una superficie total de 0.41 km², de la cual 0.41 km² corresponden a tierra firme y (0.0%) 0.0 km² es agua.
Demografía
Según el censo de 2010, había 104 personas residiendo en Hublersburg. La densidad de población era de 403,89 hab./km². De los 104 habitantes, Hublersburg estaba compuesto por el 99.04% blancos, el 0.96% eran afroamericanos, el 0% eran amerindios, el 0% eran asiáticos, el 0% eran isleños del Pacífico, el 0% eran de otras razas y el 0% pertenecían a dos o más razas. Del total de la población el 0% eran hispanos o latinos de cualquier raza.
Referencias
Enlaces externos
Lugares designados por el censo en Pensilvania
Localidades del condado de Centre
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 3,204
|
{"url":"https:\/\/www.physicsforums.com\/threads\/find-eigenvalue-for-matrix-b-3-4-12-4-12-3-12-3-4.691329\/","text":"# Find eigenvalue for matrix B= {[3,4,12],[4,-12,3],[12,3,-4]}\n\n1. May 12, 2013\n\n### LosTacos\n\n1. The problem statement, all variables and given\/known data\n\nFind eigenvalue for matrix B= {[3,4,12],[4,-12,3],[12,3,-4]}\n\n2. Relevant equations\n\n3. The attempt at a solution\n\nI set up the charactersitic polynomial and got the equation:\nPa(x) = (x-3)(x+12)(x+4) = x3 + 132 - 144 + 144 = x3 + 132\n\nSo I have 3 eigenvalues: 0, 13, -13. Is this correct?\n\n2. May 12, 2013\n\n### LosTacos\n\nActually I forgot to calculate teh determinants so I got:\n\nPa(x) = (x-3)(x+12)(x+4) + 2197 = x3 + 13x2 + 2053\n\n3. May 12, 2013\n\n### hsetennis\n\nThose are the correct eigenvalues (if it is conventional to include 0 in your class). It may be good to note multiplicity of eigenvalues.\n\n4. May 12, 2013\n\n### LosTacos\n\nFrom the characteristic polynomial x3 + 13x2 + 2053, how do I get the correct eigenvalues?\n\n5. May 12, 2013\n\n### Staff: Mentor\n\nTwo of them are correct, but 0 is not an eigenvalue. It should be -13 (a repeated eigenvalue).\n\nYou can't, since this isn't the correct characteristic polynomial. The eigenvalues are the roots of the characteristic polynomial.\n\n6. May 12, 2013\n\n### LosTacos\n\nOkay I understand. So my eigenvalues are 13 and -13. If I was asked to find the basis for both of these, how do I go about doing that. I tried to solve the equation [13I2 - A I 0] however if ran into a wall. I row reduced it to get the matrix = {[2, 2\/5, 6\/5], [0,1,3], [0,0,1]}. But I wasnt sure where to go from there\n\n7. May 12, 2013\n\n### Staff: Mentor\n\nYou should be solving the matrix equation (13I3 - A)x = 0, or equivalently, (A - 13I)x = 0.\nThis would be the work to find the eigenvector for \u03bb = 13.\nThis is incorrect. Show me the matrix you started with, and a step or two of your work.\n\n8. May 12, 2013\n\n### LosTacos\n\n(A - 13I)x = 0:\n\n{[10, 4, 12, 0],[4, 1, 3, 0],[12, 3, 17]} = {[1, 2\/5, 6\/5],[4, 1, 3, 0],[12, 3, 17, 0]} = {[1, 2\/5, 6\/5, 0], [0, -3\/5, -9\/5, 0],[0, -9\/5, 13\/5, 0]} = {[1, 2\/5, 6\/5, 0],[0, 1, 3, 0], [0, 0, 8, 0]}\n\n9. May 13, 2013\n\n### Staff: Mentor\n\nYou started off with an incorrect matrix.\n\nHere is A:\n$$\\begin{bmatrix} 3 & 4 & 12\\\\ 4 & -12 & 3 \\\\ 12 & 3 &-4 \\end{bmatrix}$$\nTo get A - 13I, subtract 13 from the entries on the main diagonal.","date":"2018-02-20 04:25:00","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.5246335864067078, \"perplexity\": 1290.110402253069}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2018-09\/segments\/1518891812873.22\/warc\/CC-MAIN-20180220030745-20180220050745-00038.warc.gz\"}"}
| null | null |
Rihanna standing in solidarity with Colin Kaepernick is admirable
by Davie Nguyen
As Americans, we all know how big and important the NFL Super Bowl is. Many great artists such as Maroon 5, Justin Timberlake, Lady Gaga and Beyoncé were all invited on to sing and perform during the previous halftime shows.
According to CNN, San Francisco's 49ers quarterback Colin Kaepernick sparked controversy when he sat and then kneeled during the National Anthem in 2016, before the NFL preseason and regular season games.
"I am not going to stand up to show pride in a flag for a country that oppresses black people and people of color," Kaepernick told the NFL Media.
His actions have been misconstrued as unpatriotic, ungrateful, disrespectful to the flag, military and country. Kaepernick's purpose for kneeling was to speak out against police brutality and the social injustices that black people face.
Even if you're for or against Kaepernick's actions, he had every right to use his freedom of speech to kneel.
Rihanna, a singer, fashion designer and businesswoman is also in support of Kaepernick.
She recently turned down the invitation to play during the 2019 NFL halftime show. She stated that she could not be a sellout and that she did not agree on some of the policies of the NFL.
Rihanna had every right to turn down the offer by the NFL to perform. Although it could have been a great opportunity for her, Rihanna already has a big following and has always done things her way.
Rihanna released 50 shades of concealer for all sorts of skin types, many of what other make up brands lack on being more inclusive. She also introduced her Savage x Fenty lingerie line in 2018, which was a way for her to celebrate confidence and inclusivity for all shapes and shades. She has always been a huge supporter of being inclusivity and she has done a remarkable job at showing that and has definitely pushed the boundaries among the beauty and fashion industry, too.
It doesn't come as a surprise to me as to why she would turn down this offer, either. It goes against everything that she's worked hard for and Rihanna is known for being a firm believer in standing up for her people.
Working with the NFL would mean that she is essentially being an enabler. She did not want to work with them in any way or have anything to do with it and I cannot really blame her.
Honestly, Rihanna doesn't have much to lose, either. If anything, I feel that the NFL needs her more than she needs them.
Rihanna has done a lot for her community and has stood beside women of color. Her decision in turning down the halftime offer is definitely a Rihanna move. Even if she had accepted the invitation to play during the show, she really wouldn't be gaining anything from it. Turning down the NFL might a huge deal to some, but there is a fine line between her morals and her fame.
I think this is a great integrity move on her part, too. I feel that many celebrities would relish the opportunity to play for the Super Bowl, but its artists like Rihanna that prove otherwise. She seems to be unbothered by the comments in response to her the declining the halftime show because the only thing she really should be concerned about is finishing up her long-awaited ninth album that her fans have been bugging her about.
We really do love to see an inspiring queen like Rihanna taking a stand against such a controversial belief, but nevertheless, it is forever admirable.
Featured Illustration: Olivia Varnell
colin kaepernickfentyHalftimeinclusiveNFLperformancepolice brutalityrihanna
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: Netflix's 'Living Undocumented' is a sobering eye-opener on immigrant life
Davie Nguyen
Instagram's new 'Restrict' feature is a positive step in preventing bullying
#cyberthugs
Like-minded thinking against the Paris Accord decision
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{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 2,030
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\section{Introduction and main results}\label{intro}\setcounter{equation}{0}
Let $G\in H_{m\ts p}^\iy$, that is, $G$ is an $m\ts p$ matrix function whose entries are $H^\iy$ functions on the open unit disc $\BD$. The \emph{$H^\iy$-corona problem} asks for a function $X\in H_{p\ts m}^\iy$ such that
\begin{equation}\label{corona}
G(z)X(z)=I_m\quad (z\in\BD).
\end{equation}
This problem has its roots in the paper \cite{Carl62} for the case $m=1$, and in \cite{Fuhr68} for the case $m>1$. Since then it has been studied in various contexts for which we refer to the books {\cite{Helton87,Nikol86,Nikol02,Peller03}} and the recent papers {\cite{FKR2a,FKR2b,Treil04,TW05,TrentZh06}}. See also the introduction of \cite{FKR1} for the role of equation \eqref{corona} in mathematical systems and control theory problems. The problem is also closely related to the Leech problem \cite{Leech} (see also the comments in \cite{KaashRov14}) where the identity matrix $I_m$ in the right hand side of \eqref{corona} is replaced by another $H^\iy$ matrix function of appropriate size. In the Leech problem as well as in the corona problem norm constraints on the solution $X$ are often the main issue. { When norm constraints are not the main issue one often refers to \eqref{corona} as a \emph{Bezout problem} in a $H^\iy$ setting}.
We view the present paper as an addition to the papers \cite{FKR2a} and \cite{FKR2b} which deal with the {Bezout-corona} problem in the setting of stable rational matrix functions. Here we consider equation \eqref{corona} in a Wiener space setting. We assume that $G$ belongs to the Wiener space $\sW_+^{m\ts p}$ and we look for solutions $X$ which belong to the Wiener space $\sW_+^{p\ts m}$. In other words, $G \in H_{m\ts p}^\iy$ and $X\in H_{p\ts m}^\iy$ and both have the additional property that their Taylor coefficients at zero are absolutely summable. In this case we refer to \eqref{corona} as the \emph{ {Wiener-Bezout problem}}. We shall be interested in the description of all Wiener solutions and the least square Wiener solution. The {Wiener-Bezout} problem includes problem \eqref{corona} for the case when $G$ is a stable rational matrix function and the solution $X$ is required to be stable rational matrix function too; see \cite{FKR2a} and \cite{FKR2b}. For more information on Wiener spaces we refer the reader to the final paragraph of this introduction.
Assuming $G\in H_{m\ts p}^\iy$, we shall also be interested in solutions $X$ to \eqref{corona} that belong to $H_{p\ts m}^2$, where $H_{p\ts m}^2$ stands for the linear spaces consisting of all $p \ts m$ matrices with entries in $H^2$. In that case we refer to \eqref{corona} as the {$H^2$-Bezout} problem.
Recall, cf., \cite[Theorem 3.61]{Peller03} or \cite[Section 2]{FtHK-IEOT}, that the $H^\infty$-corona problem is solvable if and only if $T_G$ admits a right inverse. Here $T_G$ is the analytic Toeplitz operator
\[
T_G=\begin{bmatrix}
G_0&0&0&\cdots\\
G_1&G_0&0&\cdots\\
G_2&G_1&G_0&\cdots\\
\vdots&\vdots&\vdots
\end{bmatrix}: \ell_+^2(\BC^p) \to \ell_+^2(\BC^m),
\]
where $G_0, G_1, G_2, \ldots$ are the Taylor coefficients of $G$ at zero. Note that $T_G$ has a right inverse if and only if $T_GT_G^*$ is strictly positive. {Since $\sW_+^{p\ts m}\subset H^\iy_{p\ts m},$} for the {Wiener-Bezout} problem to be solvable $T_GT_G^*$ has to be strictly positive. We shall see that this condition is also sufficient and allows one to give a description of all solutions to the {Wiener-Bezout} problem in a simpler and more concrete form than for the general $H^\iy$-corona problem.
For our first main result we need to introduce two matrices $\Xi_0 $ and $\tht_0 $, and a $p\ts p$ matrix function $Y$ analytic on $\BD$ as follows. Let $G\in H_{m\ts p}^\iy$, and assume that $T_GT_G^*$ is strictly positive. Then:
\begin{itemize}
\item [(M1)] $\Xi_0 $ is the $p\ts m$ matrix defined by $\Xi_0 = E_p^*T_G^*(T_GT_G^*)^{-1}E_m$;
\item [(M2)] $\tht_0 $ is the $p\ts k$ matrix defined by
\begin{equation}\label{deftht0}
\Theta_0\Theta_0^* = I_p - E_p^*T_G^*(T_GT_G^*)^{-1}T_GE_p,\quad
\kr \Theta_0 = \{ 0 \}.
\end{equation}
\end{itemize}
Here for any positive integer $n$ we write $E_n $ for the canonical embedding of $\BC^n$ onto the first coordinate space of $\ell_+^2(\BC^n)$, that is,
\begin{equation}
\label{defEn}
E_n = \begin{bmatrix}
I_n & 0 & 0 & 0 & \cdots \,\,\\
\end{bmatrix}{}^\top:\mathbb{C}^n \rightarrow \ell_+^2(\mathbb{C}^n).
\end{equation}
Since $\kr \Theta_0 = \{ 0 \}$, the integer $k$ in item (b) is equal to the rank of the matrix $I_p - E_p^*T_G^*(T_GT_G^*)^{-1}T_GE_p$. We shall see (Lemma \ref{L:MatRes} in the next section) that this rank is equal to $p-m$, even in {the} $H^\iy$ {setting.} Finally, we define $Y$ to be the analytic $p\ts p$ matrix function on $\BD$ given by
\begin{align}\label{defY}
Y(z)=I_p-zE_p^*(I-zS_p^*)^{-1}T_G^*(T_GT_G^*)^{-1}H_GE_p\quad (z\in\BD).
\end{align}
Here for any positive integer $n$ the operator $S_n$ is the block forward shift on $\BC^n$. Furthermore, $H_G$ is the Hankel operator defined by $G$, that is,
\[
H_G=\begin{bmatrix}
G_1&G_2&G_3&\cdots\\
G_2&G_3&G_4&\cdots\\
G_3&G_4&G_5&\cdots\\
\vdots&\vdots&\vdots
\end{bmatrix}: \ell_+^2(\BC^p) \to \ell_+^2(\BC^m).
\]
In other {words,} the Taylor coefficients of $Y_0, Y_1, Y_2, \cdots $ of $Y$ at zero are given by
\begin{equation}
\label{defYj}
Y_0=I_p \ands \begin{bmatrix}Y_1\\ Y_2\\ \vdots\end{bmatrix}=-T_G^* (T_G T_G^*)^{-1} \begin{bmatrix}G_1\\ G_2\\ \vdots\end{bmatrix}.
\end{equation}
Note that the operator $T_G^*(T_GT_G^*)^{-1}$ appearing in the definitions of the matrices $\Xi$ and {$\tht_0$} and the function $Y$ is the Moore-Penrose right inverse of $T_G$. In a less explicit form the function Y already appears in the papers \cite{FKR2a, FKR2b}. The central role of this function is a new aspect of the present paper.
Finally, with the function $Y$ and the two matrices $\Xi$ and {$\tht_0$} we associate
the following two functions
\begin{equation}
\label{defXiTheta}
\Xi(z) =Y(z) \Xi_0 \ands \tht(z) =Y(z) \tht_0 \quad (z\in \BD).
\end{equation}
The next theorem is our main result in the Wiener space setting. It shows that with these three entities $\Xi_0$, $\tht_0$ and $Y$ all solutions to the {Wiener-Bezout problem} can be described explicitly, and that the function $\Xi$ defined by the first identity in \eqref{defXiTheta} is the least squares solution.
\begin{thm}\label{thmmain1}
Let $G\in \sW_+^{m\ts p}$, and assume that $T_GT_G^*$ is strictly positive. Then the matrix function $Y$ defined by \eqref{defY} belongs to the Wiener space $\sW_+^{p\ts p}$, $\det Y(z)\not =0$ for each $|z|\leq 1$, and
\begin{align}\label{invY}
Y(z)^{-1}=I_p+zE_p^*T_G^*(T_GT_G^*)^{-1}H_G(I-z S_p)^{-1}E_p\quad ( {z\in\BD}).
\end{align}
In particular, $Y^{-1}$ is a Wiener function, and hence $Y$ is invertible outer. Furthermore,
\begin{itemize}
\item[\textup{(i)}] $G(z)Y(z)=G_0$ for each $|z|\leq 1$,
\item[\textup{(ii)}]
the function $\tht$ defined by the second identity in \eqref{defXiTheta} belongs to $\sW_+^{p\ts (p-m)}$ \textup{(}in particular, $k=p-m$\textup{)}, and $\tht$ is an inner function with $\im T_\tht=\kr T_G$,
\item[\textup{(iii)}] the function $H(z):=(\tht_0^*\tht_0)^{-1}\tht_0^*(I_p-\Xi_0G_0) Y(z) ^{-1}$ belongs to the Wiener space $\sW_+^{(p-m)\ts p}$, and
\begin{equation}
\label{invGH1}
\det \begin{bmatrix} G(z)\\[.2cm] H(z) \end{bmatrix}\not =0 \ \mbox{and}\
\begin{bmatrix}
G(z)\\[.2cm] H(z) \end{bmatrix}^{-1}=Y(z)\begin{bmatrix}\Xi_0 &\tht_0 \end{bmatrix} \quad (|z|\leq 1).
\end{equation}
\end{itemize}
Furthermore, for any $V\in \sW_+^{(p-m)\ts m}$ the function
\begin{equation}\label{allsolW}
X(z)=Y(z)\Xi_0+Y(z)\tht_0V(z)\quad (|z|\leq 1)
\end{equation}
is a solution to the {Wiener-Bezout} problem associated with $G$, and all {solutions are obtained} in this way. Moreover, with $X$ given by \eqref{allsolW} we have
\begin{equation}
\label{H2idW}
\|X(\cdot)u\|^2_{H^2_p}=\|Y(\cdot)\Xi_0 u\|^2_{H^2_p}+\|V(\cdot)u\|^2_{H^2_{p-m}}
\quad (u\in\BC^m).
\end{equation}
In particular, the function $\Xi(z)=Y(z)\Xi_0$ is the least squares solution to the {Wiener-Bezout} problem associated with $G$.
\end{thm}
Item (iii) in the above theorem is closely related to Tolkonnikkov's lemma \cite{Tol81} (see also \cite[Appendix 3, item 10]{Nikol86}). In fact, from Tolkonnikkov's lemma it follows that \eqref{invGH1} holds true with $H$ {on the unit circle $\BT$} being given by
\begin{equation}
\label{TolH}
H(\z)=\tht^*\big(\z)(I_p-\Xi(z)G(\z)\big) \quad (\z\in \BT).
\end{equation}
At the end of Section \ref{secWiener} (see Remark \ref{remHwtH}) we shall show that the function $H$ defined by the above formula and the function $H$ defined in item (iii) of the above theorem are one and the same function. Specifying \eqref{invGH1} for $z=0$ we see that
\begin{equation}
\label{invXiTheta1}
\mat{cc}{\Xi_0 & \Theta_0}^{-1}=\mat{c}{G_0\\ H_0}\quad\mbox{with}\quad H_0=(\Theta_0^*\Theta_0)^{-1}\Theta_0^*(I_p-\Xi_0 G_0).
\end{equation}
Lemma \ref{L:MatRes} in the next section shows that this inversion formula remains true if $G$ is just an $H^\iy$ function.
Theorem \ref{T:H2cor}, which is our second main result, presents a (partial) analogue of Theorem \ref{thmmain1} in an $H^\iy/H^2 $ setting. Let $G\in H_{m\ts p}^\iy$, and assume that $T_GT_G^*$ to be strictly positive. Then the function $Y$ is still well defined on the open unit {disc} $\BD$ and $\det Y(z)\not =0$ for each $z\in \BD$. However, in general, the entries of $Y$ and $Y^{-1}$ are just $H^2$ functions, and formula \eqref{allsolW} yields $H^2$ solutions rather than $H^\iy$ solutions. Moreover, if the free parameter $V$ in \eqref{allsolW} is taken from $H_{(p-m)\ts m}^2$, then all $H^2$ solutions are obtained by \eqref{allsolW} and the $H^2$ norm in the identity \eqref{H2idW} appears in a natural way.
Finally, in Section \ref{Hinfty} we shall prove that item (ii) carries over to an $H^\iy$ setting (see Proposition \ref{P:Theta}). The fact that $\tht$ is inner with $\im T_\tht=\kr T_G$ follows from Lemma 2.1 in \cite{FtHK-8}. A more direct proof is given at the end of Section~\ref{Hinfty}. The statement that $k=p-m$ is new in the $H^\iy$ setting. For the proof see the final part of Lemma \ref{L:MatRes}.
The paper consists of five sections, including the present introduction. In the second section we present a number of auxiliary results which are all valid in the $H^\iy$ setting. Section \ref{secWiener} contains the proof of Theorem \ref{thmmain1}. Section~\ref{HiyH2} deals with the role of the function $Y$ in the $H^\iy$ case and presents a partial analogue of Theorem \ref{thmmain1}, including the description of all $H^2$ solutions. In the final section we present a few concluding remarks and compute the function $Y$ for the case when $G(z)=\begin{bmatrix} 1+z & -z \end{bmatrix}$.
\paragraph{Notation and terminology.}
By $\sW$ we denote the Wiener space (cf., item (a) in \cite[Section XXIX.2]{GGK2}) consisting of all functions on the unit circle that have an absolutely summable Fourier expansion, and $\sW^{r\ts s}$ stands for the linear space of all ${r\ts s}$ matrix functions of which the entries belong to $\sW$. Thus
\[
F\in \sW^{r\ts s} \ \Longleftrightarrow\ F(e^{it})=\sum_{\nu=-\iy}^\iy F_\nu e^{ it\nu}, \ \mbox{where}\ \sum _{\nu=-\iy}^\iy \|F_\nu\|<\iy.
\]
As usual we refer to $F_\nu$ as the $\nu$-th Fourier coefficient of $F$. We also need the space $\sW_+^{r\ts s}$ which consists of all $F\in \sW^{r\ts s}$ that have an analytic extension to the open unit disc $\BD$, that is,
\[
F\in \sW_+^{r\ts s} \ \Longleftrightarrow\ F(e^{it})=\sum_{\nu=0}^\iy F_\nu e^{ it\nu}, \ \mbox{where}\ \sum _{\nu=0}^\iy \|F_\nu\|<\iy.
\]
Each $F\in \sW^{r\ts s}$ is continuous on the unit circle, and therefore each $F\in \sW^{r\ts s}$ defines a (block) Toeplitz operator $T_F$ mapping $\ell^2_+(\BC^s)$ into $\ell^2_+(\BC^r)$. With $F\in \sW^{r\ts s}$, we associate the function $F^*\in \sW^{s\ts r}$ defined by $F^*(z)=F(1/\bar{z})^*$ for each $z\in\BT$. Then $T_{F^*}=T_F^*$. Finally, note that $\sW_+^{r\ts s}\subset H_{r\ts s}^\iy\subset H_{r\ts s}^2$, where $H_{r\ts s}^\iy$ and $H_{r\ts s}^2$ stand for the linear spaces consisting of all $r \ts s$ matrices with entries in $H^\iy$ and $H^2$, respectively.
\section{Auxiliary results in an $H^\infty$ setting}\label{Hinfty}
\setcounter{equation}{0}
Throughout this section let $G\in H^\infty_{m\ts p}$ and assume that $T_GT_G^*$ is strictly positive. We shall be dealing with the function $Y$ defined by \eqref{defY} and the matrices $\Xi_0$ and $\tht_0$ defined by items (M1) and (M2) in the previous section. Note that the function $Y$ and the matrices $\Xi_0$ and $\tht_0$ are well defined when $G\in H^\infty_{m\ts p}$ and $T_GT_G^*$ is strictly positive; it is not required for this that $G$ belongs to a Wiener space.
In this section we shall derive a number of auxiliary results that will be useful in proving Theorem \ref{thmmain1} in Section \ref{secWiener}. These auxiliary results will also allow us to present a partial generalization of Theorem \ref{thmmain1} in a $H^\iy/H^2$ {context in Section \ref{HiyH2}.}
The first result only involves the matrices $G_0$, $\Xi_0$ and $\tht_0$.
\begin{lem}\label{L:MatRes}
Let $\Xi_0$ and $\Theta_0$ be as in items \textup{(M1)} and \textup{(M2)} in the previous section. Then the matrix $\begin{bmatrix} \Xi_0&\Theta_0\end{bmatrix}$ is invertible with inverse given by
\begin{equation}
\label{invXiTheta}
\mat{cc}{\Xi_0 & \Theta_0}^{-1}=\mat{c}{G_0\\ H_0}\quad\mbox{with}\quad H_0=(\Theta_0^*\Theta_0)^{-1}\Theta_0^*(I_p-\Xi_0 G_0).
\end{equation}
In particular, we have $k=p-m$ and $\im \tht_0=\kr G_0$.
\end{lem}
\begin{proof}[\bf Proof]
Note that $G_0=E_m^*T_G E_p$ and $G_0 E_p^*=E_m^*T_G$. Hence $E_m^*T_G=E_m^*T_GE_pE_p^*$. These identities give
\begin{align*}
G_0\Xi_0&=G_0E_p^*T_G^*(T_GT_G^*)^{-1}E_m\\
&=E_m^*T_G T_G^*(T_GT_G^*)^{-1}E_m=E_m^*E_m=I_m,
\end{align*}
and
\begin{align*}
G_0\Theta_0\Theta_0^*&=E_m^*T_G E_p(I_p-E_p^* T_G^*(T_GT_G^*)^{-1}T_GE_p)\\
&=(E_m^*-E_m^*T_G E_pE_p^* T_G^*(T_GT_G^*)^{-1})T_GE_p\\
&=(E_m^*-E_m^*T_G T_G^*(T_GT_G^*)^{-1})T_GE_p=(E_m^*-E_m^*)T_GE_p=0.
\end{align*}
Since $\im \Theta_0^*=\BC^k$, the latter implies $G_0\Theta_0=0$.
With the identities $G_0\Xi_0=I_m$ and $G_0\Theta_0=0$ we obtain
\[
(I-\Xi_0 G_0)\Xi_0=\Xi_0-\Xi_0=0\ands
(I-\Xi_0 G_0)\Theta_0=\Theta_0-0=\Theta_0.
\]
Note that $(\Theta_0^*\Theta)^{-1}\Theta_0^*$ is a left inverse of $\Theta_0$. Hence
\[
H_0\Xi_0=0\ands H_0\Theta_0=I_k.
\]
Combining the above identities shows
\begin{equation}
\label{ids2}
\mat{cc}{\Xi_0 & \Theta_0} \mat{c}{G_0\\ H_0}=I_p\ands
\mat{c}{G_0\\ H_0}\mat{cc}{\Xi_0 & \Theta_0}=\mat{cc}{I_m& 0\\0& I_k}.
\end{equation}
It follows that $\begin{bmatrix}\Xi_0 & \tht_0\end{bmatrix}$ is invertible and {that} its inverse is given by \eqref{invXiTheta}. In particular, $\begin{bmatrix}\Xi_0 & \Theta_0\end{bmatrix}$ is a square matrix, which implies $p=m+k$. Hence $k=p-m$. Moreover, $G_0\tht_0=0$ implies $\im \tht_0\subset \kr G_0$. We have $\kr\tht_0=\{0\}$, so that $\rank \tht_0=p-m$. Hence $\dim \im\tht_0=p-m$. On the other hand, we have $\im G_0=\BC^m$, which implies $ \dim \kr G_0=p-m$. Therefore $\im \tht_0= \kr G_0$.
\end{proof}
Lemma \ref{L:MatRes} can be seen as the special case of Proposition \ref{P:YH} below where $z=0$. To derive the later result we require the following observation about the function $Y$.
\begin{prop}\label{propY2}
Let $G\in H^\infty_{m\ts p}$ and assume that $T_GT_G^*$ is strictly positive. Then the function $Y$ defined by \eqref{defY} is analytic on $\BD$, $\det Y(z)\not =0$ for each $z\in \BD$, and
\begin{equation}\label{invY2}
Y(z)^{-1}=I_p+zE_p^*T_G^*(T_GT_G^*)^{-1}H_G(I-z S_p)^{-1}E_p\quad (z\in\BD).
\end{equation}
In particular, the function $Y(\cdot )^{-1}$ is analytic on $\BD$. Moreover, we have
\begin{equation}\label{GYG0}
G(z)Y(z)=G_0 \quad (z\in\BD).
\end{equation}
\end{prop}
\begin{proof}[\bf Proof.]
That fact that $S_p$ has spectral radius equal to 1, yields that $Y$ is analytic on $\BD$. Since $S_p^*T_G^*=T_G^*S_m^*$ we can rewrite $Y$ as
\begin{align*}
Y(z)
&=I_p-zE_p^*(I-zS_p^*)^{-1}T_G^*(T_GT_G^*)^{-1}H_GE_p\\
&=I_p-zE_p^*T_G^*(I-zS_m^*)^{-1}(T_GT_G^*)^{-1}H_GE_p\\
&=D+zC(I-zA)^{-1}B,
\end{align*}
where in the last identity
\[
A=S_m^*,\quad B=(T_GT_G^*)^{-1}H_GE_p,\quad C=-E_p^*T_G^*,\quad D=I_p.
\]
Note that $H_GE_p=S_m^*T_G E_p$ and
\begin{align*}
S_m^*T_GE_pE_p^*T_G^*
&=S_m^*T_G(I-S_pS_p^*)T_G^*
=S_m^*T_GT_G^*-S_m^*S_mT_GT_G^*S_m^*\\
&=S_m^*T_GT_G^*-T_GT_G^*S_m^*.
\end{align*}
This yields that $A^\ts:=A-BD^{-1}C$ can be written as
\begin{align*}
A^\ts
&=S_m^*+(T_GT_G^*)^{-1}H_GE_pE_p^*T_G^*
=S_m^*+(T_GT_G^*)^{-1}S_m^*T_GE_pE_p^*T_G^*\\
&=S_m^*+(T_GT_G^*)^{-1}(S_m^*T_GT_G^*-T_GT_G^*S_m^*)
=(T_GT_G^*)^{-1}S_m^*T_GT_G^*.
\end{align*}
Thus $A^\ts$ is similar to $S_m^*$, and hence has spectral radius equal to 1. Then, by standard state space inversion results, cf., Theorem 2.1 in \cite{BGKR08} (with $\l=1/z$), it follows that $Y(z)$ is invertible for each $z\in\BD$ with inverse given by
\begin{align*}
Y(z)^{-1}
&=D^{-1}-zD^{-1}C(I-zA^\ts)^{-1}BD^{-1}\\
&=I+zE_p^*T_G^*(I-z(T_GT_G^*)^{-1}S_m^*T_GT_G^*)^{-1}(T_GT_G^*)^{-1}H_GE_p\\
&=I+zE_p^*T_G^*(T_GT_G^*)^{-1}(I-zS_m^*)^{-1}H_GE_p.
\end{align*}
Since $S_m^*H_G=H_GS_p$, we have $(I-zS_m^*)^{-1}H_G=H_G(I-zS_p)^{-1}$, and hence \eqref{invY2} holds. Note that the spectral radius of $S_p$ is equal to 1, which implies that the function $Y(\cdot )^{-1}$ is analytic on $\BD$.
Finally, we prove that \eqref{GYG0} holds. Let $Y_0, Y_1, Y_2, \ldots$ be the Taylor coefficients of $Y$ at zero. {As observed in \eqref{defYj}, we have} $Y_0=I_p$ and
\begin{equation}
\label{defY2a}
\begin{bmatrix}Y_1\\ Y_2\\ \vdots\end{bmatrix}=-T_G^* (T_G T_G^*)^{-1} \begin{bmatrix}G_1\\ G_2\\ \vdots\end{bmatrix}, \quad \mbox{and hence}\quad T_G\begin{bmatrix}Y_1\\ Y_2\\ \vdots\end{bmatrix}=-\begin{bmatrix}G_1\\ G_2\\ \vdots\end{bmatrix}.
\end{equation}
The latter identity is equivalent to
\[
G(z)\left(\frac{Y(z)-I_p}{z}\right)=-\frac{G(z)-G_0}{z} \quad (z\in \BD).
\]
Multiplying both sides of the above identity by $z$ and adding $G(z)$ on either side yields \eqref{GYG0}.
\end{proof}
\begin{prop}\label{P:YH}
Let $G\in H_{m\ts p}^\iy$ and assume that $T_GT_G^*$ is strictly positive. Let $Y$ be the function defined by \eqref{defY}, and define the functions $\Xi$ and $\tht$ by \eqref{defXiTheta}, with $\Xi_0$ and $\Theta_0$ the matrices in items \textup{(M1)} and \textup{(M2)} of the previous section. Consider the matrix function $H$ defined by
\begin{equation}\label{defH}
H(z)= H_0Y(z)^{-1},\ z\in\BD,\quad \mbox{with}\quad H_0=(\tht_0^*\tht_0)^{-1}(I_p-\Xi_0G_0).
\end{equation}
Then $H$ is analytic on $\BD$,
\begin{equation}
\label{invGH2}
\det \begin{bmatrix} G(z)\\[.2cm] H(z) \end{bmatrix}\not =0 \quad \mbox{and}\quad
\begin{bmatrix}
G(z)\\[.2cm] H(z) \end{bmatrix}^{-1}=\begin{bmatrix}\Xi(z) &\tht(z) \end{bmatrix} \quad (z\in \BD).
\end{equation}
\end{prop}
\begin{proof}[\bf Proof.]
Since $Y$ is analytic on $\BD$, clearly $H$ defined by \eqref{defH} is analytic on $\BD$. Furthermore, using Proposition \ref{propY2} we find that $G(z)=G_0 Y(z)^{-1}$, $z\in\BD$. Thus
\[
\mat{c}{G(z)\\ H(z)}=\mat{c}{G_0\\ H_0}Y(z)^{-1},\quad \mat{cc}{\Xi(z)& \tht(z)}=Y(z)\mat{cc}{\Xi_0 & \tht_0}\quad (z\in\BD).
\]
This shows that our claim reduces to the case $z=0$, which was proved in Lemma \ref{L:MatRes}.
\end{proof}
We conclude with two auxiliary results, the first is about the function $\Xi$ and the second about $\tht$.
\begin{lem}\label{lemXi2}
Let $G\in H_{m\ts p}^\iy$ and assume that $T_GT_G^*$ is strictly positive. Then the function $\Xi$ defined by the first part of \eqref{defXiTheta} is also given by
\begin{equation}
\label{altdefXi}
\Xi(z) =E_p^*(I-zS_p^*)^{-1}T_G^*(T_GT_G^*)^{-1}E_m\quad (z\in \BD)
\end{equation}
\end{lem}
\begin{proof}[\bf Proof]
Recall that $\Xi_0=E_p^*T_G^*(T_GT_G^*)^{-1}E_m$ This yields
\begin{align*}
H_G E_p\Xi_0
&=S_m^*T_GE_pE_p^*T_G^*(T_GT_G^*)^{-1}E_m\\
&=S_m^*T_G(I-S_pS_p^*)T_G^*(T_GT_G^*)^{-1}E_m\\
&=S_m^*E_m-S_m^*S_mT_GT_G^*S_m^*(T_GT_G^*)^{-1}E_m\\
&=-T_GT_G^*S_m^*(T_GT_G^*)^{-1}E_m.
\end{align*}
With this observation we obtain that the function $\Xi$ is also given by
\begin{align*}
\Xi(z)
&=Y(z)\Xi_0
=\Big(I-zE_p^*(I-zS_p^*)^{-1}T_G^*(T_GT_G^*)^{-1}H_GE_p\Big)\Xi_0\\
&=\Xi_0+zE_p^*(I-zS_p^*)^{-1}T_G^*S_m^*(T_GT_G^*)^{-1}E_m\\
&=E_p^*\Big(I+z(I-zS_p^*)^{-1}S_p^*\Big)T_G^*(T_GT_G^*)^{-1}E_m\\
&=E_p^*(I-zS_p^*)^{-1}T_G^*(T_GT_G^*)^{-1}E_m.
\end{align*}
This proves \eqref{altdefXi}.
\end{proof}
\begin{prop}\label{P:Theta}
Let $G\in H_{m\ts p}^\iy$ and assume that $T_GT_G^*$ is strictly positive. The function $\tht$ defined in \eqref{defXiTheta} belongs to $H^\iy_{p\ts (m-p)}$ and is an inner function with $\im T_\tht=\kr T_G$.
\end{prop}
\begin{proof}[\bf Proof.]
Using the definition of $Y$ in \eqref{defY} and the fact $H_GE_p=S_m^*T_GE_p$, we see that $\tht$ is also given by
\[
\tht(z)=(I_p-zE_p^*(I-zS_p^*)^{-1}T_G^*(T_G T_G^*)^{-1}S_m^*T_GE_p)\tht_0\quad (z\in\BD).
\]
By comparing this formula with \cite[Eq. (2.1)]{FtHK-8} we conclude that $\tht$ coincides (up to multiplication with a constant unitary matrix from the right) with the inner function $\wt{\tht}$ satisfying $\im T_G^*= \ell_+^2(\BC^p)\ominus T_{\wt{\tht}} \ell_+^2(\BC^k)$, where $k$ is the number of columns of the matrix $\wt{\tht}(0)$. The existence of $\wt{\tht}$ is guaranteed by the Beurling-Lax theorem. Since $\kr T_G= (\im T_G^*)^\perp$, we conclude that $\kr T_G=\im T_\tht$. Finally, that $k=p-m$, and thus $\tht\in H^\iy_{p\ts (m-p)}$, follows from Lemma \ref{L:MatRes}.
\end{proof}
Note the proof of Proposition \ref{P:Theta} relies heavily on \cite[Lemma 2.1]{FtHK-8}. We also add something to the observations made in Section 2 of \cite{FtHK-8}, namely that $k=p-m$, i.e., $\tht\in H^\iy_{p\in(p-m)}$. This was proved in \cite[Lemma 2.2]{FKR2a} for the case that $G$ is a rational matrix function. We show here that the observation extends to the non-rational case. Next we {give a more direct proof of} Proposition \ref{P:Theta}.
\paragraph{Direct proof of Proposition \ref{P:Theta}.} Let $\tht$ be the analytic matrix function on $\BD$ defined by the second identity in \eqref{defXiTheta}. We already know (see the final part of Lemma \ref{L:MatRes} that $\tht_0$ has size $p\ts (p-m)$, and hence $\tht$ is a matrix function of size $p\ts (p-m)$. To prove that $\tht$ is inner, let $ \ga_j$ be $j$-th column of the block Toeplitz matrix defined by $\tht$. Thus
\begin{equation}
\label{defgas}
\begin{bmatrix} \ga_0& \ga_1& \ga_2&\ \cdots \end{bmatrix}=\begin{bmatrix}
Y_0\tht_0& 0& 0& \cdots \\
Y_1\tht_0&Y_0\tht_0& 0& \cdots \\
Y_2\tht_0&Y_1\tht_0&Y_0\tht_0 &\\
\vdots&\vdots&&\ddots
\end{bmatrix}.
\end{equation}
Note that $ \ga_0, \ga_1, \ga_2, \cdots$ are bounded linear operators from $\BC^{p-m}$ into $\ell_+^2(\BC^p)$. This follows from the first identity in \eqref{defY2a}, the fact that $T_G^*(T_GT_G^*)^{-1}$ is a bounded operator from $\ell_+^2(\BC^m)$ into $\ell_+^2(\BC^p)$, and the fact that the first collumn of $H_G$ is a bounded operator from $\BC^p$ {into $\ell_+^2(\BC^m)$. To prove that $\tht$ is inner it suffices to show that
\begin{itemize}
\item[(C1)] $\ga_j$ is an isometry mapping $\BC^{p-m}$ into $\ell_+^2(\BC^p)$ for $j=0, 1, 2, \dots$;
\item[(C2)] $\im \ga_j \perp \im \ga_k$ for $k\not =j$.
\end{itemize}
To see this, assume that both conditions are satisfied. Then the operator $T$ defined by be the infinite block lower triangular matrix on the right hand side of \eqref{defgas} is an isometry mapping $\ell_+^2(\BC^{p-m})$ into $\ell_+^2(\BC^{p-m})$. Moreover, $ S_pT=TS_{p-m}$. It follows that $T$ is a Toeplitz operator, and its defining function $\tht(\cdot)=Y(\cdot)\tht_0$ belongs to $H_{p\ts (p-m)}^\iy$; cf., \cite[Section XXIII.3]{GGK2}. Thus $T=T_\tht$, and $\tht$ is inner because $T_\tht=T$ is an isometry, \cite[Section XXVI.3]{GGK2} or \cite[Proposition 2.6.2]{FB10}.
In order to show that conditions (C1) and (C2) are satisfied we need the following two lemmas.
\begin{lem}\label{lemtht1}
Let $G\in H_{m\ts p}^\iy$, and assume that $T_GT_G^*$ is strictly positive. Then
\begin{equation*}
\sum_{i=0}^\iy Y_i^*Y_{i+j}=
\left\{
\begin{array}{cl}
I_p +E_p^*H_G^*(T_GT_G^*)^{-1}H_G E_p &\mbox{when $j=0$},\\[.3cm]
-G_0^*E_m^*(S_m^*)^{j-1}(T_GT_G^*)^{-1}H_G E_p &\mbox{when $j= 1,2, \ldots $}.
\end{array}
\right.
\end{equation*}
\end{lem}
\begin{proof}[\bf Proof]
Note that
\begin{align}
&\sum_{i=0}^\iy Y_i^*Y_{i+j}=Y_0^* Y_j+ \begin{bmatrix} Y_1^* & Y_2^*& \cdots \end{bmatrix} \begin{bmatrix} Y_{j+1}\\ Y_{j+2}\\ \vdots \end{bmatrix}\nn\\
&\hspace{.5cm}=Y_0^* Y_j+ E_p^*H_G^*(T_GT_G^*)^{-1}T_G (S_p^*)^j T_G^*(T_GT_G^*)^{-1}H_G E_p\nn\\
&\hspace{.5cm}=Y_0^* Y_j+ E_p^*H_G^*(T_GT_G^*)^{-1}T_G T_G^*(S_m^*)^j (T_GT_G^*)^{-1}H_G E_p\nn\\
&\hspace{.5cm}=Y_0^* Y_j+ E_p^*H_G^*(S_m^*)^j (T_GT_G^*)^{-1}H_G E_p, \quad j=0, 1, \ldots. \label{Y*Y}
\end{align}
Using $Y_0=I_p$ we see that with $j=0$ the identity \eqref{Y*Y} yields the first part of the lemma.
Next assume that $j>0$. Recall that $H_G E_p=S_m^*E_p$. Taking adjoints in the latter identity and {using} $Y_0=I_p$ again, we see that \eqref{Y*Y} can be rewritten as
\begin{align*}
\sum_{i=0}^\iy Y_i^*Y_{i+j}&=Y_j +E_p^*T_G^*S_m(S_m^*)^j (T_GT_G^*)^{-1}H_G E_p\\
&=Y_j +E_p^*T_G^*S_mS_m^*(S_m^*)^{j -1}(T_GT_G^*)^{-1}H_G E_p\\
&=C_1-C_2,
\end{align*}
where
\begin{align*}
C_1&= E_p^*T_G^*(S_m^*)^{j -1}(T_GT_G^*)^{-1}H_G E_p\\
&= E_p^*(S_p^*)^{j -1}{T_G^*}(T_GT_G^*)^{-1}H_G E_p=-Y_j,
\end{align*}
and
\begin{align*}
C_2&=E_p^*T_G^*E_m E_m^*(S_m^*)^{j -1}(T_GT_G^*)^{-1}H_G E_p\\
&=G_0 E_m^*(S_m^*)^{j -1}(T_GT_G^*)^{-1}H_G E_p.
\end{align*}
Thus
\begin{align*}
\sum_{i=0}^\iy Y_i^*Y_{i+j}&=Y_j +C_1-C_2=-G_0 E_m^*(S_m^*)^{j -1}(T_GT_G^*)^{-1}H_G E_p.
\end{align*}
This proves the second part of the lemma.
\end{proof}
\begin{lem}\label{lemtht2}
Let $G\in H_{m\ts p}^\iy$, and assume that $T_GT_G^*$ is strictly positive. Then
\begin{equation}
\label{eqtht0*}
\tht_0^*\Big(I_p +E_p^*H_G^*(T_GT_G^*)^{-1}H_G E_p\Big)\tht_0=I_{p-m}.
\end{equation}
\end{lem}
\begin{proof}[\bf Proof]
Using the definition of $\tht_0\tht_0^*$ in \eqref{deftht0} we see that
\begin{equation*}
E_p^*H_G^*(T_GT_G^*)^{-1}H_G E_p\tht_0\tht_0^*=A-B,
\end{equation*}
where
\begin{align*}
A&= E_p^*H_G^*(T_GT_G^*)^{-1}H_G E_p,\\
B&=E_p^*H_G^*(T_GT_G^*)^{-1}H_G E_pE_p^*T_G^*(T_GT_G^*)^{-1}T_GE_p\\
&=E_p^*H_G^*(T_GT_G^*)^{-1}S_m^*T_G E_pE_p^*T_G^*(T_GT_G^*)^{-1}T_GE_p.
\end{align*}
Here we used that $H_GE_p=S_m^*T_G E_p$. Next using $E_pE_p^*=I-S_pS_p^*$ we write $B$ as $B=B_1-B_2$, where
\begin{align*}
B_1&=E_p^*H_G^*(T_GT_G^*)^{-1}S_m^*T_GT_G^*(T_GT_G^*)^{-1}T_GE_p\\
&=E_p^*H_G^*(T_GT_G^*)^{-1}S_m^*T_GE_p\\
&=E_p^*H_G^*(T_GT_G^*)^{-1}H_GE_p=A,
\end{align*}
and
\begin{align*}
B_2&= E_p^*H_G^*(T_GT_G^*)^{-1}S_m^*T_G S_pS_p^*T_G^*(T_GT_G^*)^{-1}T_GE_p\\
&= E_p^*H_G^*(T_GT_G^*)^{-1}S_m^* S_m T_GT_G^*S_m^*(T_GT_G^*)^{-1}T_GE_p\\
&= E_p^*H_G^*(T_GT_G^*)^{-1}T_GT_G^*S_m^*(T_GT_G^*)^{-1}T_GE_p\\
&= E_p^*H_G^*S_m^*(T_GT_G^*)^{-1}T_GE_p\\
&= E_p^*T_G^* S_mS_m^*(T_GT_G^*)^{-1}T_GE_p.
\end{align*}
Next we use $S_mS_m^*= I -E_mE_m^*$ to show that
\begin{align}
B_2&=E_p^*T_G^* (T_GT_G^*)^{-1}T_GE_p-E_p^*T_G^* E_mE_m^*(T_GT_G^*)^{-1}T_GE_p\nn\\
&=E_p^*T_G^* (T_GT_G^*)^{-1}T_GE_p-G_0^*E_m^*(T_GT_G^*)^{-1}T_GE_p. \label{altB2}
\end{align}
Recall (see the final part of Lemma \ref{L:MatRes}) that $\tht_0^*G_0^*=0$, and hence $\tht_0^*B_2=\tht_0^*E_p^*T_G^* (T_GT_G^*)^{-1}T_GE_p$. Since $A=B_1$ and $\tht_0\tht_0^*$ is given by \eqref{deftht0}, we conclude that
\begin{align*}
&\tht_0\tht_0^*\Big(I_p +E_p^*H_G^*(T_GT_G^*)^{-1}H_G E_p\Big)\tht_0\tht_0^*=\\
&\hspace{1cm}=\tht_0\tht_0^*\tht_0\tht^*+\tht_0\tht_0^*E_p^*H_G^*(T_GT_G^*)^{-1}H_G E_p\tht_0\tht_0^*\\
&\hspace{1cm}=\tht_0\tht_0^*\tht_0\tht^*+\tht_0\tht_0^*(A-B)\\
&\hspace{1cm}=\tht_0\tht_0^*\tht_0\tht^*+\tht_0\tht_0^*(A-B_1+B_2)\\
&\hspace{1cm}=\tht_0\tht_0^*\tht_0\tht^*+\tht_0\tht_0^*B_2 \\
&\hspace{1cm}=\tht_0\tht_0^*\tht_0\tht^*+\tht_0\tht_0^*E_p^*T_G^* (T_GT_G^*)^{-1}T_GE_p \\
&\hspace{1cm}=\tht_0\tht_0^*\Big(I_p -E_p^*T_G^* (T_GT_G^*)^{-1}T_GE_p+ E_p^*T_G^* (T_GT_G^*)^{-1}T_GE_p\Big) \\
&\hspace{1cm}= \tht_0\tht_0^*.
\end{align*}
Hence $\tht_0\tht_0^*\Big(I_p +E_p^*H_G^*(T_GT_G^*)^{-1}H_G E_p\Big)\tht_0\tht_0^*=\tht_0\tht_0^*$. But then, using that $\tht_0^*$ is surjective and $\tht_0$ is injective, we obtain \eqref{eqtht0*}, and the lemma is proved.
\end{proof}
We proceed by showing that (C1) and (C2) are satisfied. Let $\ga_0, \ga_1, \ga_2, \cdots$ be given by \eqref{defgas}. Using the first part of Lemma \ref{lemtht1} and formula \eqref{eqtht0*} we obtain for each $u\in \BC^{p-m}$ that
\begin{align*}
\|\ga_j u\|^2&
= \inn{\ga_j^* \ga_j u}{u}
=\inn{\tht_0^*\Big(\sum_{i=0}^\iy Y_i^*Y_i\Big)\tht_0 u}{u}\\
&=\inn{\tht_0^*\Big(I_p +E_p^*H_G^*(T_GT_G^*)^{-1}H_G E_p\Big)\tht_0 u}{u}\\
&=\inn{u}{u}=\|u\|^2 \quad (j=0,1,2, \cdots).
\end{align*}
Thus (C1) holds.
Next, in order to derive (C2), we use the second part of Lemma \ref{lemtht1} and the fact that $\tht_0^*G_0^*=0$. For $j>k$ this yields
\begin{align*}
\ga_j^*\ga_k&=\tht_0^*\Big(\sum_{i=0}^\iy Y_i^* Y_{i+j-k}\Big)\tht_0\\
&=-\tht_0^*G_0^*E_m^*(S_m^*)^{j-k-1}(T_GT_G^*)^{-1}H_G E_p \tht_0=0.
\end{align*}
It follows that $\im \ga_j \perp \im \ga_k$ for $j>k$. Interchanging the role of $j$ and $k$ then yields (C2).
Finally, we prove $\kr T_G = \im T_{\tht}$. Recall that $G_0\tht_0=0$ by the final part of Lemma \ref{L:MatRes}. Hence using \eqref{GYG0} we have
\[
G(z)\tht(z)=G(z)Y(z)\tht_0=G_0\tht_0=0 \quad(z\in \BD).
\]
This implies $T_GT_\tht=0$, and thus $\im T_{\tht}\subset \kr T_G$. To prove the reverse inclusion, take $f=\begin{bmatrix}f_0& f_1&f_2& \cdots \end{bmatrix}{}^\perp$ in $\kr T_G$, and put $F(z)=E_p(I-zS_p^*)^{-1}f$. Since $G(z)F(z)=0$ on $\BD$, the second part of \eqref{invGH2} shows that
\begin{align*}
F(z)&=\begin{bmatrix}\Xi(z) &\tht(z) \end{bmatrix}\begin{bmatrix}
G(z)\\[.2cm] H(z) \end{bmatrix}F(z)\\
&=\begin{bmatrix}\Xi(z) &\tht(z) \end{bmatrix}\begin{bmatrix}
0\\[.2cm] H(z) {F(z)} \end{bmatrix}=\tht(z) H(z)F(z) \quad (z\in \BD).
\end{align*}
It follows that $f= {T_{\tht}}T_Hf$, and thus $f\in \im {T_{\tht}}$ which proves that $\kr T_G\subset \im {T_{\tht}}$, and therefore $\kr T_G = \im T_{\tht}$. This completes the direct {proof of Proposition \ref{P:Theta}.}
\section{Proof of Theorem 1.1}\label{secWiener}\setcounter{equation}{0}
In this section we prove Theorem \ref{thmmain1}. For that purpose we first derive the following lemma.
\begin{lem}\label{lemW1} Let $G\in \sW_+^{m\ts p}$, and assume that $T_GT_G^*$ is strictly positive. Then $(T_GT_G^*)^{-1}$ maps $\ell_+^1(\BC^m)$ into itself.
\end{lem}
\begin{proof}[\bf Proof.]
We split the proof into five parts. In the first part we review a few general facts about Toeplitz and Hankel operators (cf., Sections 2.1--2.3 in \cite{BS90} and Chapter XXIII in \cite{GGK2}), and we recall an inversion formula from \cite{FKR2a}.
\smallskip\noindent\textsc{Part 1.}
Let $F$ belong to the Wiener space $ \sW_+^{r\ts s}$. Then the Toeplitz operator $T_F$ and the Hankel operator $H_F$ both map $\ell_+^1 (\BC^s)$ (seen as a linear sub-manifold of $\ell_+^2(\BC^s)$) into $\ell_+^1(\BC^r)$ (seen as a linear sub-manifold of $\ell_+^2 (\BC^r)$). Moreover, the induced operators acting between these $\ell_+^1$ spaces are bounded too. Furthermore, $H_F$ is compact as an operator from $\ell_+^2 (\BC^s)$ into $\ell_+^2(\BC^r)$ as well as when viewed as an operator from $\ell_+^1 (\BC^s)$ into $\ell_+^1(\BC^r)$ (cf., \cite[Sections 2.1]{BS90}). Finally, if $u$ is a ${s\ts t}$ matrix, then the functions $\va$ and $\psi$ given by
\[
\va(z)=E_r^*(I-zS_r^*)^{-1} T_FE_s u \ands \psi(z)=E_r^*(I-zS_r^*)^{-1}H_F E_s u
\]
belong to the Wiener space $\sW_+^{r \ts t}$.
Next, we recall some facts from \cite[Section 2]{FKR2a}. Define $R=G G^*$. See the last paragraph of the introduction for the definition of $G^*$. Note that $R\in \sW^{m\ts m}$. The fact that $T_GT_G^*$ is strictly positive implies that the matrix $R(z) $ is positive definite for each $z\in \BT$, and hence the Toeplitz operator $T_R$ acting on $\ell_+^2 (\BC^m)$ is invertible. Moreover, see \cite[Eq. (2.4)]{FKR2a}, we have
\begin{equation}\label{TRinv1}
(T_GT_G^*)^{-1}= T_R^{-1}+T_R^{-1}H_G(I-H_G^*T_R^{-1}H_G)^{-1}H_G^*T_R^{-1}.
\end{equation}
\smallskip\noindent\textsc{Part 2.}
Since $R$ belongs to $\sW^{m\ts m}$ and $R(z) $ is positive definite for each $z\in \BT$, the function $R$ admits a a canonical spectral factorization (see Corollary 2.1 in \cite[Section III.2]{CG81}), that is, $R=R_+^*R_+$ where $R_+$ belongs to $\sW_+^{m\ts m}$ and $\det R(z)\not =0$ for each $z$ in the closed unit disc. This implies that $T_R=T_{R_+^*} T_{R_+}$ and both $T_{R_+}$ and $T_{R_+^*}$ are invertible. In fact, $(T_{R_+})^{-1}= T_{R_+^{-1}}$ and $(T_{R_+^*})^{-1}=T_{(R_+^{-1})^*}$ are both Toeplitz operators. We conclude that $T_R$ is invertible and that its inverse is given by
\[
T_R^{-1}=(T_{R_+})^{-1}(T_{R_+^* })^{-1}.
\]
From the remarks in the first paragraph of the proof it then follows that the operators $(T_{R_+})^{-1}$ and $(T_{R_+^*} )^{-1}$ map $\ell_+^1 (\BC^m)$ into itself
and act as bounded linear operators on this space. Hence the same holds true for $T_R^{-1}$. Moreover $T_R^{-1}$, as an operator on $\ell_+^1 (\BC^m)$, is again invertible.
\smallskip\noindent\textsc{Part 3.} From the final remark in the first paragraph of the first part of the proof we know that the Hankel operator $H_G$ maps $\ell_+^1 (\BC^p)$ into $\ell_+^1 (\BC^m)$. An analogous result holds true for $H_G^*$. To see this note that $H_G^*=H_{G_*}$, where $G_*$ is the function in $\sW_+^{p\ts m}$ given by:
\[
G_*(z)=G(\bar{z})^*=G_0^*+zG_0^*+z^2G_2^*+\cdots \quad (|z|\leq 1).
\]
Using the result of Part 1 of the proof we conclude that $I-H_G^*T_R^{-1}H_G$ maps $\ell_+^1 (\BC^p)$ into itself and act as bounded linear operator on this space.
\smallskip\noindent\textsc{Part 4.} Put $M=I-H_G^*T_R^{-1}H_G$. In this part we show that $M$ is invertible as an operator on $\ell_+^1 (\BC^p)$. To do this we use the fact that $H_G$ acts as a compact operator from $\ell_+^1 (\BC^p)$ to $\ell_+^1 (\BC^m)$. {It follows} that $M$ as an operator on $\ell_+^1 (\BC^p)$ is of the form identity operator plus a compact one. Hence $M$ as an operator on $\ell_+^1 (\BC^p)$ is a Fredholm operator of index zero. {In order to} show that $M$ as an operator on $\ell_+^1 (\BC^p)$ is {invertible, it then suffices} to prove that $M$ on $\ell_+^1 (\BC^p)$ is one-to-one. Take $h\in \ell_+^1 (\BC^p)$, and assume that $Mh=0$. Since $\ell_+^1 (\BC^p)$ is contained in $\ell_+^2 (\BC^p)$, it follows that $h\in \ell_+^2 (\BC^p)$. But on $\ell_+^2 (\BC^p)$ the operator $M$ is invertible. Thus $h=0$, and $M$ is one-to-one on $\ell_+^1 (\BC^p)$. Therefore $I-H_G^*T_R^{-1}H_G$ is invertible as an operator on $\ell_+^1 (\BC^p)$.
\smallskip\noindent\textsc{Part 5.} The results of the preceding parts of the proof show that the operators appearing in \eqref{TRinv1} all map $\ell^1$ spaces into $\ell^1$ spaces, and hence $(T_GT_G^*)^{-1}$ maps $\ell_+^1(\BC^m)$ into itself.
\end{proof}
\begin{proof}[\bf Proof of Theorem \ref{thmmain1}.]
We split the proof into three parts.
\smallskip
\noindent\textsc{Part 1.} In this part we show that the function $Y$ defined by \eqref{defY} has the desired properties. First we show that $Y$ belongs to the Wiener space $ \sW_+^{p\ts p}$. To do this note that $T_G^*=T_{G^*}$, and hence $T_G^*$ maps $\ell_+^1(\BC^m)$ into $\ell_+^1(\BC^p)$. But then Lemma~\ref{lemW1} tells us that $T_G^*(T_GT_G^*)^{-1}$ maps $\ell_+^1(\BC^m)$ into $\ell_+^1(\BC^p)$. Since $G\in \sW_+^{m\ts p}$, its Taylor coefficients $G_0, G_1, G_2, \ldots$ at zero are absolutely summable in norm, and thus we can use \eqref{defYj} to show that the same holds true for the Taylor coefficients at zero of $Y$. Therefore $Y\in \sW_+^{p\ts p}$.
Next we show that $\det Y(z)\not =0$ when $|z|\leq 1$. For $|z|<1$ this follows from Proposition \ref{propY2}. We shall prove that $\det Y(z)\not= 0$ for all $z\in \BT$ by contradiction. Assume that there exists $\l\in \BT$ such that $\det Y(\l) =0$. Then there exists $u\not = 0$ such that $Y(\l)u = 0$. Since $G$ and $Y$ are Wiener functions, $G$ and $Y$ extend continuously to $\BT$. Thus the equality in \eqref{GYG0} from Proposition \ref{propY2} also holds for each $|z|=1$. It follows that $G_0 u = G(\l)Y(\l)u =0$. So $u\in \kr G_0$. From the final part of Lemma \ref{L:MatRes} we know that $\kr G_0 = \im \tht_0$. But then $u = \tht_0 v$ for some $v\in \BC^{p-m}$, and $\tht(\l)v = Y(\l)\tht_0 v = Y(\l)u = 0$. We obtain that $v= I_{p-m}v= \Theta^*(\l)\Theta(\l)v =0$. This implies that $u =\Theta_0v =0$, which contradicts our assumption that $u\not = 0$. We conclude that $\det Y(z)\not =0$ for all $|z|\leq 1$.
By Wiener's theorem, the fact that $ Y\in \sW_+^{p\ts p}$ and $\det Y(z)\not =0$ for all $|z|\leq 1$ implies that $Y^{-1}$ also belongs to $\sW_+^{p\ts p}$. Finally, formula \eqref{invY} follows from \eqref{invY2}. Thus $Y$ has all properties mentioned in the first paragraph of Theorem \ref{thmmain1}.
\smallskip
\noindent\textsc{Part 2.} In this part we deal with items (i)--(iii).
Note that Proposition \ref{propY2} and the final part of Lemma \ref{L:MatRes} show that the statements in items (i) and (ii) in Theorem \ref{thmmain1} hold true, {noting that $Y,\, Y^{-1}\in\sW_+^{p\ts p}$ implies that the functions $\Xi$, $\tht$ and $H$ are analytic Wiener functions as well}. Furthermore, item (iii) follows from Proposition \ref{P:YH} and the fact that $G$, $H$, and $Y$ extend to continuous functions on $\BT$. This proves items (i)--(iii) Theorem \ref{thmmain1}.
\smallskip
\noindent\textsc{Part 3.} It remains to prove the statements in the final paragraph of
Theorem \ref{thmmain1}. Put $\Xi(z)=Y(z)\Xi_0$. Clearly $\Xi \in \sW_+^{p\ts m}$. {Using \eqref{GYG0} from Proposition \ref{propY2}}, we have
\[
G(z)\Xi(z)=G(z)Y(z)\Xi_0=G_0\Xi_0\quad (z\in \BD).
\]
Among other things, equality \eqref{invXiTheta} shows that $G_0\Xi_0=I_m$. It follows that $\Xi$ is a solution to the {Wiener-Bezout} problem \eqref{corona}. From the equality \eqref{invXiTheta} it also follows that $G_0\tht_0=0$. Hence for $X$ given by \eqref{allsolW} with $V$ belonging to $\sW_+^{(p-m)\ts m}$ we have
\begin{align*}
G(z)X(z)&= G(z)Y(z)(\Xi_0+\tht_0 V(z))\\
&=G_0\Xi_0+G_0\tht_0V(z)=I_m \quad (z\in \BD).
\end{align*}
Note that $X$ given by \eqref{allsolW} belongs to $\sW_+^{p\ts m}$, and thus all $X$ given by \eqref{allsolW} are solutions to the {Wiener-Bezout} problem associated with $G$.
We proceed by proving \eqref{H2idW}. To do this let $V\in \sW_+^{(p-m)\ts m}$, and let $X$ be given by \eqref{allsolW}. From Lemma \ref{lemXi2} we know that $\Xi$ is given by \eqref{altdefXi}. This implies that
\[
\im T_\Xi E_m=\im T_G^*( T_G T_G^*)^{-1}E_m\subset \im T_G^*=(\im T_\tht)^\perp.
\]
Thus for each $u\in \BC^m$ the vector $T_\Xi E_mu$ is orthogonal to $\im T_\tht$
Using this orthogonality we have
\begin{align}
\|X(\cdot)u\|^2_{H^2_p}&=\|T_X E_m u\|^2_{\ell_+^2(\BC^p)}=\|T_\Xi E_mu + T_\tht T_V E_m u\|^2_{\ell_+^2(\BC^p)}\nn \\
&=\|T_\Xi E_m u\|^2 +\|T_\tht T_V E_m u\|^2_{\ell_+^2(\BC^p)}\nn \\
&=\|T_\Xi E_m u|^2+\| T_V E_m u\|^2_{\ell_+^2(\BC^p)}\nn \\
&= \|\Xi(\cdot)u\|^2_{H^2_p}+ \|V(\cdot)u\|^2_{H^2_p},
\label{prH2idW}
\end{align}
which proves \eqref{H2idW}.
Finally, let $X\in \sW_+^{p\ts m}$ be a solution to the {Wiener-Bezout} problem associated with $G$. Thus $G(z)X(z)=I_m$ for $z\in \BD$. Define $V(z)=H(z)X(z)$, $z\in \BD$, where $H$ is defined in
item (iii) of Theorem \ref{thmmain1}. Then $V$ belongs to the Wiener space $W_+^{(p-m)\ts m}$, and formula \eqref{invGH1} shows that
\begin{align*}
X(z)&=\begin{bmatrix} \Xi(z)& \tht(z)\end{bmatrix}\begin{bmatrix} G(z)\\ H(z)\end{bmatrix}X(z)\\
&= \Xi(z)G(z)X(z)+\tht(z)H(z)X(z)=\Xi(z)+\tht(z)V(z) \quad (|z|\leq 1).
\end{align*}
Using the formulas for $ \Xi(z)$ and $\tht(z)$ in \eqref{defXiTheta} we see that $X$ admits the representation \eqref{allsolW}.
\end{proof}
\begin{remark}\label{remHwtH}
In the Wiener setting the function $H$ defined in item (iii) of Theorem \ref{thmmain1} and the function $H$ defined by \eqref{TolH} are equal. To be more precise, put
\begin{align*}
H(z)&=(\tht_0^*\tht_0)^{-1}\tht_0^*(I_p-\Xi_0G_0) Y(z) ^{-1} \quad (|z|\leq 1), \\
\wt{H}(\z)&=\tht^*\big(\z)(I_p-\Xi(z)G(\z)\big) \quad (|\z|=1).
\end{align*}
Then $H=\wt{H}$. To see this fix $|\z|=1$. {According to \eqref{invXiTheta} we have
\[
H(\z)Y(\z)\mat{cc}{\tht_0&\Xi_0}=H_0 \mat{cc}{\tht_0&\Xi_0}
=\mat{cc}{I_{p-m}& 0}.
\]}
On the other hand, according item (i) in Theorem \ref{thmmain1} we have $G(\z)Y(\z)=G_0$. Furthermore, by definition, $\Xi(\z)=Y(\z)\Xi_0$. It follows that
\begin{align*}
\wt{H}(\z)Y(\z)&=\tht^*\big(\z)(Y(\z)-\Xi(\z)G(\z)Y(z)\big) \\
&=\tht^*\big(\z)(Y(\z)-\Xi(z)G_0\big)=\tht^*(\z)Y(\z)\big(I-\Xi_0G_0\big).
\end{align*}
Again using \eqref{invXiTheta}, we obtain $G_0\tht_0=0$ and $G_0\Xi_0=I_m$, such that
\[
(I-\Xi_0G_0)\mat{cc}{\tht_0&\Xi_0}=\mat{cc}{\tht_0&0}.
\]
This yields
\begin{align*}
\wt{H}(\z)Y(\z)\mat{cc}{\tht_0&\Xi_0}&
=\tht^*(\z)Y(\z)\mat{cc}{\tht_0&0}
=\tht^*(\z)\mat{cc}{\tht(\z)&0}\\
&=\mat{cc}{\tht(\z)&0}=\mat{cc}{I_{p-m}&0}.
\end{align*}
Since $\mat{cc}{\tht_0&\Xi_0}$ and $Y(\z)$ both are invertible, we obtain that $H(\z)=\wt{H}(\z)$. But $\z$ is an arbitrary point on $\BT$. Therefore, $H=\wt{H}$.
\end{remark}
\section{Solutions to the {$H^2$-Bezout} problem}
\label{HiyH2}\setcounter{equation}{0}
Let $G\in H^\iy_{m\ts p}$ and assume $T_GT_G^*$ is strictly positive. If $G$ is not in $\sW_+^{m\ts p}$, then the function $\Xi$ defined in \eqref{defXiTheta} will, in general, not be in $\sW_+^{p\ts m}$, and hence not a solution to the {Wiener-Bezout} problem associated with $G$. However, by Propositions \ref{propY2} and \ref{P:YH}, {the function} $\Xi$ is still analytic on $\BD$ and satisfies $G(z)\Xi(z)=I_m$ for each $z\in\BD$. It turns out that r$\Xi$ is in $H^2_{p\ts m}$ and hence a solution to the {$H^2$-Bezout} problem associated with $G$. In fact, extending the description of all solutions to the {Wiener-Bezout} problem of Theorem \ref{thmmain1} via \eqref{allsolW} to one where $V$ is taken from $H^2_{(p-m)\ts m}$, all solutions to the {$H^2$-Bezout} problem are obtained, even if $G\not\in\sW_+^{m\ts p}$. The details are given in the following theorem.
\begin{thm}\label{T:H2cor}
Let $G\in H^\iy_{m\ts p}$ such that $T_GT_G^*$ is strictly positive. Define the functions $\Xi$ and $\tht$ by \eqref{defXiTheta}, with $\Xi_0$ and $\tht_0$ as in \textup{(M1)} and \textup{(M2)}. Then $\Xi\in H^2_{p\ts m}$, $\tht\in H^\iy_{p\ts (m-p)}$ is inner with $\im T_\tht=\kr T_G$, and for any $V\in H^2_{(p-m)\ts m}$ the function
\begin{equation}\label{H2sol}
X(z)=\Xi(z)+\tht(z)V(z)\quad (z\in\BD)
\end{equation}
is a solution to the {$H^2$-Bezout} problem associated with $G$. Moreover, all solutions are obtained in this way. Furthermore, for $X$ given by \eqref{H2sol}, with $V$ in $H^2_{(p-m)\ts m}$, we have
\begin{equation}\label{H2LeastSquare}
\|X(\cdot)u\|^2_{H^2_p}=\|\Xi(\cdot)u\|^2_{H^2_p}+\|V(\cdot)u\|^2_{H^2_{p-m}}
\quad (u\in\BC^m).
\end{equation}
In particular, $\Xi$ is the last square solution to the {$H^2$-Bezout} problem associated with $G$.
\end{thm}
Theorem \ref{T:H2cor} gives a variation on the last part of our main result, Theorem \ref{thmmain1} above, under the weaker assumption $G\in H^\iy_{m\ts p}$. Variations on the other claims made in Theorem \ref{thmmain1}, e.g., \eqref{invY} and items (i)--(iii), under this weaker assumption were proved in Propositions \ref{propY2}, \ref{P:YH} and \ref{P:Theta} above.
We shall first prove the next proposition, which contains the key observation needed in the proof of Theorem \ref{T:H2cor}.
\begin{prop}\label{P:YY-1H2}
Let $G\in H^\iy_{m\ts p}$ such that $T_GT_G^*$ is strictly positive. Then the function $Y$ defined by \eqref{defY} as well as the function $Y(\cdot )^{-1}$ are in $H^2_{p\ts p}$. In particular, $\det Y(z)\not =0$ for almost every $z\in\BT$.
\end{prop}
In order to prove Proposition \ref{P:YY-1H2} we require some additional notation. Let $F\in H_{r\ts s}^2$. Then $F$ admits a Taylor expansion
\begin{equation}\label{F-Taylor}
F(z)=F_0+zF_1+z^2F_2+\cdots \quad (z\in\BD)
\end{equation}
and induces a bounded operator
\begin{equation*
\ga_F=\mat{c}{F_0\\F_1\\\vdots}:\BC^s\to\ell^2_+(\BC^r)\ \ \mbox{with}\ \
\|\ga_Fu\|_{\ell^2_+(\BC^r)}=\|F(\cdot)u\|_{H^2_r}\ \ (u\in\BC^s).
\end{equation*}
In fact, an analytic $r\ts s$ matrix function $F$ as in \eqref{F-Taylor} is in $H_{r\ts s}^2$ if and only if $\ga_F$ above induces a bounded operator from $\BC^s$ into $\ell^2_+(\BC^r)$. On the other hand, if $K$ is a bounded operator from $\BC^s$ into $\ell^2_+(\BC^r)$, then $K=\ga_F$ for some $F\in H_{r\ts s}^2$; in this case $F_n:=E_r^* S_r^{*n}K$ is the $n$-th Taylor coefficient of $F$.
With $F\in H_{r\ts s}^2$ we associate a function ${F_*}$ defined by
\begin{equation}
\label{defF*}
F_*(z)=F(\bar{z})^*=F_0^*+zF_1^*+z^2F_2^*+\cdots \quad (|z|<1).
\end{equation}
Then $F_*\in H^2_{s\ts r}$. However, $\ga_F$ and $\ga_{F_*}$ need not have the same operator norm. In contrast, for $F$ in $H_{r\ts s}^\iy$, we have ${F_*}\in H_{s\ts r}^\iy$ and $\|T_F\|=\|F\|_\iy=\|{F_*}\|_\iy=\|T_{\wtil{F}}\|$.
\begin{proof}[\bf Proof of Proposition \ref{P:YY-1H2}]
Identifying $\ell^2_+(\BC^p)$ with $\BC^p\oplus \ell^2_+(\BC^p)$, we see that
\[
\ga_Y=\mat{c}{I_p\\
-T_G^*(T_GT_G^*)^{-1}H_GE_p}:\BC^p\to \mat{c}{\BC^p\\ \ell^2_+(\BC^p)},
\]
which is clearly bounded as an operator from $\BC^p$ into $\ell^2_+(\BC^p)$. Hence $Y\in H^2_{p\ts p}$.
Now define $F$ on $\BD$ by
\[
F(z)=I+zE_p^*(I-zS_p^*)^{-1}H_G^*(T_GT_G^*)^{-1}T_GE_p\quad (z\in\BD).
\]
Again identifying $\ell^2_+(\BC^p)$ with $\BC^p\oplus \ell^2_+(\BC^p)$, this in turn shows that
\[
\ga_{F}=\mat{c}{I_p\\ H_G^*(T_GT_G^*)^{-1}T_GE_p} :\BC^p\to \mat{c}{\BC^p\\ \ell^2_+(\BC^p)}.
\]
Hence $\ga_{F}$ is bounded, and thus $F$ is in $H^2_{p\ts p}$. Moreover, by \eqref{invY2}, we have
\[
F_*(z)=I+zE_p^*T_G^*(T_GT_G^*)^{-1}H_G(I-zS_p)^{-1}E_p=Y(z)^{-1}\quad (z\in\BD).
\]
Since $F\in H^2_{p\ts p}$, we obtain that $F_*\in H^2_{p\ts p}$.
Hence $Y(\cdot )^{-1}$ is in $H^2_{p\ts p}$.
Since both $Y$ and $F$ are in $H^2_{p\ts p}$ with $Y(z)F(z)=I_p$ for every $z\in\BD$, the non-tangential limits of $F$ and $Y$ exist a.e.\ on $\BT$ and, by continuity, the identity $Y(z)F(z)=I_p$ extends to all points on $\BT$ where the non-tangential limits of both exist. Thus $Y(z)$ is invertible for almost every $z\in\BT$.
\end{proof}
\begin{proof}[\bf Proof of Theorem \ref{T:H2cor}.]
Since $ Y(\cdot)^{-1}$ is in $ H^2_{p\ts p}$ and $\Xi(z)=Y(z)\Xi_0$, $z\in\BD$, we have $\Xi\in H^2_{p\ts m}$. The claim regarding $\tht$ follows from Proposition \ref{P:Theta}. Let $V\in H^2_{(p-m)\ts m}$. The preceding observations about $\Xi$ and $\tht$ show that the function $X$ given by \eqref{H2sol} is in $H^2_{p\ts m}$. By \eqref{invGH2} we have $G(z)\Xi(z)=I_m$ and $G(z)\tht(z)=0$, so that $G(z)X(z)=I_m$ for each $z\in\BD$. Hence for each $V\in H^2_{(p-m)\ts m}$, the function $X$ given by \eqref{H2sol} is a solution to the {$H^2$-Bezout} problem associated with $G$.
Next we show that all solutions to the {$H^2$-Bezout} problem associated with $G$ are obtained through \eqref{H2sol}. To do this, we first note that \eqref{altdefXi} implies that $\ga_\Xi=T_G^*(T_GT_G^*)^{-1}E_m$.
Now let $X\in H^2_{p\ts m}$ be a solution to \eqref{corona}. Then $\ga_{X}$ is bounded and \eqref{corona} translates to $T_G \ga_{X}=E_m$. We thus obtain that
\[
T_G^*(T_GT_G^*)^{-1}T_G \ga_{X}=T_G^*(T_GT_G^*)^{-1}E_m=\ga_\Xi.
\]
Note that $T_G^*(T_GT_G^*)^{-1}T_G=I-P_{\kr T_G}=I-T_\tht T_\tht^*$. Hence
\[
\ga_{X}=T_G^*(T_GT_G^*)^{-1}T_G\ga_{X} + T_\tht T_\tht^* \ga_{X}
=\ga_\Xi +T_\tht \ga_V,
\]
where $V\in H^2_{(p-m)\ts m}$ is determined by $\ga_V=T_\tht^* \ga_{X}$. The above identity implies $X$ is given by \eqref{H2sol} with $V\in H^2_{(p-m)\ts m}$ such that $\ga_V=T_\tht^* \ga_{X}$.
It remains to derive the identity \eqref{H2LeastSquare}. But this can be done by using the same argumentation as in the proof of Theorem \ref{thmmain1} (see \eqref{prH2idW}); we omit the details.
\end{proof}
Let $G\in H^\iy_{m\ts p}$ be such that $T_GT_G^*$ is strictly positive. Then $Y\in H^2_{p\ts p}$, by Proposition \ref{P:YY-1H2}. Now assume $Y\in H^\iy_{p\ts p}$. In that case all solutions to the $H^\iy$-corona problem associated with $G$ are given by formula \eqref{allsolW}. More precisely we have the following proposition.
\begin{prop}\label{propHinf}
Let $G\in H^\iy_{m\ts p}$ be such that $T_GT_G^*$ is strictly positive, and assume that the function $Y$ defined by \eqref{defY} belongs to $Y\in H^\iy_{p\ts p}$. Then $Y$ is invertible outer, and all solutions to the $H^\iy$-corona problem are given by \eqref{allsolW} where the free parameter is any $V\in H^\iy_{(p-m)\ts m}$.
\end{prop}
\begin{proof}[\bf Proof]
Assume the function $Y$ defined by \eqref{defY} belongs to $Y\in H^\iy_{p\ts p}$. Then $\Xi$ defined in \eqref{defXiTheta} is in $H^\infty_{p\times p-m}$, and hence $\Xi$ is a solution to the $H^\iy$-corona problem associated with $G$. Since the inner function $\tht$ is in $H^\infty_{p\times p-m}$, we obtain that $X$ defined by \eqref{allsolW} is in $H^\iy_{p\ts m}$ whenever the parameter $V$ is in $H^\iy_{(p-m)\ts m}$. Hence the map $V\mapsto X$ in \eqref{allsolW} produces solutions to the $H^\iy$-corona problem when restricted to parameters $V\in H^\iy_{(p-m)\ts m}$.
Next we show that all solutions to the $H^\iy$-corona problem associated with $G$ are obtained by \eqref{H2sol} when the parameters $V$ are restricted to $H^\iy_{(p-m)\ts m}$. Assume $X\in H^\iy_{p\ts m}$ satisfies \eqref{corona}. Then $X$ is also a $H^2$-solution of \eqref{corona}, and hence $X$ is given by \eqref{H2sol} for some $V\in H^2_{(p-m)\ts m}$. It remains to show that $V\in H^\iy_{(p-m)\ts m}$. The latter follows by considering the values of $V$ in $\BT$, and noting that for almost every $\z\in\BT$ we have
\begin{align*}
\|V(\z)\|=\|\tht(\z)V(\z)\|&=\|X(\z)-\Xi(\z)\|\leq \\
& \leq\|X(\z)\|+\|\Xi(\z)\|\leq \|X\|_\iy+\|\Xi\|_\iy.
\end{align*}
Hence $\|V\|_\iy\leq \|X\|_\iy+\|\Xi\|_\iy<\infty$, and thus $V\in H^\iy_{(p-m)\ts m}$.
We conclude with the proof that $Y\in H^\iy_{p\ts p}$ implies that the function $Y(\cdot)^{-1}$ also belongs to $H^\iy_{p\ts p}$, i.e., that $Y$ is invertible outer. To see that this is the case, recall from Section \ref{secWiener}, that the function $H$ defined by \eqref{defH}, on the circle is given by
\[
H(z)=\tht(z)^*(I-\Xi(z)G(z))\quad (\mbox{a.e. }z\in\BT).
\]
(Note that this observation does not require $G\in\sW_{m\ts p}^+$.) Since $\tht$, $\Xi$ and $G$ are all $H^\iy$-functions, it follows that $H$ is essentially bounded on $\BT$, and thus $H\in H^\iy_{(p-m) \ts p}$. This implies that the function
\[
z\mapsto \mat{c}{G(z)\\ H(z)}=\mat{c}{G_0\\ H_0}Y(z)^{-1}
\]
is in $H^{\iy}_{p\ts p}$. By the invertibility of $\sbm{G_0\\ H_0}$, it follows that $Y^{-1}$ is in $H^\iy_{p\ts p}$, as claimed.
\end{proof}
Note that the description of the solutions to the $H^\iy$-corona problem associated with $G$ obtained in this way is much simpler than the one obtained in \cite[Remark 4.1]{FtHK-8}. However, while the description \eqref{H2sol} has a favorable behavior with respect to the $H^2$-norm (see \eqref{H2LeastSquare}), there is no clear connection between the supremum norms of the parameter $V$ and the solution $X$ related through \eqref{H2sol}, making it a less suitable way to describe solutions with an additional bound on the supremum norm.
Furthermore, at this stage it is unknown whether the function $Y$ in \eqref{defY} belongs to $H^\iy_{p\ts p}$, or not. Can it happen that $Y$ does not belong to $H^\iy_{p\ts p}$, and if so, under what conditions on $G$ does $Y$ belong to $H^\iy_{p\ts p}$? Theorem \ref{thmmain1} yields that $Y\in H^\iy_{p\ts p}$ whenever $G\in \sW_+^{m\ts p}$.
\section{Concluding remarks}
\setcounter{equation}{0}
\begin{remark}\label{R:Gconst}
Let us assume that the $m\ts p$ matrix function $G$ is a constant function, that is, $G(z)=G_0$ for all $z\in \BD$. In that case the Bezout-corona equation \eqref{corona} reduces to
\begin{equation}\label{constG1}
G_0X(z)=I_m.
\end{equation}
This equation has a solution if and only if the $m\ts p$ matrix $G_0$ is right invertible, and in that case a straightforward application of Theorem \ref{thmmain1} shows that all Wiener class solutions of equation \eqref{constG1}
are given by
\begin{equation}\label{solconstG1}
X(z)=G_0^*(G_0 G_0^*)^{-1}+\t_0 V(z), \qquad V\in \sW_+^{(p-m)\ts m}.
\end{equation}
Here $\t_0$ is an isometry mapping $\BC^{p-m}$ onto $\kr G_0$. This result can also be derived directly by elementary linear algebra, using that $G_0^*(G_0 G_0^*)^{-1}$ is the Moore-Penrose right inverse of $G_0$. Note the definition of $\t_0$ implies that $\t_0 \t_0^*$ is the orthogonal projection of $\BC^p$ onto $\kr G_0$, and hence (cf., \eqref{deftht0}) we have
\[
\t_0 \t_0^*=I_p-G_0^*(G_0 G_0^*)^{-1}G_0 \ands \kr \t_0 =\{0\}.
\]
Finally, in this particular case the function defined by \eqref{defY} is just identically equal to the $p\ts p$ identity matrix.
\end{remark}
\begin{remark}\label{R:allsol2} Let $G\in \sW_+^{m\ts p}$, and assume that $T_GT_G^*$ is strictly positive. Let $Y\in \sW_+^{p\ts p}$ be given by \eqref{defY}. Then $\det Y(z)\not =0$ and $G(z)=G_0 Y(z)^{-1}$ for each $|z|\leq 1$. Hence equation \eqref{corona} can be rewritten as
\[
G_0\Big(Y(z)^{-1}X(z)\Big)=I_m.
\]
But then we can apply the result of the previous remark to show that the set of all Wiener solutions to the Wiener-Bezout problem defined by $G$ is given by
\[
X(z)=Y(z)\Big(G_0^*(G_0 G_0^*)^{-1}+\t_0 V(z)\Big), \qquad V\in \sW_+^{(p-m)\ts m}.
\]
The above representation of the set of all Wiener solutions differs from and is less informative than the one given by \eqref{allsolW}. For instance, in general, the function $Y(\cdot) G_0^*(G_0 G_0^*)^{-1}$ is not the least {squares solution.}
\end{remark}
\begin{remark}\label{R:Yinv2a} If $G$ is a polynomial, then the function $Y(\cdot)^{-1}$ is also a polynomial and its degree is less than or equal to the degree of $G$. This fact is a corollary of formula \eqref{invY} in Theorem \ref{thmmain1}. However, in general, the assumption $G$ is a polynomial does not imply that $Y$ is a polynomial. To see this we take $G(z)=\begin{bmatrix} 1+z & -z \end{bmatrix}$ as in Example 1 in \cite[Section 5]{FKR2a} and show that for this specific choice of $G$ the function $Y$ is given by
\begin{align}\label{Yex}
Y(z)={\frac{1}{1+zq}\mat{cc}{1-(1-q)z & z \\ -(1-q)z & 1+z}}.
\end{align}
Here $q=\half(3-\sqrt{5})\in(0,1/2)$, which satisfies
\begin{align}\label{qids}
q^2-3q+1=0,\quad \sqrt{q}=1-q \ands \frac{q(1-q)}{1-2q}=1.
\end{align}
We compute \eqref{Yex} via the formula for the Taylor coefficients of $Y$ given in \eqref{defYj}. For this purpose we rewrite the right hand side in the second identity of \eqref{defYj} as $-T_G^*(T_GT_G^*)^{-1}H_G E_2$, and we compute this operator following the approach of \cite{FKR2a}. Recall (see \cite[Eq. (2.4)]{FKR2a} or \eqref{TRinv1}) that
\[
(T_GT_G^*)^{-1}= T_R^{-1}+T_R^{-1}H_G(I-H_G^*T_R^{-1}H_G)^{-1}H_G^*T_R^{-1},
\]
where $R=GG^*$. In the present example, where $G(z)=\begin{bmatrix} 1+z & -z \end{bmatrix}$, we have $R(z)=G(z)G(1/\bar{z})^*=3+z+z^{-1}$, and
hence $R(z)$ is strictly positive on $\BT$. If follows that $R$ admits an outer spectral factorization, namely
\[
R(z)=\phi(1/\bar{z})^*\phi(z), \ \mbox{with $\phi(z)=q^{-\half}(1+zq)$ and $q=\half(3-\sqrt{5})$}.
\]
Furthermore, $R(z)^{-1}=\psi(z)\psi(1/\bar{z})^*$ with
\[
\psi(z)=\sqrt{q}(1+zq)^{-1}=\sum_{\nu=0}^\infty \sqrt{q}(-q)^\nu z^\nu, \quad (z\in\BD).
\]
It follows that $(T_R)^{-1}=T_\psi T_\psi^*$, and
\begin{align*}
T_\psi=\sqrt{q}\mat{cccc}{v &Sv&S^2v&\cdots}\ \mbox{with}\ v=\mat{ccccc}{1&-q&(-q)^2&(-q)^3&\cdots}^*.
\end{align*}
Here $S$ denotes the forward shift operator on $\ell^2_+:=\ell^2_+(\BC)$. Since $G(z)=\begin{bmatrix} 1+z & -z \end{bmatrix}$, we have
\begin{align*}
T_G=\mat{ccccccc}{1&0&0&0&0&0&\cdots\\ 1&-1&1&0&0&0&\cdots\\ 0&0&1&-1&1&0&\cdots\\ \vdots&\vdots&\vdots&\vdots&\vdots&\vdots&},\quad
H_G=\mat{ccccc}{1&-1&0&0&\cdots\\ 0&0&0&0&\cdots\\ 0&0&0&0&\cdots\\ \vdots&\vdots&\vdots&\vdots&}.
\end{align*}
We then obtain
\[
T_R^{-1}H_G=T_\psi T_\psi^* H_G=\sqrt{q} T_\psi H_G= q\mat{cccccc}{v&-v&0&0&0&\cdots}.
\]
Identifying $\ell^2_+$ with $\BC^2\oplus\ell^2_+$, we get
\small{
\[
(I-H_G^* T_R^{-1} H_G)^{-1}
=\mat{ccc}{1-q & q &0\\ q & 1-q &0 \\ 0& 0& I_{\ell^2_+}}^{-1}
=\mat{ccc}{1/q & -1/\sqrt{q} &0\\ -1/\sqrt{q} & 1/q &0 \\ 0& 0& I_{\ell^2_+}}.
\]
}
Putting the above computations together yields
\begin{align*}
(T_GT_G^*)^{-1}
&=T_R^{-1}+q^2\mat{cc}{v & -v}\mat{cc}{1/q & -1/\sqrt{q}\\ -1/\sqrt{q} & 1/q} \mat{c}{v^*\\ -v^*}\\
&=T_{R}^{-1}+v \mat{cc}{1 &-1}\mat{cc}{q & -q\sqrt{q}\\ -q\sqrt{q} & q}\mat{c}{1\\-1}v^*\\
&=T_{R}^{-1}+v \mat{cc}{1 &-1}\mat{cc}{q & -(1-2q)\\ -(1-2q) & q}\mat{c}{1\\-1}v^*\\
&=T_{R}^{-1}+2(1-q)vv^* =T_{R}^{-1}+2\sqrt{q}\,vv^*.
\end{align*}
In the third step we used $q\sqrt{q}=q(1-q)=1-2q$ which follows from the second and third identity in \eqref{qids}. Combining the formula for $(T_GT_G^*)^{-1}$ with the one for $T_R^{-1}H_G$ yields
\begin{align*}
(T_GT_G^*)^{-1}H_G E_2
&=T_{R}^{-1}H_G E_2+2\sqrt{q}\,vv^*H_G E_2\\
&=q\mat{cc}{v&-v}+2\sqrt{q}\mat{cc}{v& -v}\\
&=q({1+2/\sqrt{q}})\mat{cc}{v& -v}=q(1-2q)^{-1}\mat{cc}{v& -v}.
\end{align*}
To see that the latter identity holds, note that $1-3q+q^2=0$ implies $3-q=1/q$, so that together with $q\sqrt{q}=1-2q$ we obtain
\[
1+2/\sqrt{q}=\frac{\sqrt{q}+2}{\sqrt{q}}=\frac{(1-q)+2}{\sqrt{q}}=\frac{3-q}{\sqrt{q}}=\frac{1}{q\sqrt{q}}=(1-2q)^{-1}.
\]
Next note that $T_G^*v=vG(-q)^*.$ By \eqref{defYj} we then obtain that for $\nu=1,2,\ldots$ that
\begin{equation*}
Y_\nu=\frac{-q}{1-2q}(-q)^{\nu-1} N=\frac{(-q)^\nu}{1-2q}N,
\end{equation*}
where
\[
N=\mat{cc}{G(-q)^* & -G(-q)^*}=\mat{cc}{\sqrt{q}&-\sqrt{q}\\ q & -q}
=\mat{cc}{1-q&-(1-q)\\ q & -q}.
\]
Hence
\begin{align*}
&Y(z)
=I_2+\sum_{\nu=1}^\infty \frac{(-q)^\nu}{1-2q}N z^\nu=I_2+\frac{-qz}{(1-2q)(1+zq)}N\\
&\ \ =\frac{1}{(1-2q)(1+zq)}\mat{cc}{(1-2q)(1+zq)- q(1-q)z & q(1-q)z \\ -q^2z & (1-2q)(1+zq)+zq^2}\\
&\ \ =\frac{1}{(1-2q)(1+zq)}\mat{cc}{(1-2q)-q^2z & (1-2q)z \\ -q^2z & (1-2q)(1+z)}\\
&\ \ = {\frac{1}{1+zq}\mat{cc}{1-(1-q)z & z \\ -(1-q)z & 1+z}}.
\end{align*}
{Here we used $(1-2q)(1+zq)=1-2q+qz-2q^2z$ and $q(1-q)=1-2q$ in the last but one identity, and $q^2/(1-2q)=q(1-q)^2/(1-2q)=1-q$ (which follows from the last two identities in \eqref{qids}) in the last identity.} Hence we obtain $Y$ is given by \eqref{Yex} as claimed.
Using similar calculations as in the previous remark one can prove that for $G(z)=\begin{bmatrix} 1+z & -z \end{bmatrix}$ the matrices $\Xi_0$ and $\tht_0$ are given by
\[
\Xi_0= \frac{q}{1-2q}\begin{bmatrix} 1-q \\ q \end{bmatrix} \ands \tht_0 = \frac{1}{\sqrt{q}}\begin{bmatrix}0\\ 1\end{bmatrix},
\]
where $q=\half(3-\sqrt{5})$. Note, however, that these formulas for $\Xi_0$ and $\tht_0$ can be derived from earlier results in \cite{FKR2a} and \cite{FKR2b}. Indeed, $\Xi_0$ is obtained by taking $z=0$ in $X(z)$ on \cite[Page 414]{FKR2a}, and the formula for $\tht_0$ is obtained by taking $z=0$ in the formula for $\tht(z)$ appearing in the final paragraph of~\cite{FKR2b}.
\end{remark}
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 7,263
|
PT. Angkasa Pura () ist ein staatliches Unternehmen des indonesischen Verkehrsministeriums, das für die Verwaltung der Flughäfen und der Flugsicherung in Indonesien verantwortlich ist. PT. Angkasa Pura besteht aus zwei Unternehmensteilen:
PT. Angkasa Pura I mit der Flughafenkapazität für 30.700.440 Passagiere und dem Hauptsitz in Jakarta
PT. Angkasa Pura II mit der Flughafenkapazität für 30.815.000 Passagiere und dem Hauptsitz am internationalen Flughafen Soekarno-Hatta in Tangerang
Beide Flughafenbetreiber leiden derzeit unter massiven Unterkapazitäten: Während das Passagieraufkommen bei Angkasa Pusa I die Zahl 49.237.437 erreichte, war es bei Angkasa Pura II schon bei 62.215.834 Passagieren.
Geschichte
PT. Angkasa Pura I wurde im Jahr 1964 unter dem Namen Perusahaan Negara (PN) Angkasa Pura "Kemayoran" gegründet. PT. Angkasa Pura II wurde erst Zwanzig Jahre später, am 13. August 1984, gegründet.
Einzelnachweise
Flughafenbetreiber
Gegründet 1964
Unternehmen (Jakarta)
Luftverkehr (Indonesien)
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 4,294
|
The following is a partial list of goalscorers in All-Ireland Senior Hurling Championship finals. See List of FIFA World Cup final goalscorers a similar list but in soccer not hurling.
Scoring in Gaelic games: Most scores are points but there are goals too.
For a team to score more than three goals in a final is a rarity, occurring in 2000 and 2010. When Lar Corbett (for Tipp, 2010) scored a hat-trick, only Eddie O'Brien (for Cork, 1970) had done it in a final. But the 2013 replay had Clare scoring five goals, including a Shane O'Donnell hat-trick.
The last final to finish goalless was in 2020.
Finals goalscorers
Pre-1921
1921 to 1996: Introduction of the Liam MacCarthy Cup
1997 to present
Goalless finals
1999
2004
2020
Goalscoring goalkeepers
John Commins (1) 1986
Anthony Nash (2) 2013 (draw), 2013 (replay)
Men with multiple goals
They include:
References
External links
Finals goalscorers
Hurling-related lists
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 9,471
|
The forthcoming contest, FK Khujand vs FC Dordoi Bishkek will be streamed live for . You can watch the tie on smartphones and tablets.
* 18+ Only. T&C Applies - Geo restrictions apply for FK Khujand vs FC Dordoi Bishkek. Funded account required or to have placed a bet in the last 24 hours to qualify. Gamble Responsibly - BeGambleAware.org.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 1,807
|
Q: Docker local file download I'm trying to dockerize my SDK as
docker run --rm -it -v /home/ubuntu/work/yoctosdk/:/workdir crops/extsdk-container --url file:///home/ubuntu/work/yocto/poky/build/tmp/deploy/sdk/poky-glibc-x86_64-core-image-minimal-i586-toolchain-2.4.1.sh
and unfortunately I am getting
Attempting to download file:///home/ubuntu/work/yocto/poky/build/tmp/deploy/sdk/poky-glibc-x86_64-core-image-minimal-i586-toolchain-2.4.1.sh
curl: (37) Couldn't open file /home/ubuntu/work/yocto/poky/build/tmp/deploy/sdk/poky-glibc-x86_64-core-image-minimal-i586-toolchain-2.4.1.sh
Unable to download "file:///home/ubuntu/work/yocto/poky/build/tmp/deploy/sdk/poky-glibc-x86_64-core-image-minimal-i586-toolchain-2.4.1.sh".
I am trying to work around this to download and run local file within docker. What would be correct download of the local file? I am following this.
A: It is not possible by default to access files from the host machine. You need to mount folders that you want to access to the Docker container.
To make the file /home/ubuntu/work/yocto/poky/build/tmp/deploy/sdk/poky-glibc-x86_64-core-image-minimal-i586-toolchain-2.4.1.sh accessible, mount its parent directory using:
-v /home/ubuntu/work/yocto/poky/build/tmp/deploy/sdk:/home/ubuntu/work/yocto/sdk-installer
And then provide as url the path inside the docker container:
--url file:///home/ubuntu/work/yocto/sdk-installer/poky-glibc-x86_64-core-image-minimal-i586-toolchain-2.4.1.sh
Full command:
docker run --rm -it -v /home/ubuntu/work/yoctosdk/:/workdir crops/extsdk-container -v /home/ubuntu/work/yocto/poky/build/tmp/deploy/sdk:/home/ubuntu/work/yocto/sdk-installer --url file:///home/ubuntu/work/yocto/sdk-installer/poky-glibc-x86_64-core-image-minimal-i586-toolchain-2.4.1.sh
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 1,432
|
"use strict";
var __decorate = (this && this.__decorate) || function (decorators, target, key, desc) {
var c = arguments.length, r = c < 3 ? target : desc === null ? desc = Object.getOwnPropertyDescriptor(target, key) : desc, d;
if (typeof Reflect === "object" && typeof Reflect.decorate === "function") r = Reflect.decorate(decorators, target, key, desc);
else for (var i = decorators.length - 1; i >= 0; i--) if (d = decorators[i]) r = (c < 3 ? d(r) : c > 3 ? d(target, key, r) : d(target, key)) || r;
return c > 3 && r && Object.defineProperty(target, key, r), r;
};
var __metadata = (this && this.__metadata) || function (k, v) {
if (typeof Reflect === "object" && typeof Reflect.metadata === "function") return Reflect.metadata(k, v);
};
var core_1 = require('@angular/core');
var common_1 = require('@angular/common');
var router_deprecated_1 = require('@angular/router-deprecated');
var NavbarComponent = (function () {
function NavbarComponent() {
}
__decorate([
core_1.Input(),
__metadata('design:type', String)
], NavbarComponent.prototype, "brand", void 0);
__decorate([
core_1.Input(),
__metadata('design:type', Array)
], NavbarComponent.prototype, "routes", void 0);
NavbarComponent = __decorate([
core_1.Component({
selector: 'as-navbar',
templateUrl: 'app/navbar/navbar.html',
changeDetection: core_1.ChangeDetectionStrategy.OnPush,
directives: [router_deprecated_1.RouterLink, common_1.CORE_DIRECTIVES]
}),
__metadata('design:paramtypes', [])
], NavbarComponent);
return NavbarComponent;
}());
exports.NavbarComponent = NavbarComponent;
//# sourceMappingURL=navbar.component.js.map
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 2,273
|
Q: Unable to add comments to a post using a ModelForm in Django views.py
def postdetail(request,pk): # Single Post view.
post = Post.objects.get(id=pk)
comment = post.comments.all()
comment_count = comment.count()
if request.user.is_authenticated:
if request.method == 'POST':
form = CommentForm(data=request.POST)
content = request.POST['cMessage']
if form.is_valid():
print("Yes valid")
form.instance.body = content
new_comment = form.save(commit=False)
print(new_comment)
new_comment.post = post
new_comment.user = request.user
new_comment.save()
return redirect('blog-home')
else:
form = CommentForm()
context = {
'comment_form': CommentForm,
'post' : post,
'comments': comment,
'count': comment_count,
}
return render(request,'post/postdetail.html', context=context)
models.py
class Comment(models.Model):
post = models.ForeignKey(Post, on_delete=models.CASCADE, related_name='comments')
user = models.ForeignKey(User,on_delete=models.CASCADE, related_name='comments')
body = models.TextField()
created = models.DateTimeField(auto_now_add=True)
updated = models.DateTimeField(auto_now=True)
# active = models.BooleanField(default=True)
class Meta:
ordering = ('created',)
def __str__(self):
return f'Comment by {self.user} on {self.post}'
forms.py
class CommentForm(forms.ModelForm):
class Meta:
model = Comment
fields = ['body']
template
{% if request.user.is_authenticated %}
<!-- respond -->
<div class="respond">
<h3>Leave a Comment</h3>
<!-- form -->
<form name="contactForm" id="contactForm" method="post" action="">
{% csrf_token %}
<fieldset>
<div class="message group">
<label for="cMessage">Message <span class="required">*</span></label>
<textarea name="cMessage" id="cMessage" rows="10" cols="50" ></textarea>
</div>
<button type="submit" class="submit">Submit</button>
</fieldset>
</form> <!-- Form End -->
</div>
{% endif %}
There is no error being displayed neither If I am adding a comment using the shell/through admin panel but if I am trying to add the comment dynamically through the form then the comment is not getting saved.
I have added only the form in the template.
A: You have defined field body in your CommentForm. It's required in your form, because you didn't include blank=True argument in your model for this field. This means that when you POST request and check if form is valid with form.is_valid(), the form expects an element with a name body in the request. If it's not there, it will not validate and content won't be saved.
Make the following changes:
*
*Change your view to
...
if request.method == 'POST':
form = CommentForm(data=request.POST)
if form.is_valid():
new_comment = form.save(commit=False)
new_comment.post = post
new_comment.user = request.user
new_comment.save()
return redirect('blog-home')
else:
print(form.errors) # or log it to a file, if you have logging set up
form = CommentForm()
...
*Change your HTML to this:
...
<form name="contactForm" id="contactForm" method="post" action="">
{% csrf_token %}
<fieldset>
<div class="message group">
<label for="body">Message <span class="required">*</span></label>
<textarea name="body" id="cMessage" rows="10" cols="50" ></textarea>
{{ comment_form.body.errors }}
</div>
<button type="submit" class="submit">Submit</button>
</fieldset>
</form>
...
A: In views.py
def postdetail(request):
print(Comment.objects.all())
if request.method == 'POST':
form = CommentForm(data=request.POST)
content = request.POST['body']
if form.is_valid():
print("Yes valid")
new_comment = form.save(commit=False)
print(new_comment)
new_comment.post = post
new_comment.user = request.user
new_comment.save()
return redirect('blog-home')
else:
form = CommentForm()
return render(request,'temp/postdetail.html', context=context)
In html file
{% if request.user.is_authenticated %}
<div class="respond">
<h3>Leave a Comment</h3>
<form name="contactForm" id="contactForm" method="post" action="">
{% csrf_token %}
<textarea name="body"cols="30" rows="10"></textarea>
<button type="submit" class="submit">Submit</button>
</form>
</div>
{% endif %}
This worked for me.
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 2,913
|
\section{Introduction}
Let $X$ be a connected scheme. One of the basic arithmetic invariants that one
can extract from $X$ is the \emph{\'etale fundamental group} $\pi_1(X,
\overline{x})$ relative to a ``basepoint'' $\overline{x} \to X$ (where
$\overline{x}$ is the spectrum of a separably closed field).
The fundamental group was defined by Grothendieck \cite{sga1} in terms of the category of finite, \'etale
covers of $X$. It provides an analog of the usual
fundamental group of a topological space (or rather, its profinite
completion), and plays an important role in algebraic geometry and number
theory, as a precursor to the theory of \'etale cohomology.
From a categorical point of view, it unifies the classical Galois theory of
fields and covering space theory via a single framework.
In this paper, we will define an analog of the \'etale fundamental group, and
construct a form of the Galois correspondence, in
stable homotopy theory.
For example, while the classical theory of \cite{sga1} enables one to
define the fundamental (or Galois) group of a commutative ring, we will define
the fundamental group of the homotopy-theoretic analog: an $\e{\infty}$-ring
spectrum.
The idea of a type of Galois theory applicable to structured ring spectra
begins with Rognes's work in \cite{rognes}, where, for a finite group $G$,
the notion of a \emph{$G$-Galois extension} of $\e{\infty}$-ring spectra $A \to
B$ was introduced (and more generally, $E$-local $G$-Galois extensions for a
spectrum $E$).
Rognes's definition is an analog of the notion of a finite $G$-torsor of commutative rings
in the setting of ``brave new'' algebra, and it includes many highly
non-algebraic
examples in stable homotopy theory. For instance, the ``complexification'' map
$KO \to KU$ from real to complex
$K$-theory is a fundamental example of a $\mathbb{Z}/2$-Galois extension.
Rognes has also explored the more
general theory of \emph{Hopf-Galois} extensions, intended as a topological
version of the idea of a torsor over a group \emph{scheme} in algebraic
geometry, as has Hess in \cite{hess}.
More recently, the PhD thesis of Pauwels \cite{pauwels} has studied Galois theory in
tensor-triangulated categories.
In this paper, we
will take the setup of an \emph{axiomatic stable homotopy theory.}
For us, this will mean:
\renewcommand{\1}{\mathbf{1}}
\begin{definition}
An \textbf{axiomatic stable homotopy theory} is a presentable, symmetric monoidal stable
$\infty$-category $(\mathcal{C}, \otimes, \1)$ where the tensor product
commutes with all colimits.
\end{definition}
An axiomatic stable homotopy theory defines, at the level of homotopy
categories, a \emph{tensor-triangulated category}. Such axiomatic stable homotopy theories arise not only from stable
homotopy theory itself, but also from representation theory and algebra, and we
will discuss many examples below.
We will associate, to every
axiomatic stable homotopy theory $\mathcal{C}$, a profinite group (or, in general,
groupoid) which we call the
\emph{Galois group} $\pi_1( \mathcal{C})$. In order to do this, we will give a definition of a
\emph{finite cover} generalizing the notion of a Galois extension,
and, using heavily ideas from descent theory, show that these can naturally be arranged into a Galois category in the
sense of Grothendieck.
We will actually define two flavors of the fundamental group, one of which
depends only on the structure of the dualizable objects in $\mathcal{C}$ and is
appropriate to the study of ``small'' symmetric monoidal $\infty$-categories.
Our thesis is that the Galois group of a stable homotopy theory is a natural
invariant that one can attach to it; some of the (better studied) others include the
algebraic $K$-theory (of the compact objects, say), the lattice of thick
subcategories, and the Picard group. We will discuss several
examples. The classical fundamental group in algebraic geometry can be
recovered as the Galois group of the derived category of quasi-coherent
sheaves. Rognes's Galois theory (or rather, \emph{faithful} Galois theory) is
the case of $\mathcal{C} = \mod(R)$
for $R$ an $\e{\infty}$-algebra.
Given a stable homotopy theory $(\mathcal{C}, \otimes, \mathbf{1})$, the
collection of all homotopy classes of maps $\mathbf{1} \to \mathbf{1}$ is
naturally a commutative ring $R_{\mathcal{C}}$.
In general, there is always a surjection of profinite groups
\begin{equation} \label{keymap} \pi_1 \mathcal{C}
\twoheadrightarrow \pi_1^{\mathrm{et}}
\mathrm{Spec} R_{\mathcal{C}}. \end{equation}
The \'etale fundamental group of $\mathrm{Spec} R_{\mathcal{C}}$ represents the ``algebraic''
part of the Galois theory of $\mathcal{C}$.
For example, if $\mathcal{C} = \mathrm{Mod}(R)$ for $R$ an $\e{\infty}$-algebra, then
the ``algebraic'' part of the Galois theory of $\mathcal{C}$ corresponds to
those $\e{\infty}$-algebras under $R$ which are finite \'etale at the level of
homotopy groups. It is an insight of Rognes that, in general, the Galois group
contains a topological component as well: the map
\eqref{keymap} is generally not an isomorphism. The remaining Galois extensions
(which behave much differently on the level of homotopy groups) can be quite
useful computationally.
In the rest of the paper, we will describe several computations of these Galois
groups in various settings.
Our basic tool is the following result, which is a refinement of (a natural
generalization of) the main result of \cite{BR2}.
\begin{theorem} If $R$ is an even periodic $\e{\infty}$-ring with $\pi_0 R$
regular noetherian, then the Galois group of $R$ is that of the
discrete ring
$\pi_0 R$: that is, \eqref{keymap} is an isomorphism.
\end{theorem}
Using various techniques of descent theory, and a version of van Kampen's
theorem, we are able to compute Galois groups in
several other examples of stable homotopy theories ``built'' from $\mod(R)$
where $R$ is an even periodic $\e{\infty}$-ring; these include in particular many arising from
both chromatic stable homotopy theory and modular representation theory.
In particular, we prove the following three theorems.
\begin{theorem}
The Galois group of the $\infty$-category $L_{K(n)} \sp$ of $K(n)$-local
spectra is the extended Morava stabilizer group.
\end{theorem}
\begin{theorem}
The Galois group of the $\e{\infty}$-algebra $\mathrm{TMF}$ of (periodic) topological
modular forms is trivial.
\end{theorem}
\begin{theorem}
Given a finite group $G$ and a separably closed field $k$ of
characteristic $p$, the Galois group of the stable module $\infty$-category
of $k[G]$ is the profinite completion of the nerve of the category
of $G$-sets of the form $\left\{G/A\right\}$ where $ A \subset G$
is a nontrivial elementary abelian $p$-subgroup. \end{theorem}
These results suggest a number of other settings in which the computation of
Galois groups may be feasible, for example,
in stable module $\infty$-categories for finite group \emph{schemes}. We hope that these
results and ideas will, in addition, shed light on some of the other invariants
of $\e{\infty}$-ring spectra and stable
homotopy theories.
\subsection*{Acknowledgments}
I would like to thank heartily Mike Hopkins for his advice and
support over the past few years, with this project and others. In addition, I
would like to thank Bhargav Bhatt, Brian Conrad, Gijs Heuts,
Tyler Lawson, Lennart Meier, Niko Naumann, Justin Noel,
Oriol Ravent{\'o}s,
Vesna Stojanoska, and in particular Jacob Lurie, for numerous helpful discussions.
Finally, I would like to thank the referee for several corrections.
The author was supported by the NSF Graduate Fellowship under grant DGE-1144152.
\part{Descent theory}
\section{Axiomatic stable homotopy theory}
As mentioned earlier, the goal of this paper is to extract a Galois group(oid) from a \emph{stable
homotopy theory.} Once again, we restate the definition.
\begin{definition}\label{shot}
A \textbf{stable homotopy theory} is a presentable, symmetric monoidal stable $\infty$-category
$(\mathcal{C}, \otimes, \mathbf{1})$ where the tensor product commutes with all
colimits.
\end{definition}
In this section, intended mostly as background, we will describe several general features of the setting
of stable homotopy
theories. We will discuss a number of examples, and then
construct a basic class of commmutative algebra objects in any such $\mathcal{C}$ (the
so-called ``\'etale algebras'') whose associated corepresentable functors can
be described very easily.
The homotopy categories of stable homotopy theories, which acquire both a
tensor structure and a compatible triangulated structure, have been described at
length in the memoir \cite{axiomatic}. In addition, their invariants have been
studied in detail in
the program of tensor triangular geometry of Balmer (cf. \cite{Balmer} for a
survey).
\subsection{Stable $\infty$-categories}
Let $\mathcal{C}$ be a stable $\infty$-category in the sense of
\cite[Ch. 1]{higheralg}. Recall that stability is a \emph{condition} on an $\infty$-category,
rather than extra data, in the same manner that, in ordinary category theory, being an
abelian category is a property.
The homotopy category of a stable $\infty$-category is canonically
\emph{triangulated,} so that stable $\infty$-categories may be viewed as
enhancements of triangulated categories; however, as opposed to traditional
DG-enhancements, stable $\infty$-categories can be used to model phenomena in
stable homotopy theory (such as the $\infty$-category of spectra, or the
$\infty$-category of modules over a structured ring spectrum).
Here we will describe some general features of stable $\infty$-categories, and
in particular the constructions one can perform with them.
Most of this is folklore (in the setting of triangulated or DG-categories) or
in \cite{higheralg}.
\begin{definition}
Let $\mathrm{Cat}_\infty$ be the $\infty$-category of (small) $\infty$-categories. Given
$\infty$-categories $\mathcal{C}, \mathcal{D}$, the mapping space
$\hom_{\mathrm{Cat}_\infty}(\mathcal{C}, \mathcal{D})$ is the maximal $\infty$-groupoid
contained in the $\infty$-category $\mathrm{Fun}(\mathcal{C},\mathcal{D})$ of
functors $\mathcal{C} \to \mathcal{D}$.
\end{definition}
\newcommand{\mathrm{Cat}_\infty^{\mathrm{st}}}{\mathrm{Cat}_\infty^{\mathrm{st}}}
\begin{definition}
We define an $\infty$-category $\mathrm{Cat}_\infty^{\mathrm{st}}$ of (small) stable $\infty$-categories where:
\begin{enumerate}
\item The objects of $\mathrm{Cat}_\infty^{\mathrm{st}}$ are the stable $\infty$-categories which are
idempotent complete.\footnote{This can be removed, but will be assumed for
convenience.}
\item Given $\mathcal{C}, \mathcal{D} \in \mathrm{Cat}_\infty^{\mathrm{st}}$, the mapping space
$\hom_{\mathrm{Cat}_\infty^{\mathrm{st}}}(\mathcal{C}, \mathcal{D})$ is the union of connected components in
$\hom_{\mathrm{Cat}_\infty}(\mathcal{C}, \mathcal{D})$ spanned by those functors which
preserve finite limits (or, equivalently, colimits). Such functors are called \emph{exact.}
\end{enumerate}
\end{definition}
The $\infty$-category $\mathrm{Cat}_\infty^{\mathrm{st}}$ has all limits, and the forgetful functor
$\mathrm{Cat}_\infty^{\mathrm{st}} \to \mathrm{Cat}_\infty$ commutes with limits.
For example, given a diagram in $\mathrm{Cat}_\infty^{\mathrm{st}}$
\[ \xymatrix{
& \mathcal{C} \ar[d]^F \\
\mathcal{D} \ar[r]^G & \mathcal{E}
},\]
we can form a pullback $\mathcal{C} \times_{\mathcal{E}} \mathcal{D}$
consisting of triples $(X, Y, f)$ where $X \in \mathcal{C}, Y \in \mathcal{D}$,
and $f\colon F(X) \simeq G(Y)$ is an equivalence. This pullback is automatically
stable.
Although the construction is more complicated, $\mathrm{Cat}_\infty^{\mathrm{st}}$ is also cocomplete.
For example,
the colimit (in $\mathrm{Cat}_\infty$) of a \emph{filtered} diagram of stable
$\infty$-categories and exact functors is automatically stable, so that the
inclusion $\mathrm{Cat}_\infty^{\mathrm{st}} \subset \mathrm{Cat}_\infty$ preserves filtered colimits.
In general, one has:
\begin{proposition}
\label{scatispresentable}
$\mathrm{Cat}_\infty^{\mathrm{st}}$ is a presentable $\infty$-category.
\end{proposition}
\newcommand{\widehat{\mathrm{Cat}_\infty}}{\widehat{\mathrm{Cat}_\infty}}
\newcommand{\mathrm{Pr}^R}{\mathrm{Pr}^R}
To understand this, it is convenient to work with the (big) $\infty$-category
$\mathrm{Pr}^L$.
\begin{definition}[{\cite[5.5.3]{HTT}}] $\mathrm{Pr}^L$
is the $\infty$-category
of
presentable $\infty$-categories and colimit-preserving (or left adjoint)
functors.
\end{definition}
The $\infty$-category $\mathrm{Pr}^L$ is known to have all
colimits (cf. \cite[5.5.3]{HTT}). We briefly review this here.
Given a diagram $F\colon I \to \mathrm{Pr}^L$, we can form the dual
$I^{\mathrm{op}}$-indexed diagram in
the $\infty$-category $\mathrm{Pr}^R$ of presentable $\infty$-categories and
\emph{right} adjoints between them. Now we can form a \emph{limit} in $\mathrm{Pr}^R$ at
the level of underlying $\infty$-categories; by duality between $\mathrm{Pr}^L,
\mathrm{Pr}^R$ in the form $\mathrm{Pr}^L \simeq (\mathrm{Pr}^R)^{\mathrm{op}}$, this can be identified with the
colimit $\varinjlim_I F$ in $\mathrm{Pr}^L$.
In other words, for each map $f\colon i \to i'$ in
$I$, consider the induced adjunction of $\infty$-categories $L_f, R_f\colon F(i) \rightleftarrows F(i')$.
Then an object $x$ in $\varinjlim_I F$ is the data of:
\begin{enumerate}
\item For each $ i \in I$, an object $x_i \in F(i)$.
\item For each $f \colon i \to i'$, an isomorphism $x_i \simeq R_f(x_{i'})$.
\item Higher homotopies and coherences.
\end{enumerate}
For each $i$, we get a natural functor in $\mathrm{Pr}^L$, $F(i) \to \varinjlim_I F$.
We have a tautological description of the \emph{right adjoint}, which to an
object $x$ in $\varinjlim_I F$ as above returns $x_i \in F(i)$.
\begin{example}
Let $\mathcal{S}_\ast$ be the $\infty$-category of pointed spaces and pointed maps
between them. We have an endofunctor $\Sigma\colon \mathcal{S}_* \to \mathcal{S}_*$
given by suspension, whose right adjoint is the loop functor $\Omega\colon
\mathcal{S}_* \to \mathcal{S}_*$. The filtered colimit
in $\mathrm{Pr}^L$
of the diagram
\[ \mathcal{S}_* \stackrel{\Sigma}{\to} \mathcal{S}_* \stackrel{\Sigma}{\to}
\dots, \]
can be identified, by this description, as the $\infty$-category of
sequences of pointed spaces $(X_0, X_1, X_2, \dots, )$ together with
equivalences $X_n \simeq \Omega X_{n+1}$ for $n \geq 0$: in other words, one
recovers the $\infty$-category of spectra.
\end{example}
\begin{proposition} \label{procompact}
Suppose $F\colon I \to \mathrm{Pr}^L$ is a diagram where, for each $i \in I$, the
$\infty$-category $F(i)$ is compactly generated; and where, for each $i \to
i'$, the left adjoint $F(i) \to F(i')$ preserves compact objects.\footnote{This
is equivalent to the condition that the \emph{right adjoints} preserve filtered
colimits.} Then each $F(i) \to \varinjlim_I F$ preserves compact objects, and
$\varinjlim_I F$ is compactly generated.
\end{proposition}
\begin{proof}
It follows from the explicit description of $\varinjlim_I F$, in fact, that
the right adjoints to $F(i) \to \varinjlim_I F$ preserve filtered colimits;
this is dual to the statement that the left adjoints preserve compact objects.
Moreover, the images of each compact object in each $F(i)$ in $\varinjlim_I F$
can be taken as compact generators, since they are seen to detect equivalences.
\end{proof}
\newcommand{\mathrm{Pr}^{L, \omega}}{\mathrm{Pr}^{L, \omega}}
\begin{definition}
$\mathrm{Pr}^{L, \omega}$ is the $\infty$-category of compactly generated, presentable
$\infty$-categories and colimit-preserving functors which preserve compact
objects.
\end{definition}
It is fundamental that $\mathrm{Pr}^{L, \omega}$ is equivalent to the $\infty$-category of
idempotent complete, finitely cocomplete $\infty$-categories and finitely
cocontinuous functors, under the construction $\mathcal{C} \to
\mathrm{Ind}(\mathcal{C})$ starting from the latter and ending with the
former (and the dual construction that takes an object in $\mathrm{Pr}^{L, \omega}$ to its
subcategory of compact objects). \Cref{procompact} implies that colimits exist
in $\mathrm{Pr}^{L, \omega}$ and the inclusion $\mathrm{Pr}^{L, \omega} \to \mathrm{Pr}^L$ preserves them.
\begin{corollary} \label{stpr}
$\mathrm{Pr}^{L, \omega}$ is a presentable $\infty$-category.
\end{corollary}
\begin{proof}
It suffices to show that any idempotent complete, finitely cocomplete
$\infty$-category is a filtered colimit of such of bounded cardinality (when
modeled via quasi-categories, for instance). For simplicity, we will sketch the
argument for finitely cocomplete quasi-categories. The idempotent complete
case can be handled similarly by replacing filtered colimits with
$\aleph_1$-filtered colimits.
To see this, let $\mathcal{C}$ be such a quasi-category.
Consider any countable simplicial subset $\mathcal{D}$ of $\mathcal{C}$
which is a quasi-category.
We will show that $\mathcal{D}$ is contained in a bigger countable simplicial
subset $\overline{\mathcal{D}}$ of $\mathcal{C}$ which is a finitely cocomplete
quasi-category such that $\overline{\mathcal{D}} \to \mathcal{C}$ preserves
finite colimits.
This will show that $\mathcal{C}$ is the filtered union of such
subsets
$\overline{\mathcal{D}}$ (ordered by set-theoretic inclusion) and will thus complete the proof.
Thus, fix $\mathcal{D} \subset \mathcal{C}$ countable.
For each finite
simplicial set $K$, and each map $K \to \mathcal{D}$, by definition there is
an extension $K^{\rhd} \to \mathcal{C}$ which is a colimit diagram.
We can find a countable simplicial set $\mathcal{D}'$ such that $\mathcal{D}
\subset \mathcal{D}' \subset \mathcal{C}$ such that every diagram $K \to
\mathcal{D}$ extends over a diagram $K^{\rhd} \to \mathcal{D}'$ such that the
composite $K^{\rhd} \to\mathcal{D}' \to \mathcal{C}$ is a colimit diagram in
$\mathcal{C}$. Applying the small object argument (countably many times), we
can find a countable quasi-category $\mathcal{D}_1$ with $\mathcal{D} \subset \mathcal{D}_1 \subset
\mathcal{C}$ such that any diagram $K \to \mathcal{D}_1$ extends over a diagram
$K^{\rhd} \to \mathcal{D}_1$ such that the composite $K^{\rhd} \to \mathcal{D}_1 \to
\mathcal{C}$ is a colimit diagram. It follows thus that any countable
simplicial subset $\mathcal{D}$ of $\mathcal{C}$ containing all the vertices is
contained in such a (countable) $\mathcal{D}_1$. (At each stage in the small
object argument, we also have to add in fillers to all inner horns.)
Thus, consider any countable simplicial subset $\mathcal{D} \subset
\mathcal{C}$ which is a quasi-category containing all the vertices of
$\mathcal{C}$, and such that any diagram $K \to \mathcal{D}$ (for $K$ finite)
extends over a diagram $K^{\rhd} \to \mathcal{D}$ such that the composite
$K^{\rhd} \to \mathcal{C}$ is a colimit diagram. We have just shown that
$\mathcal{C}$ is a (filtered) union of such. Of course, $\mathcal{D}$ may not
have all the colimits we want. Consider the (countable) collection $S_{\mathcal{D}}$ of all diagrams
$f\colon K^{\rhd} \to \mathcal{D}$ whose composite $K^{\rhd} \stackrel{f}{\to}
\mathcal{D} \to \mathcal{C}$ is a colimit. We want to enlarge $\mathcal{D}$ so
that each of these becomes a colimit, but not too much; we want
$\mathcal{D}$ to remain countable.
For each $f \in S_{\mathcal{D}}$, consider $\mathcal{D}_{K/} \subset
\mathcal{C}_{K/}$. By construction, we have an object in $\mathcal{D}_{K/}$
which is initial in $\mathcal{C}_{K/}$. By adding a countable number of
simplices to $\mathcal{D}$, though, we can make this initial in
$\mathcal{D}_{K/}$ too; that is, there exists a $\mathcal{D}' \subset
\mathcal{D}$ with the same properties such that the object
defined is initial in $\mathcal{D}'_{K/}$.
Iterating this process (via the small object argument), we can construct a
countable simplicial subset $\overline{\mathcal{D}} \subset \mathcal{C}$,
containing $\mathcal{D}$, which is a quasi-category and such that any diagram
$K \to \overline{\mathcal{D}}$ extends over a diagram $K^{\rhd} \to
\overline{\mathcal{D}}$ which is a colimit preserved under
$\overline{\mathcal{D}} \to \mathcal{C}$. This completes the proof.
\end{proof}
We can use this to describe $\mathrm{Cat}_\infty^{\mathrm{st}}$. We have a \emph{fully
faithful} functor
\[ \mathrm{Cat}_\infty^{\mathrm{st}} \to \mathrm{Pr}^{L, \omega}, \]
which sends a stable $\infty$-category $\mathcal{C}$ to
the \emph{compactly generated}, presentable stable
$\infty$-category $\mathrm{Ind}(\mathcal{C})$.
In fact, $\mathrm{Cat}_\infty^{\mathrm{st}}$ can be identified with the $\infty$-category of stable,
presentable, and compactly generated $\infty$-categories, and
colimit-preserving functors between them that also preserve compact objects, so that $\mathrm{Cat}_\infty^{\mathrm{st}} \subset \mathrm{Pr}^{L, \omega}$ as a
full subcategory.
\begin{proof}[Proof of \Cref{scatispresentable}]
We need to show that $\mathrm{Cat}_\infty^{\mathrm{st}}$ has all colimits. Using the explicit construction
of a colimit of presentable $\infty$-categories, however, it follows that a
colimit of presentable, \emph{stable} $\infty$-categories is stable. In
particular, $\mathrm{Cat}_\infty^{\mathrm{st}}$ has colimits and they are computed in $\mathrm{Pr}^{L, \omega}$.
Finally, we need to show that any object in $\mathrm{Cat}_\infty^{\mathrm{st}}$ is a filtered union of
objects in $\mathrm{Cat}_\infty^{\mathrm{st}}$ of bounded cardinality. This can be argued similarly as
above (we just need to add stability into the mix).
\end{proof}
Compare also the treatment of stable $\infty$-categories in \cite{BGT}, which
shows (cf. \cite[Th. 4.22]{BGT}) that $\mathrm{Cat}_\infty^{\mathrm{st}}$ can be obtained as an
accessible localization of the $\infty$-category associated to a
combinatorial model category and indeed shows that $\mathrm{Cat}_\infty^{\mathrm{st}}$ is compactly
generated \cite[Cor. 4.25]{BGT}.
We will need some examples of limits and colimits in $\mathrm{Cat}_\infty^{\mathrm{st}}$.
Compare \cite[sec. 5]{BGT} for a detailed treatment.
\begin{definition}
\label{vq}
Let $\mathcal{C} \in \mathrm{Cat}_\infty^{\mathrm{st}}$ and let $\mathcal{D} \subset \mathcal{C}$ be a
full, stable idempotent complete subcategory.
We define the \textbf{Verdier quotient} $\mathcal{C}/\mathcal{D}$ to be the pushout in $\mathrm{Cat}_\infty^{\mathrm{st}}$
\[ \xymatrix{
\mathcal{D} \ar[d] \ar[r] & \mathcal{C} \ar[d] \\
0 \ar[r] & \mathcal{C}/\mathcal{D}
}.\]
\end{definition}
Fix $\mathcal{E} \in \mathrm{Cat}_\infty^{\mathrm{st}}$.
By definition, to give an exact functor $\mathcal{C}/\mathcal{D} \to
\mathcal{E}$ is equivalent to giving an exact functor $\mathcal{C} \to
\mathcal{E}$ which sends every object in $\mathcal{D}$ to a zero object; note
that this is a \emph{condition} rather than extra data.
The Verdier quotient can be described very explicitly. Namely, consider the
inclusion $\mathrm{Ind}(\mathcal{D}) \subset \mathrm{Ind}(\mathcal{C})$ of
stable $\infty$-categories. For any $X \in \mathrm{Ind}(\mathcal{C})$, there is
a
natural cofiber sequence
\[ M_{\mathcal{D}} X \to X \to L_{\mathcal{D}} X, \]
where:
\begin{enumerate}
\item $M_{\mathcal{D}} X$ is in the full stable subcategory of
$\mathrm{Ind}(\mathcal{C})$ generated under colimits by $\mathcal{D}$ (i.e.,
$\mathrm{Ind}(\mathcal{D})$).
\item For any $D \in \mathcal{D}$, $\hom_{\mathrm{Ind}(\mathcal{C})}(D,
L_{\mathcal{D}} X)$ is contractible.
\end{enumerate}
One can construct this sequence by taking $M_{\mathcal{D}}$ to be the right
adjoint to the inclusion functor $\mathrm{Ind}(\mathcal{D}) \subset
\mathrm{Ind}(\mathcal{C})$.
We say that an object $X \in \mathrm{Ind}(\mathcal{C})$ is \emph{$\mathcal{D}^{\perp}$-local}
if $M_{\mathcal{D}}X$ is contractible. The full subcategory
$\mathcal{D}^{\perp} \subset \mathrm{Ind}(\mathcal{C})$ of
$\mathcal{D}^{\perp}$-local objects is a localization of
$\mathrm{Ind}(\mathcal{C})$, with localization functor given by
$L_{\mathcal{D}}$.
We have an adjunction
\[ \mathrm{Ind}(\mathcal{C}) \rightleftarrows \mathcal{D}^{\perp}, \]
where the right adjoint, the inclusion $\mathcal{D}^{\perp} \subset
\mathcal{C}$, is fully faithful.
The inclusion $\mathcal{D}^{\perp} \subset \mathrm{Ind}(\mathcal{C})$ preserves filtered
colimits since $\mathcal{D} \subset \mathrm{Ind}(\mathcal{C})$ consists of
compact objects, so that the localization $L_{\mathcal{D}}$ preserves compact objects.
Now, the Verdier quotient can be described as the
subcategory of $\mathcal{D}^{\perp}$ spanned by compact objects (in
$\mathcal{D}^{\perp}$); it is generated under finite colimits and retracts by the image of
objects in $\mathcal{C}$.
Moreover, $\mathrm{Ind}(\mathcal{C}/\mathcal{D})$ is precisely
$\mathcal{D}^{\perp} \subset \mathrm{Ind}(\mathcal{C})$.
\begin{remark}
The pushout diagram defining the Verdier quotient is also a pullback.
\end{remark}
\begin{remark}
A version of this construction makes sense in the world of presentable, stable
$\infty$-categories (which need not be compactly generated).
\end{remark}
These Verdier quotients have been considered, for example, in \cite{miller} under the name
\emph{finite localizations.}
\subsection{Stable homotopy theories and 2-rings}
In this paper, our goal is to describe an invariant of \emph{symmetric
monoidal} stable $\infty$-categories. For our purposes, we can think of them as
\emph{commutative algebra objects} with respect to a certain \emph{tensor
product} on $\mathrm{Cat}_\infty^{\mathrm{st}}$. We begin by reviewing this and some basic properties of
stable homotopy theories, which are the ``big'' versions of these.
\begin{definition}[{\cite[4.8]{higheralg}, \cite{BFN}}]
Given $\mathcal{C}, \mathcal{D} \in \mathrm{Cat}_\infty^{\mathrm{st}}$, we define the
\emph{tensor product} $\mathcal{C} \boxtimes
\mathcal{D} \in \mathrm{Cat}_\infty^{\mathrm{st}}$ via the universal property
\begin{equation} \label{tensor} \hom_{\mathrm{Cat}_\infty^{\mathrm{st}}}( \mathcal{C} \boxtimes \mathcal{D}, \mathcal{E}) \simeq
\mathrm{Fun}'( \mathcal{C} \times \mathcal{D}, \mathcal{E}), \end{equation}
where $\mathrm{Fun}'(\mathcal{C} \times \mathcal{D}, \mathcal{E})$ consists of
those functors $\mathcal{C} \times \mathcal{D} \to \mathcal{E}$ which preserve
finite colimits in each variable separately.
\end{definition}
It is known (see \cite[4.8]{higheralg}) that this defines a symmetric
monoidal structure on $\mathrm{Cat}_\infty^{\mathrm{st}}$. The commutative algebra objects are
\emph{precisely} the symmetric monoidal, stable $\infty$-categories
$(\mathcal{C}, \otimes, \mathbf{1})$ such that the tensor product preserves
finite colimits in each variable.
\begin{definition}
We let $\mathrm{2}\text{-}\mathrm{Ring} = \mathrm{CAlg}(\mathrm{Cat}_\infty^{\mathrm{st}})$ be the $\infty$-category of commutative algebra
objects in $\mathrm{Cat}_\infty^{\mathrm{st}}$.
We will also write $\mathrm{CAlg}( \mathrm{Pr}^L_{\mathrm{st}})$ for the $\infty$-category of stable homotopy
theories (i.e., presentable stable symmetric monoidal $\infty$-categories with
bicocontinuous tensor product); this is the ``big'' version of $\mathrm{2}\text{-}\mathrm{Ring}$.
\end{definition}
The tensor product $\boxtimes\colon \mathrm{Cat}_\infty^{\mathrm{st}} \times \mathrm{Cat}_\infty^{\mathrm{st}} \to \mathrm{Cat}_\infty^{\mathrm{st}}$ preserves filtered
colimits in each variable; this follows from \eqref{tensor}. In particular, since $\mathrm{Cat}_\infty^{\mathrm{st}}$ is
a presentable $\infty$-category, it follows that $\mathrm{2}\text{-}\mathrm{Ring} $ is a presentable
$\infty$-category.
In this paper, we will define a functor
\[ \pi_{\leq 1} \colon \mathrm{2}\text{-}\mathrm{Ring} \to \mathrm{Pro}( \mathrm{Gpd}_{\mathrm{fin}})^{\mathrm{op}}, \]
where we will specify what the latter means below, called the Galois
groupoid.
The Galois groupoid will parametrize certain very special commutative algebra
objects in a given 2-ring.
Given a stable homotopy theory $(\mathcal{C}, \otimes,
\mathbf{1})$ (in the sense of \Cref{shot}), the invariant we will define will
depend only on the small subcategory $\mathcal{C}^{\mathrm{dual}}$ of
\emph{dualizable} objects in $\mathcal{C}$.
We will also define a slightly larger version of the Galois groupoid
that will see more of the ``infinitary'' structure of the stable homotopy theory, which will
make a difference in settings where the unit is not compact (such as
$K(n)$-local stable homotopy theory).
In this case, it will not be sufficient to work with $\mathrm{2}\text{-}\mathrm{Ring}$. However, the
interplay between $\mathrm{2}\text{-}\mathrm{Ring}$ and the theory of (large) stable homotopy theories
will be crucial in the following.
\begin{definition}[{Cf. \cite[4.6.1]{higheralg}}]
In a symmetric monoidal $\infty$-category $(\mathcal{C}, \otimes, \mathbf{1})$,
an object $X$ is \textbf{dualizable} if there exists an object $Y$ and maps
\[ \mathbf{1} \xrightarrow{\mathrm{coev}} Y \otimes X, \quad X \otimes Y
\xrightarrow{\mathrm{ev}} \mathbf{1}, \]
such that the composites
\[ X \simeq X \otimes \mathbf{1} \xrightarrow{1_{X} \otimes
\mathrm{coev}} X \otimes Y \otimes X \xrightarrow{\mathrm{ev} \otimes
1_X} X,
\quad Y \simeq \mathbf{1} \otimes Y \xrightarrow{\mathrm{coev} \otimes 1_Y}
Y \otimes X \otimes Y \xrightarrow{1_Y \otimes \mathrm{ev}} Y
\]
are homotopic to the respective identities.
In other words, $X$ is dualizable if and only if it is dualizable in the
homotopy category with its induced symmetric monoidal structure.
\end{definition}
These definitions force natural homotopy equivalences
\begin{equation} \label{duality} \hom_{\mathcal{C}}(Z, Z' \otimes X )
\simeq \hom_{\mathcal{C}}(Z \otimes Y, Z'), \quad Z, Z' \in \mathcal{C}.
\end{equation}
Now let $(\mathcal{C}, \otimes, \mathbf{1})$ be a stable homotopy theory. The
collection of all dualizable objects in $\mathcal{C}$
(cf. also \cite[sec. 2.1]{axiomatic})
is a \emph{stable}
and idempotent complete subcategory, which is closed under the monoidal product. Moreover, suppose that $\mathbf{1}$ is $\kappa$-compact for some
regular cardinal $\kappa$. Then
\eqref{duality} with $Z = \mathbf{1}$ forces any dualizable object $Y$ to be
$\kappa$-compact as well. In particular, it follows that the subcategory of
$\mathcal{C}$ spanned by the dualizable objects is (essentially) small and
belongs to $\mathrm{2}\text{-}\mathrm{Ring}$. (By contrast, no amount of compactness is sufficient to
imply dualizability).
We thus have the two constructions:
\begin{enumerate}
\item Given a stable homotopy theory, take the symmetric monoidal, stable
$\infty$-category of dualizable objects, which is a 2-ring.
\item Given an object $\mathcal{C} \in \mathrm{2}\text{-}\mathrm{Ring}$, $\mathrm{Ind}(\mathcal{C})$ is
a stable homotopy theory.
\end{enumerate}
These two constructions are generally not inverse to one another. However, the
``finitary'' version of the Galois group we will define will be unable to see
the difference.
Next, we will describe some basic constructions in $\mathrm{2}\text{-}\mathrm{Ring}$.
The $\infty$-category $\mathrm{2}\text{-}\mathrm{Ring}$ has all limits, and these may be computed at the level of the
underlying $\infty$-categories.
As such, these homotopy limit constructions can be used to build new examples
of 2-rings from old ones.
These constructions will also apply to stable homotopy theories.
To start with, we discuss Verdier quotients.
\begin{definition}
Let $(\mathcal{C}, \otimes, \mathbf{1}) \in \mathrm{2}\text{-}\mathrm{Ring}$ and let $\mathcal{I}
\subset \mathcal{C}$ be a full stable, idempotent complete subcategory. We say that $\mathcal{I}$ is an
\textbf{ideal} or \textbf{$\otimes$-ideal} if whenever $X \in \mathcal{C}, Y \in \mathcal{I}$, the tensor
product $X \otimes Y \in \mathcal{C}$ actually belongs to $\mathcal{I}$.
\end{definition}
If $\mathcal{I}
\subset \mathcal{C}$ is an ideal, then the Verdier quotient
$\mathcal{C}/\mathcal{I}$ naturally inherits the structure of an object in
$\mathrm{2}\text{-}\mathrm{Ring}$. This follows naturally from \cite[Proposition 2.2.1.9]{higheralg} and the explicit
construction of the Verdier quotient. By definition,
$\mathrm{Ind}(\mathcal{C}/\mathcal{I})$
consists of the objects $X \in \mathrm{Ind}(\mathcal{C})$ which have the
property that $\hom_{\mathrm{Ind}(\mathcal{C})}(I, X) $ is contractible when $I
\in \mathcal{I}$. We can describe this as the localization of
$\mathrm{Ind}(\mathcal{C})$ at the collection of maps $f\colon X \to Y$ whose
cofiber belongs to $\mathrm{Ind}(\mathcal{I})$. These maps, however, form an
ideal since $\mathcal{I}$ is an ideal.
As before, given $\mathcal{D} \in \mathrm{2}\text{-}\mathrm{Ring}$, we have a natural fully faithful inclusion
\[ \hom_{\mathrm{2}\text{-}\mathrm{Ring}}(\mathcal{C}/\mathcal{I}, \mathcal{D}) \subset
\hom_{\mathrm{2}\text{-}\mathrm{Ring}}(\mathcal{C}, \mathcal{D}), \]
where the image of the map consists of all symmetric monoidal functors
$\mathcal{C} \to \mathcal{D}$ which take every object in $\mathcal{I}$ to a
zero object.
Finally, we describe some \emph{free} constructions.
Let $\sp$ be the $\infty$-category of spectra, and let $\mathcal{C}$ be a
small symmetric monoidal $\infty$-category. Then the $\infty$-category
$\mathrm{Fun}(\mathcal{C}^{\mathrm{op}}, \sp)$ is a stable homotopy theory under the
\emph{Day convolution product} \cite[4.8.1]{higheralg}. Consider the collection of compact objects in
here, which we will write as the ``monoid algebra'' $\sp^\omega[\mathcal{C}]$.
One has the universal property
\[ \hom_{\mathrm{2}\text{-}\mathrm{Ring}}( \sp^\omega[\mathcal{C}], \mathcal{D}) \simeq
\mathrm{Fun}_{\otimes}( \mathcal{C}, \mathcal{D}), \]
i.e.,
an equivalence
between functors of 2-rings $\sp[\mathcal{C}] \to \mathcal{D}$ and
symmetric monoidal functors $\mathcal{C} \to \mathcal{D}$. We can also define the free
stable homotopy theory on $\mathcal{C}$ as the $\mathrm{Ind}$-completion of this
2-ring, or equivalently as $\mathrm{Fun}(\mathcal{C}^{\mathrm{op}}, \sp)$.
\begin{example}
The free symmetric monoidal $\infty$-category on a single object is the
disjoint union $\bigsqcup_{n \geq 0} B \Sigma_n$, or the groupoid of finite
sets and isomorphisms between them, with $\sqcup$ as the symmetric monoidal
product. Using this, we can describe the ``free stable homotopy theory'' on a
single object. As above, an object in this stable homotopy theory consists of giving a spectrum $X_n$ with a
$\Sigma_n$-action for each $n$; the tensor structure comes from a convolution
product. If we consider the compact objects in here, we obtain the free 2-ring
on a given object.
\end{example}
Finally, we will need to discuss a bit of algebra internal to $\mathcal{C}$.
\begin{definition}
There is a natural $\infty$-category of \emph{commutative
algebra objects} in $\mathcal{C}$ (cf. \cite[Ch. 2]{higheralg}) which we will denote by $\mathrm{CAlg}(\mathcal{C})$.
When $\mathcal{C} = \sp$ is the $\infty$-category, we will just write $\mathrm{CAlg}$
for the $\infty$-category of $\e{\infty}$-ring spectra.
\end{definition}
Recall that a commutative algebra object in $\mathcal{C}$ consists of an object
$X \in \mathcal{C}$ together with a multiplication map $m\colon X \otimes X \to X$
and a unit map $\mathbf{1}\to X$, which satisfy the classical axioms of a
commutative algebra object up to coherent homotopy; for instance, when
$\mathcal{C} = \sp$, one obtains the classical notion of an $\e{\infty}$-ring.
The amount of homotopy coherence is sufficient to produce the following:
\begin{definition}[{\cite[Sec. 4.5]{higheralg}}]
Let $\mathcal{C}$ be a stable homotopy theory.
Given $A \in \mathrm{CAlg}(\mathcal{C})$, there is a natural $\infty$-category
$\mathrm{Mod}_{\mathcal{C}}(A)$ of $A$-module objects internal to $\mathcal{C}$.
The $\infty$-category
$\mathrm{Mod}_{\mathcal{C}}(A)$ acquires the structure of a stable homotopy theory with
the relative $A$-linear tensor product.
\end{definition}
The relative $A$-linear tensor product requires the formation of geometric
realizations, so we need infinite colimits to exist in $\mathcal{C}$ for the
above construction to make sense in general.
\subsection{Examples}
Stable homotopy theories and 2-rings occur widely in ``nature,'' and in this section, we
describe a few basic classes of such widely occurring examples.
We begin with two of the most fundamental ones.
\begin{example}[Derived categories]
The derived $\infty$-category $D(R)$ of a commutative ring $R$ (cf. \cite[Sec.
1.3]{higheralg})
with the derived tensor product is a stable homotopy theory.
\end{example}
\begin{example}[Modules over an $\e{\infty}$-ring]
As a more general example, the $\infty$-category $\mathrm{Mod}(R)$ of modules over an
$\e{\infty}$-ring spectrum $R$ with the relative smash product is a stable
homotopy theory.
For instance, taking $R = S^0$, we get the $\infty$-category $\sp$ of spectra.
This is the primary example (together with $E$-localized versions)
considered in \cite{rognes}.
\end{example}
\begin{example}[Quasi-coherent sheaves]
\label{qcohintro}
Let $X$ be a scheme (or algebraic stack, or even prestack). To $X$, one can
associate a stable homotopy theory $\mathrm{QCoh}(X)$ of \emph{quasi-coherent
complexes} on $X$. By definition, $\mathrm{QCoh}(X)$ is the homotopy limit of the
derived $\infty$-categories $D(R)$ where $\mathrm{Spec} R \to X$ ranges over all maps from
affine schemes to $X$. For more discussion, see \cite{BFN}.
\end{example}
\begin{example}
\label{modclosed}
Consider a cartesian diagram of $\e{\infty}$-rings
\[ \xymatrix{
A \times_{A''} A' \ar[d] \ar[r] & A \ar[d] \\
A' \ar[r] & A''
}.\]
We obtain a diagram of stable homotopy theories
\[ \xymatrix{
\mathrm{Mod}(A \times_{A''} A') \ar[d] \ar[r] & \mathrm{Mod}(A) \ar[d] \\
\mathrm{Mod}(A') \ar[r] & \mathrm{Mod}( A'')
},\]
and in particular a symmetric monoidal functor
\[ \mathrm{Mod}(A \times_{A''} A') \to \mathrm{Mod}(A) \times_{\mathrm{Mod}(A'')} \mathrm{Mod}(A').\]
This functor is generally not an equivalence in $\mathrm{2}\text{-}\mathrm{Ring}$.
This functor is \emph{always} fully faithful.
However, if $A ,A',
A''$ are \emph{connective} and $A \to A'', A' \to A''$ induce surjections on
$\pi_0$, then it is proved in \cite[Theorem 7.2]{DAGIX} that
the functor induces an equivalence on the \emph{connective} objects or, more
generally, on the $k$-connective objects for any $k \in \mathbb{Z}$.
In particular, if we let $\mathrm{Mod}^\omega$ denote perfect modules, we have an equivalence of 2-rings
\[ \mathrm{Mod}^\omega( A \times_{A''} A') \simeq \mathrm{Mod}^{\omega}(A) \times_{\mathrm{Mod}^{\omega}(A'')}
\mathrm{Mod}^{\omega}(A') , \]
since an $A \times_{A''} A'$-module is perfect if and only if its base-changes
to $A, A'$ are.
However, the $\mathrm{Ind}$-construction generally does not commute even with finite
limits.
\end{example}
\begin{example}[Functor categories]
As another example of a (weak) 2-limit, we consider any $\infty$-category
$K$ and a stable homotopy theory $\mathcal{C}$; then $\mathrm{Fun}(K,
\mathcal{C})$ is naturally a stable homotopy theory under the ``pointwise''
tensor product. If $K = BG$ for a group $G$, then this example endows the
$\infty$-category of objects in $\mathcal{C}$ with a $G$-action with the
structure of a stable homotopy theory.
\end{example}
Finally, we list several other miscellaneous examples of stable homotopy
theories.
\begin{example}[Hopf algebras]
\label{Hopfalg}
Let $A$ be a finite-dimensional cocommutative Hopf algebra over the field $k$. In this case, the
(ordinary) category $\mathcal{A}$ of discrete $A$-modules has a natural symmetric monoidal structure
via the $k$-linear tensor product. In particular, its \emph{derived}
$\infty$-category $D(\mathcal{A})$
is naturally symmetric monoidal, and is thus a stable homotopy theory.
Stated more algebro-geometrically, $\mathrm{Spec} A^{\vee}$ is a group scheme $G$ over the
field $k$, and $D(\mathcal{A})$ is the
$\infty$-category of quasi-coherent sheaves of complexes on the classifying
stack $BG$.
\end{example}
\begin{example}[Stable module $\infty$-categories]
\label{stmodcat}
Let $A$ be a finite-dimensional cocommutative Hopf algebra over the field $k$. Consider the
subcategory $D(\mathcal{A})^{\omega} \subset D(\mathcal{A})$ (where $\mathcal{A}$ is the abelian category
of $A$-modules, as in \Cref{Hopfalg}) of $A$-module spectra which are perfect as $k$-module spectra.
Inside $D(\mathcal{A})^{\omega}$ is the subcategory $\mathcal{I}$ of those
objects which
are perfect as $A$-module spectra. This subcategory is stable, and is an
\emph{ideal} by the observation (a projection formula of sorts) that the
$k$-linear tensor product of $A$
with any $A$-module
is free as an $A$-module.
\begin{definition}
The \textbf{stable module $\infty$-category} $\mathrm{St}_A = \mathrm{Ind}(
D(\mathcal{A})^{\omega}/\mathcal{I})$ is the $\mathrm{Ind}$-completion of the Verdier quotient
$D(\mathcal{A})^{\omega}/\mathcal{I}$.
If $A = k[G]$ is the group algebra of a finite group $G$, we write $\mathrm{St}_G(k)$
for $\mathrm{St}_{k[G]}$.
\end{definition}
The stable module $\infty$-categories of finite-dimensional Hopf algebras
(especially group algebras) and their
various invariants (such as the Picard groups and the thick
subcategories) have been studied
extensively in the modular representation theory literature.
For a recent survey, see \cite{BIK}.
\end{example}
\begin{example}[Bousfield localizations]
Let $\mathcal{C}$ be a stable homotopy theory, and let $E \in \mathcal{C}$. In
this case, there is a naturally associated stable homotopy theory $L_E
\mathcal{C}$ of \emph{$E$-local objects}. By definition, $L_E \mathcal{C}$ is
a full subcategory of $\mathcal{C}$; an object $X \in
\mathcal{C}$ belongs to $L_E \mathcal{C}$ if and only if whenever $Y \in
\mathcal{C}$ satisfies $Y \otimes E \simeq 0$, the spectrum
$\hom_{\mathcal{C}}(Y, X)$ is contractible.
The $\infty$-category $L_E \mathcal{C}$ is symmetric monoidal under the
\emph{$E$-localized tensor product}: since the tensor product of two $E$-local
objects need not be $E$-local, one needs to localize further.
For example, the unit object in $L_E \mathcal{C}$ is $L_E \mathbf{1}$.
There is a natural adjunction
\[ \mathcal{C} \rightleftarrows L_E \mathcal{C}, \]
where the (symmetric monoidal) left adjoint sends an object to its
$E$-localization, and where the (lax symmetric monoidal) right adjoint is the
inclusion.
\end{example}
\subsection{Morita theory}
Let $(\mathcal{C}, \otimes, \mathbf{1})$ be a stable homotopy theory. In
general, there is a very useful criterion for recognizing when $\mathcal{C}$ is
equivalent (as a stable homotopy theory) to the $\infty$-category of modules
over an $\e{\infty}$-ring.
Note first that if $R$ is an $\e{\infty}$-ring, then the unit object of $\mathrm{Mod}(R)$
is a compact generator. The following result,
which for stable $\infty$-categories (without the symmetric monoidal structure)
is due to Schwede-Shipley \cite{schwedeshipley} (preceded by ideas of Rickard
and others on tilting theory),
asserts the converse.
\begin{theorem}[{\cite[Proposition 8.1.2.7]{higheralg}}]
\label{luriess}
Let $\mathcal{C}$ be a stable homotopy theory where $\mathbf{1}$ is a compact
generator. Then there is a natural symmetric monoidal equivalence
\[ \mathrm{Mod}(R) \simeq \mathcal{C} , \]
where $R \simeq \mathrm{End}_{\mathcal{C}}(\mathbf{1})$ is naturally an
$\e{\infty}$-ring.
\end{theorem}
In general, given a symmetric monoidal stable $\infty$-category $\mathcal{C}$,
the endomorphism ring $R = \mathrm{End}_{\mathcal{C}}( \mathbf{1})$ is
\emph{always} naturally an $\e{\infty}$-ring, and
one has a natural adjunction
\[ \mathrm{Mod}(R) \rightleftarrows \mathcal{C}, \]
where the left adjoint ``tensors up'' an $R$-module with $\mathbf{1} \in
\mathcal{C}$, and the right adjoint sends $X \in \mathcal{C}$ to the mapping
spectrum
$\hom_{\mathcal{C}}(\mathbf{1}, X)$, which naturally acquires the structure of
an $R$-module. The left adjoint is symmetric monoidal, and the right adjoint is
\emph{lax} symmetric monoidal. In general, one does not expect the right
adjoint to preserve filtered colimits: it does so if and only if $\mathbf{1}$
is compact. In this case, if $\mathbf{1}$ is compact, we get a fully faithful
inclusion
\[ \mathrm{Mod}(R) \subset \mathcal{C}, \]
which exhibits $\mathrm{Mod}(R)$ as a \emph{colocalization} of $\mathcal{C}$. If
$\mathbf{1}$ is not compact, we at least get a fully faithful inclusion of the
\emph{perfect} $R$-modules into $\mathcal{C}$.
For example, let $G$ be a finite $p$-group and $k$ be a field of characteristic
$p$. In this case, every finite-dimensional $G$-representation on a $k$-vector space
is unipotent: any such has a finite filtration whose subquotients are isomorphic to
the trivial representation.
From this, one might suspect that one has an equivalence
of stable homotopy theories
\( \mathrm{Fun}( BG, \mathrm{Mod}(k)) \simeq \mathrm{Mod} ( k^{hG}), \)
where $k^{hG}$ is the $\e{\infty}$-ring of endomorphisms of the unit object
$k$, but this fails because the unit object of $\mathrm{Mod}( k[G])$ fails to be
compact: taking $G$-homotopy fixed points does not commute with homotopy
colimits. However, by fixing this reasoning, one obtains an equivalence
\begin{equation} \label{reppgroup} \mathrm{Fun}( BG, \mathrm{Mod}^\omega(k)) \simeq \mathrm{Mod}^{\omega}( k^{hG}), \end{equation}
between perfect $k$-module spectra with a $G$-action and perfect
$k^{hG}$-modules.
If one works with stable module $\infty$-categories, then the unit object \emph{is}
compact (more or less by fiat) and one has:
\begin{theorem}[Keller \cite{keller}] \label{keller} Let $G$ be a finite $p$-group and $k$ a
field of characteristic $p$. Then we
have an equivalence of symmetric monoidal $\infty$-categories
\[ \mathrm{Mod}( k^{tG}) \simeq \mathrm{St}_G(k), \]
between the $\infty$-category of modules over the Tate $\e{\infty}$-ring $k^{tG}$
and the stable module $\infty$-category of $G$-representations over $k$.
\end{theorem}
The \emph{Tate construction} $k^{tG}$, for our purposes, can be \emph{defined} as the endomorphism
$\e{\infty}$-ring of the unit object in the stable module $\infty$-category
$\mathrm{St}_G(k)$. As a $k$-module spectrum, it can also be obtained as the cofiber of
the \emph{norm map} $k_{hG} \to k^{hG}$.
We also refer to \cite[sec. 2]{toruspic} for
further discussion on this point.
\subsection{\'Etale algebras}
Let $R$ be an $\e{\infty}$-ring spectrum.
Given an $\e{\infty}$-$R$-algebra $R'$, recall that the homotopy groups
$\pi_* R'$ form a graded-commutative $\pi_*R$-algebra.
In general, there is no reason for a given graded-commutative $\pi_* R$-algebra
to be realizable as the homotopy groups in this way, although one often has
various obstruction theories (see for instance \cite{robinsonobstruct, rezkHM,
goersshopkins}
for examples of obstruction theories in different contexts) to attack such questions. There is, however,
always one case in which the obstruction theories degenerate completely.
\begin{definition}
An $\e{\infty}$-$R$-algebra $R'$ is \textbf{\'etale} if:
\begin{enumerate}
\item The map $\pi_0 R \to \pi_0 R'$ is \'etale (in the sense of ordinary
commutative algebra).
\item The natural map $\pi_0 R' \otimes_{\pi_0 R} \pi_* R \to \pi_* R'$ is an
isomorphism.
\end{enumerate}
\end{definition}
The basic result in this setting is that the theory of \'etale algebras
is entirely algebraic: the obstructions to existence and uniqueness all vanish.
\begin{theorem}[{\cite[Theorem 7.5.4.2]{higheralg}}]
\label{etaletopinv}
Let $R$ be an $\e{\infty}$-ring. Then the $\infty$-category of \'etale
$R$-algebras is equivalent (under $\pi_0$) to the ordinary category of \'etale
$\pi_0 R$-algebras.
\end{theorem}
One can show more, in fact: given an \'etale $R$-algebra $R'$, then for any
$\e{\infty}$ $R$-algebra $R''$, the natural map
\[ \hom_{R/}(R', R'') \to \hom_{\pi_0 R/}( \pi_0 R', \pi_0 R'') \]
is a homotopy equivalence. Using an adjoint functor theorem approach (and the
infinitesimal criterion for \'etaleness), one may
even \emph{define} $R'$ in terms of $\pi_0 R'$ in this manner, although
checking that it has the desired homotopy groups takes additional work. In
particular, note that \'etale $R$-algebras are \emph{0-cotruncated} objects of
the $\infty$-category $\mathrm{CAlg}_{R/}$: that is, the space of maps out of any such
is always homotopy discrete.
The finite covers that we shall consider in this paper will also
have this property.
\begin{example}
This implies that one can adjoin $n$th roots of unity to the sphere spectrum
$S^0$ once $n$ is inverted. An argument of Hopkins implies that the inversion
of $n$ is necessary: for $p > 2$, one cannot adjoin a $p$th root of unity to $p$-adic
$K$-theory, as one sees by considering the $\theta$-operator on $K(1)$-local
$\e{\infty}$-rings under $K$-theory (cf. \cite{kone}) which satisfies $x^p = \psi(x) - p \theta(x)$ where $\psi$
is a homomorphism on $\pi_0$.
If one could adjoin $\zeta_p$ to $p$-adic $K$-theory, then
one would have $-p\theta( \zeta_p) = 1 - \zeta_p^a$ for some unit $a \in
(\mathbb{Z}/p\mathbb{Z})^{\times}$, but $p$ does not divide $1 -
\zeta_p^a$ in $\mathbb{Z}_p[\zeta_p]$.
\end{example}
Let $(\mathcal{C}, \otimes, \mathbf{1})$ be a stable homotopy theory.
We will now attempt to do the above in $\mathcal{C}$ itself.
We will obtain some of the simplest classes of objects in $\mathrm{CAlg}(\mathcal{C})$.
The following notation will be convenient.
\begin{definition}
Given a stable homotopy theory $(\mathcal{C}, \otimes, \mathbf{1})$, we will
write
\begin{equation}
\pi_* X \simeq \pi_* \hom_{\mathcal{C}}( \mathbf{1}, X).
\end{equation}
\end{definition}
In particular, $\pi_* \mathbf{1} \simeq \pi_*
\mathrm{End}_{\mathcal{C}}(\mathbf{1}, \mathbf{1})$ is a graded-commutative
ring, and
for any $X \in \mathcal{C}$, $\pi_* X$ is naturally a $\pi_* \mathbf{1}$-module.
\begin{remark}
Of course, $\pi_*$ does not commute with infinite direct sums unless
$\mathbf{1}$ is compact. For example, $\pi_*$ fails to commute with direct sums
in $L_{K(n)} \sp$ (which is actually compactly generated, albeit not by the
unit object).
\end{remark}
Let $(\mathcal{C}, \otimes, \mathbf{1})$ be a stable homotopy theory.
As in the previous section, we have an adjunction
of symmetric monoidal $\infty$-categories
\[ \left(\cdot \otimes_R \mathbf{1}, \hom_{\mathcal{C}}(\mathbf{1}, \cdot)
\right) \colon \mathrm{Mod}(R) \rightleftarrows \mathcal{C}, \]
where $R = \mathrm{End}_{\mathcal{C}}(\mathbf{1})$ is an $\e{\infty}$-ring.
Given an \'etale $\pi_0 R \simeq \pi_0 \mathbf{1}$-algebra $R_0'$, we can thus
construct an \'etale $R$-algebra $R'$ and an associated object $R' \otimes_R
\mathbf{1} \in \mathrm{CAlg}(\mathcal{C})$. The object $R' \otimes_R \mathbf{1}$ naturally acquires the
structure of a commutative algebra, and, by playing again with
adjunctions, we find that
\[ \hom_{\mathrm{CAlg}(\mathcal{C})}(R' \otimes_{R} \mathbf{1}, T) \simeq \hom_{\pi_0
\mathbf{1}}(R'_0, \pi_0 T), \quad T \in \mathrm{CAlg}(\mathcal{C}). \]
\begin{definition}
\label{classicaletale}
The objects of $\mathrm{CAlg}(\mathcal{C})$ obtained in this manner are called
\textbf{classically \'etale.}
\end{definition}
The classically \'etale objects in $\mathrm{CAlg}(\mathcal{C})$ span a
subcategory of $\mathrm{CAlg}(\mathcal{C})$. In general, this is not equivalent to the
category of \'etale $\pi_0 R$-algebras if $\mathbf{1}$ is not compact (for example, $\mathrm{Mod}(R) \to \mathcal{C}$
need not be conservative; take $\mathcal{C} = L_{K(n)} \sp$ and $L_{K(n)} S^0
\otimes \mathbb{Q}$).
However, note that the functor
\[ \mathrm{Mod}^\omega(R) \to \mathcal{C}, \]
from the $\infty$-category $\mathrm{Mod}^\omega(R)$ of perfect $R$-modules into
$\mathcal{C}$,
is \emph{always} fully faithful. It follows that there is a full subcategory of
$\mathrm{CAlg}( \mathcal{C})$ \emph{equivalent} to the category of \emph{finite} \'etale
$\pi_0 R$-algebras. This subcategory will give us the ``algebraic'' part of the
Galois group of $\mathcal{C}$.
We now specialize to the case of \emph{idempotents.}
Let $(\mathcal{C}, \otimes, \mathbf{1})$ be a stable homotopy theory, and $A
\in \mathrm{CAlg}(\mathcal{C})$ a commutative algebra object, so that $\pi_0 A$ is a
commutative ring.
\begin{definition}
An \textbf{idempotent} of $A$ is an idempotent of the commutative ring $\pi_0 A$.
We will denote the set of idempotents of $A$ by $\mathrm{Idem}(A)$.
\end{definition}
The set $\mathrm{Idem}(A)$ acquires some additional structure; as the set of
idempotents in a commutative ring, it is naturally a \emph{Boolean algebra}
under the multiplication in $\pi_0 A$ and the addition that takes idempotents
$e, e'$ and forms $e + e' - ee'$.
For future reference, recall the following:
\newcommand{\mathrm{Bool}}{\mathrm{Bool}}
\begin{definition}
A \textbf{Boolean algebra} is a commutative ring $B$ such that $x^2 = x$ for
every $x \in B$. The collection of all Boolean algebras forms a full subcategory
$\mathrm{Bool}$ of the category of commutative rings.
\end{definition}
Suppose given an idempotent $e$ of $A$, so that $1-e$ is also an idempotent.
In this case, we can obtain a \emph{splitting}
\[ A \simeq A[e^{-1}] \times A[(1-e)^{-1}] \]
as a product of two objects in $\mathrm{CAlg}(\mathcal{C})$, as observed in
\cite{mayidem}.
To see this, we may reduce to the case when $A = \mathbf{1}$, by replacing
$\mathcal{C}$ by $\mathrm{Mod}_{\mathcal{C}}(A)$. In this case, we obtain the splitting
from the discussion above in \Cref{classicaletale}: $A[e^{-1}]$ and $A[(1 -
e)^{-1}]$ are both classically \'etale and in the thick subcategory
generated by $A$.
Conversely, given such a
splitting, we obtain corresponding idempotents, e.g., reducing to the case of an
$\e{\infty}$-ring.
Suppose the unit object $\mathbf{1} \in \mathcal{C}$ decomposes as a product
$\mathbf{1}_1 \times \mathbf{1}_2 \in \mathrm{CAlg}(\mathcal{C})$. In this case, we have
a decomposition at the level of stable homotopy theories
\[ \mathcal{C} \simeq \mathrm{Mod}_{\mathcal{C}}( \mathbf{1}_1) \times
\mathrm{Mod}_{\mathcal{C}}( \mathbf{1}_2), \]
so in practice, most stable homotopy theories that in practice we will be
interested in will have no such nontrivial idempotents. However, the theory of
idempotents will be very important for us in this paper.
For example, using the theory of idempotents, we can describe maps \emph{out of} a product
of commutative algebras.
\begin{proposition} \label{prode}
Let $A, B \in \mathrm{CAlg}( \mathcal{C})$. Then if $C \in \mathrm{CAlg}( \mathcal{C})$, then we
have a homotopy equivalence
\[ \hom_{\mathrm{CAlg}(\mathcal{C})}(A \times B, C) \simeq \bigsqcup_{C \simeq C_1
\times C_2} \hom_{\mathrm{CAlg}(\mathcal{C})}(A, C_1) \times
\hom_{\mathrm{CAlg}(\mathcal{C})}(B, C_2), \]
where the disjoint union is taken over all decompositions $C \simeq C_1 \times
C_2$ in $\mathrm{CAlg}(\mathcal{C})$ (i.e., over idempotents in $C$).
\end{proposition}
\begin{proof}
Starting with a map $A \times B \to C$, we get a decomposition of $C$ into two
factors coming from the two natural idempotents in $A \times B$, whose images
in $C$ give two orthogonal idempotents summing to $1$. Conversely, starting with something in the
right-hand-side, given via maps $A \to C_1$ and $B \to C_2$ and an equivalence
$C \simeq C_1 \times C_2$, we can take the product
of the two maps to get $A \times B \to C$.
The equivalence follows from the universal property of localization.
\end{proof}
For example, consider the case of $A, B = \mathbf{1}$. In this case, we find
that, if $C \in \mathrm{CAlg}(\mathcal{C})$, then
\[ \hom_{\mathrm{CAlg}(\mathcal{C})}(\mathbf{1} \times \mathbf{1}, C) \]
is homotopy discrete, and
consists of the \emph{set} of idempotents in $C$. We could have obtained this
from the theory of ``classically \'etale'' objects earlier.
Using this description as a corepresentable functor, we find:
\begin{corollary}
\label{idemlimit}
The functor $A \mapsto \mathrm{Idem}(A)$, $\mathrm{CAlg}(\mathcal{C}) \to \mathrm{Bool}$, commutes with limits.
\end{corollary}
\begin{remark}
\label{sq0rem}
\Cref{idemlimit} can also be proved directly.
Since $\pi_* $ commutes with arbitrary products in $\mathcal{C}$, it follows
that $A \mapsto \mathrm{Idem}(A)$ commutes with arbitrary products. It thus suffices to
show that if we have a pullback diagram
\[ \xymatrix{
A \ar[d] \ar[r] & B \ar[d] \\
C \ar[r] & D
},\]
in $\mathrm{CAlg}(\mathcal{C})$,
then the induced diagram of Boolean algebras
\[ \xymatrix{
\mathrm{Idem}(A) \ar[d] \ar[r] & \mathrm{Idem}(B) \ar[d] \\
\mathrm{Idem}(C) \ar[r] & \mathrm{Idem}(D )
}\]
is also cartesian.
In fact, we have a surjective map of commutative rings $\pi_0(A) \to \pi_0(B)
\times_{\pi_0(D)} \pi_0(C)$ whose kernel is the image of the connecting
homomorphism $\pi_1(D) \to \pi_0(A)$. It thus suffices to show that the
product of two elements in the image of this connecting homomorphism vanishes,
since square-zero ideals do not affect idempotents.
Equivalently, we claim that if $x,y \in \pi_0(A)$ map to zero in $\pi_0(B)$
and $\pi_0(C)$, then $xy = 0$.
In fact, $x$ and $y$ define maps $A \to A$ and, in fact,
endomorphisms of the exact triangle
\[ A \to B \oplus C \to D, \]
and each is nullhomotopic on $B \oplus C$ and on $D$.
A diagram chase with exact triangles now shows that $xy$ defines the
\emph{zero map} $A \to A$, as desired.
\end{remark}
\section{Descent theory}
\label{sec:descent}
Let $A \to B$ be a faithfully flat map of discrete commutative rings.
Grothendieck's theory of \emph{faithfully flat descent} (cf. \cite[Exp.
VIII]{sga1}) can be used to describe
the category $\mathrm{Mod}^{\mathrm{disc}}(A)$ of (discrete, or classical) $A$-modules in terms of the
three categories $\mathrm{Mod}^{\mathrm{disc}}(B), \mathrm{Mod}^{\mathrm{disc}}(B \otimes_A B), \mathrm{Mod}^{\mathrm{disc}}(B \otimes_A B \otimes_A B)$.
Namely, it identifies the category $\mathrm{Mod}^{\mathrm{disc}}(A)$ with the category of $B$-modules
with \emph{descent data}, or states that the diagram
\[ \mathrm{Mod}^{\mathrm{disc}}(A) \to \mathrm{Mod}^{\mathrm{disc}}(B) \rightrightarrows \mathrm{Mod}^{\mathrm{disc}}(B \otimes_A B) \triplearrows
\mathrm{Mod}^{\mathrm{disc}}(B \otimes_A B \otimes_A B), \]
is a limit diagram in the 2-category of categories. This diagram of
categories comes from the
\emph{cobar construction} on $A \to B$, which is the augmented cosimplicial
commutative ring
\[ A \to B \rightrightarrows B \otimes_A B \triplearrows \dots . \]
Grothendieck's theorem can be proved via the \emph{Barr-Beck theorem,} by
showing that if $A \to B$ is faithfully flat, the natural
tensor-forgetful adjunction $\mathrm{Mod}^{\mathrm{disc}}(A)
\rightleftarrows \mathrm{Mod}^{\mathrm{disc}}(B)$ is
comonadic.
Such results are extremely useful in practice, for instance because the
category of $B$-modules may be much easier to study. From another point of
view, these results imply that any $A$-module $M$ can be expressed as an equalizer
of $B$-modules (and maps of $A$-modules), via
\[ M \to M \otimes_A B \rightrightarrows M \otimes_A B \otimes_A B, \]
where the two maps are $m \otimes b \mapsto m \otimes b \otimes 1$ and $m
\otimes b \mapsto m \otimes 1 \otimes b$.
In the setting of ``brave new'' algebra, descent theory for maps of $\e{\infty}$
(or weaker) algebras has been extensively considered in the papers
\cite{DAGdesc, DAGss}.
In this setting, one has a map of $\e{\infty}$-rings $A \to B$, and one wishes to
describe the stable $\infty$-category $\mathrm{Mod}(A)$ in terms of the stable
$\infty$-categories $\mathrm{Mod}(B), \mathrm{Mod}(B \otimes_A B), \dots $.
A sample result would run along the following lines.
\begin{theorem}[{\cite[Theorem 6.1]{DAGss}}]\label{luried}
Let $A \to B$ be a map of $\e{\infty}$-rings such that $\pi_0 (A) \to \pi_0(B)$
is faithfully flat and the map $\pi_*(A) \otimes_{\pi_0(A)} \pi_0( B) \to \pi_*
(B)$ is an isomorphism. Then the adjunction $\mathrm{Mod}(A) \rightleftarrows \mathrm{Mod}(B)$ is
comonadic, so that $\mathrm{Mod}(A)$ can be recovered as the totalization of the
cosimplicial $\infty$-category
\[ \mathrm{Mod}(B) \rightrightarrows \mathrm{Mod}(B \otimes_A B) \triplearrows \dots. \]
\end{theorem}
In practice, the condition of faithful flatness on $\pi_*(A) \to \pi_*(B)$ can
be weakened significantly; there are numerous examples of morphisms of
$\e{\infty}$-rings which do not behave well on the level of $\pi_0$ but under
which one does have a good theory of descent (e.g., the conclusion of
\Cref{luried} holds).
For instance, there is a good theory of descent along $KO \to KU$, and this can be
used to describe features of the $\infty$-category $\mathrm{Mod}(KO)$ in terms of the
$\infty$-category $\mathrm{Mod}(KU)$.
One advantage of considering descent in this more
general setting is that $KU$ is \emph{much simpler} algebraically: its
homotopy groups are given by $\pi_*(KU) \simeq \mathbb{Z}[\beta^{\pm }]$, which
is a regular ring, even one-dimensional (if one pays attention to the
grading), while $\pi_*(KO)$ is of infinite homological dimension.
There are many additional tricks one has when working with modules over a more
tractable $\e{\infty}$-ring such as $KU$; we shall see a couple of them below in
the proof of \Cref{etalegalois}.
\begin{remark}
For some applications of these ideas to computations, see the paper \cite{thick} (for
descriptions of thick subcategories) and
\cite{GL, MS, HMS} (for calculations of certain Picard groups).
\end{remark}
In this section, we will describe a class of maps of $\e{\infty}$-rings $A \to
B$ that have an \emph{especially good} theory of descent. We will actually work
in more generality, and fix a stable homotopy theory $(\mathcal{C}, \otimes,
\mathbf{1})$, and isolate a class of commutative algebra objects for which
the analogous theory of descent (internal to $\mathcal{C}$) works especially
well (so well, in fact, that it will be tautologically preserved by any
morphism of stable homotopy theories). Namely, we will define $A \in \mathrm{CAlg}(\mathcal{C})$ to be
\emph{descendable} if the thick $\otimes$-ideal that $A$ generates contains the
unit object $\mathbf{1} \in \mathcal{C}$. This definition, which is motivated by the
\emph{nilpotence technology} of Devinatz, Hopkins, Smith, and Ravenel
\cite{HS, DHS} (one part of which states that the map $L_n S^0 \to
E_n$ from the $E_n$-local sphere to Morava $E$-theory $E_n$ satisfies this
property), is enough to imply that the conclusion of \Cref{luried}
holds, and has the virtue of being purely diagrammatic. The definition has
also been recently
and independently considered by Balmer \cite{balmersep} (under the name ``nil-faithfulness'')
in the setting of tensor-triangulated categories.
In the rest of the section, we will give several
examples of descendable morphisms, and describe in
\Cref{lindesc}
an application to descent for \emph{2-modules} (or linear
$\infty$-categories), which has applications to the study of the \emph{Brauer
group}. This provides a slight strengthening of the descent results in
\cite{DAGQC, DAGdesc}.
\subsection{Comonads and descent}
The language of $\infty$-categories gives very powerful tools for proving
descent theorems such as \Cref{luried} as well as its generalizations;
specifically, the Barr-Beck-Lurie theorem of \cite{higheralg} gives a criterion
to check when an adjunction is comonadic (in the $\infty$-categorical sense),
although the result is usually stated in its equivalent form for monadic
adjunctions.
This result has recently been reproved from the point of view of weighted
(co)limits by Riehl-Verity \cite{RV}.
\begin{theorem}[{Barr-Beck-Lurie \cite[Section 4.7]{higheralg}}]
Let $F, G\colon \mathcal{C} \rightleftarrows \mathcal{D}$ be an adjunction between
$\infty$-categories. Then
the adjunction is comonadic if and only if:
\begin{enumerate}
\item $F$ is conservative.
\item Given a cosimplicial object $X^\bullet$ in $\mathcal{C}$ such that
$F(X^\bullet)$ admits a splitting, then $\mathrm{Tot}(X^\bullet)$ exists in
$\mathcal{C}$ and the map $F( \mathrm{Tot}(X^\bullet)) \to \mathrm{Tot}
F(X^\bullet)$ is an equivalence.
\end{enumerate}
\end{theorem}
In practice, we will be working with presentable $\infty$-categories, so the
existence of totalizations will be assured. The conditions of the
Barr-Beck-Lurie theorem are thus automatically satisfied if $F$ preserves
\emph{all} totalizations (as sometimes happens) and is conservative.
\begin{example}
Let $A \to B$ be a morphism of $\e{\infty}$-rings. The forgetful functor $\mathrm{Mod}(B) \to
\mathrm{Mod}(A)$ is conservative and preserves all
limits and \emph{colimits}. By the adjoint functor theorem, it is a
left adjoint. (The right adjoint to this functor sends an $A$-module $M$ to the $B$-module
$\hom_A(B, M)$.) By the Barr-Beck-Lurie theorem, this adjunction is comonadic.
\end{example}
However,
we will need to consider the more general case.
Given a comonadic adjunction as above, one can recover any object $C \in \mathcal{C}$ as the homotopy
limit of the \emph{cobar construction}
\begin{equation} \label{cobar} C \to \left(TC \rightrightarrows T^2 C \triplearrows
\dots \right), \end{equation}
where $T = GF$ is the induced comonad on $\mathcal{C}$.
The cobar construction is a cosimplicial diagram in $\mathcal{C}$ consisting of
objects which are in the image of $G$.
Here a fundamental distinction between $\infty$-category theory and 1-category
theory appears. In 1-category theory, the limit of a cosimplicial diagram can
be computed as a (reflexive) \emph{equalizer}; only the first zeroth and first
stage of the cosimplicial diagram are relevant. In $n$-category theory (i.e.,
$(n, 1)$-category theory), one only needs to work with the $n$-truncation of a
cosimplicial object. But in an $\infty$-category $\mathcal{C}$, given a
cosimplicial diagram $X^\bullet \colon \Delta \to \mathcal{C}$, one obtains a
\emph{tower} of partial totalizations
\[ \dots \to \mathrm{Tot}_n(X^\bullet) \to \mathrm{Tot}_{n-1}(X^\bullet) \to
\dots \to \mathrm{Tot}_1(X^\bullet) \to \mathrm{Tot}_0(X^\bullet), \]
whose homotopy inverse limit is the totalization or inverse limit
$\mathrm{Tot}(X^\bullet)$. By definition, $\mathrm{Tot}_n(X^\bullet)$ is the
inverse limit of the $n$-truncation of $X^\bullet$.
In an $n$-category, the above tower stabilizes at a finite stage: that is,
the successive maps $\mathrm{Tot}_m(X^\bullet) \to
\mathrm{Tot}_{m-1}(X^\bullet)$ become
equivalences for $m$ large (in fact, $m > n $). In
$\infty$-category theory, this is almost never expected. For example, it will
never hold for the cobar constructions that we obtain from descent
along maps of $\e{\infty}$-rings except in trivial cases. In particular, \eqref{cobar} is an infinite homotopy limit rather than
a finite one.
Nonetheless, there are certain types of towers that exhibit a weaker form
of stabilization, and behave close to finite
homotopy limits if one is willing to include retracts. Even with
$\infty$-categories, there are several instances where this weaker form of
stabilization occurs, and it is the purpose of this section to discuss that.
\subsection{Pro-objects}
Consider the following two towers of abelian groups:
\[ \xymatrix{
\vdots \ar[d] \\
\mathbb{Z} \ar[d]^2 \\
\mathbb{Z} \ar[d]^2 \\
\mathbb{Z}
} \quad \quad \quad \quad\quad\quad\quad\xymatrix{
\vdots \ar[d] \\
\mathbb{Z} \ar[d]^0 \\
\mathbb{Z} \ar[d]^0 \\
\mathbb{Z}
}.\]
Both of these have inverse limit zero. However, there is an essential
difference between the two. The second inverse system has inverse limit zero
for essentially ``diagrammatic'' reasons. In particular, the inverse limit
would remain zero if we applied any additive functor whatsoever. The first
inverse system has inverse limit zero for a more ``accidental'' reason: that
there are no integers infinitely divisible by two. If we tensored this inverse
system with $\mathbb{Z}[1/2]$, the inverse limit would be $\mathbb{Z}[1/2]$.
The essential difference can be described efficiently using the theory of
\emph{pro-objects}: the second inverse system is actually \emph{pro-zero},
while the first inverse system is a more complicated pro-object. The theory of
pro-objects (and, in particular, constant pro-objects) in
$\infty$-categories will be integral to our
discussion of descent, so we spend the present subsection reviewing it.
We begin by describing the construction that associates to a given $\infty$-category an
$\infty$-category of pro-objects. Although we have already used freely the
(dual) $\mathrm{Ind}$-construction, we review it formally for convenience.
\begin{definition}[{\cite[Section 5.3]{HTT}}]
Let $\mathcal{C}$ be an $\infty$-category with finite limits. Then the
$\infty$-category $\mathrm{Pro}(\mathcal{C})$ is an $\infty$-category with \emph{all}
limits, receiving a map $\mathcal{C} \to \mathrm{Pro}(\mathcal{C})$ with the following
properties:
\begin{enumerate}
\item $\mathcal{C} \to \mathrm{Pro}(\mathcal{C})$ respects finite limits.
\item Given an $\infty$-category $\mathcal{D}$ with all limits, restriction
induces an equivalence of $\infty$-categories
\[ \mathrm{Fun}^R(\mathrm{Pro}(\mathcal{C}), \mathcal{D}) \simeq
\mathrm{Fun}^\omega(\mathcal{C}, \mathcal{D}) \]
between the $\infty$-category
$\mathrm{Fun}^R(\mathrm{Pro}(\mathcal{C}), \mathcal{D}) $ of limit-preserving functors
$\mathrm{Pro}(\mathcal{C}) \to \mathcal{D}$ and the $\infty$-category
$\mathrm{Fun}^\omega(\mathcal{C}, \mathcal{D})$
of functors
$\mathcal{C} \to \mathcal{D}$ which preserve finite limits.
\end{enumerate}
\end{definition}
There are several situations in which the $\infty$-categories of pro-objects
can be explicitly described.
We refer to \cite[Sec. 3.2]{BHH} for a detailed discussion.
\begin{example}[{Cf. \cite[7.1.6]{HTT}}]
The $\infty$-category $\mathrm{Pro}(\mathcal{S})$
(where $\mathcal{S}$, as
usual, is the $\infty$-category of spaces)
can be described via
\[ \mathrm{Pro}(\mathcal{S}) \simeq
\mathrm{Fun}_{\mathrm{acc}}^{\omega-\mathrm{ct}}(\mathcal{S},
\mathcal{S})^{\mathrm{op}}; \]
that is, $\mathrm{Pro}(\mathcal{S})$ is anti-equivalent to the $\infty$-category of
accessible\footnote{In other words, commuting with sufficiently filtered
colimits.} functors $\mathcal{S} \to \mathcal{S}$ which respect finite limits.
This association sends a given space $X$ to the functor $\mathrm{Hom}(X,
\cdot)$ and sends formal cofiltered limits to filtered colimits of functors. \end{example}
\begin{example}
Similarly, one can describe the $\infty$-category
$\mathrm{Pro}(\sp)$ of \emph{pro-spectra} as the opposite to the $\infty$-category of
accessible, exact functors $\sp \to \sp$ (a spectrum $X$ is sent to
$\hom_{\sp}(X, \cdot)$ via the co-Yoneda embedding).
\end{example}
By construction, any object in $\mathrm{Pro}(\mathcal{C})$ can be written as a ``formal'' filtered
inverse limit of objects in $\mathcal{C}$: that is, $\mathcal{C}$ generates
$\mathrm{Pro}(\mathcal{C})$ under cofiltered limits. Moreover, $\mathcal{C}
\subset \mathrm{Pro}(\mathcal{C})$ as a full subcategory. If $\mathcal{C}$ is
idempotent complete, then $\mathcal{C} \subset \mathrm{Pro}(\mathcal{C})$ consists of
the cocompact objects.
\begin{remark}
If $\mathcal{C}$ is an ordinary category, then $\mathrm{Pro}(\mathcal{C})$ is a
discrete category (the usual pro-category) too.
\end{remark}
We now discuss the inclusion $\mathcal{C} \subset \mathrm{Pro}(\mathcal{C})$, where
$\mathcal{C}$ is an $\infty$-category with finite limits.
\begin{definition}
An object in $\mathrm{Pro}(\mathcal{C})$ is \textbf{constant} if it is equivalent to an
object in the image of $\mathcal{C} \to \mathrm{Pro}(\mathcal{C})$.
\end{definition}
\begin{proposition}
\label{whenisproobjconst}
Let $\mathcal{C}$ have finite limits.
A cofiltered diagram $F\colon I \to \mathcal{C}$ defines a constant pro-object if and
only if the following two conditions are satisfied:
\begin{enumerate}
\item $F$ admits a limit in $\mathcal{C}$.
\item Given any functor $G\colon \mathcal{C} \to \mathcal{D}$ preserving finite
limits, the inverse limit of $F$ is preserved
under $G$.
\end{enumerate}
\end{proposition}
In other words, the inverse limit of $F$ is required to exist for essentially
``diagrammatic reasons.''
\begin{proof}
One direction of this is easy to see (take $\mathcal{D} = \mathrm{Pro}(\mathcal{C})$).
Conversely, if $F$ defines a constant pro-object, then given $\mathcal{C} \to
\mathcal{D}$, we consider the commutative diagram
\[ \xymatrix{
\mathcal{C} \ar[d] \ar[r]^G & \mathcal{D} \ar[d] \\
\mathrm{Pro}(\mathcal{C}) \ar[r]^{\widetilde{G}} & \mathrm{Pro}(\mathcal{D})
}.\]
The functor $F\colon I \to \mathcal{C} \to \mathrm{Pro}(\mathcal{C})$ has an inverse limit,
which actually lands inside the full subcategory
$\mathcal{C} \subset \mathrm{Pro}(\mathcal{C})$. Since $\widetilde{G}\colon \mathrm{Pro}(\mathcal{C}) \to
\mathrm{Pro}(\mathcal{D})$ preserves all limits, it follows formally that $\widetilde{G} \circ F$
has an inverse limit lying inside $\mathcal{D} \subset \mathrm{Pro}(\mathcal{D})$ and
that $G$ preserves the inverse limit.
\end{proof}
\begin{example}[Split cosimplicial objects] \label{splitconst}
Let $\mathcal{C}$ be an $\infty$-category with finite limits.
Let $X^\bullet$ be a cosimplicial object of $\mathcal{C} $.
Suppose $X^\bullet$ extends to a \emph{split, augmented cosimplicial object}.
In this case, the pro-object associated to the
$\mathrm{Tot}$ tower of $X^\bullet$ (i.e., the tower
$\left\{\mathrm{Tot}_n X^\bullet\right\}$) is constant.
In fact,
let $\mathcal{D}$ be any $\infty$-category, and let $F\colon
\mathcal{C} \to \mathcal{D}$ be a functor. Let
$\overline{X}\colon \Delta^+ \to \mathcal{C}$ be the augmented cosimplicial object
extending $X^\bullet$ that can be split.
Then, by \cite[Section
4.7.3]{higheralg}, the composite
diagram
\[ \Delta_+ \stackrel{\overline{X}}{\to} \mathcal{C}
\stackrel{F}{\to} \mathcal{D}, \]
is a limit diagram: that is, $F( \overline{X}^{-1}) \simeq \mathrm{Tot} F(
X^\bullet)$, and in particular $\mathrm{Tot} F( X^\bullet)$ exists.
Suppose $\mathcal{D}$ admits finite limits and $F$ preserves finite limits.
Then $F( \mathrm{Tot}_n X^\bullet) \simeq \mathrm{Tot}_n F( X^\bullet)$, since
$F$ preserves finite limits, so that
\[ F(\overline{X}^{-1}) \simeq \mathrm{holim}_n \mathrm{Tot}_n F(X^\bullet) \simeq \mathrm{holim}_n F(
\mathrm{Tot}_n X^\bullet), \]
in $\mathcal{D}$. In particular, the tower $F( \mathrm{Tot}_n X^\bullet)$
converges to $F(\overline{X}^{-1})$.
By \Cref{whenisproobjconst}, this proves constancy as desired.
\end{example}
\begin{example}[Idempotent towers]
Let $X \in \mathcal{C}$ and let $e\colon X \to X$ be an \emph{idempotent} self-map;
this means not only that $e^2 \simeq e$, but a choice of coherent homotopies,
which can be expressed by the condition that one has an \emph{action} of the
monoid $\left\{1, x\right\}$ with two elements (where $x^2 =x$) on $X$. In this
case, the tower
\[
\dots \to X \stackrel{e}{\to} X \stackrel{e}{\to} X
,\]
is pro-constant if it admits a homotopy limit (e.g., if $\mathcal{C}$ is
idempotent complete). This holds for the same reasons: the image of an
idempotent is always a \emph{universal} limit (see \cite[Section 4.4.5]{HTT}).
\end{example}
Conversely, the fact that a pro-object indexed by a cofiltered diagram $F\colon I
\to\mathcal{C}$ is constant has many useful implications coming from the fact
that the inverse limit of $F$ is ``universal.''
\begin{example}
Let $(\mathcal{C}, \otimes, \mathbf{1})$ be a stable homotopy theory. Given
a cofiltered diagram $F\colon I \to \mathcal{C}$, it follows that if the induced
pro-object is constant, then for any $X \in \mathcal{C}$, the natural map
\[ (\varprojlim_I F(i)) \otimes X \to \varprojlim_I (F(i) \otimes X),\]
is an equivalence. See \Cref{dualthing}
below for a partial converse.
\end{example}
Next, we show that in a finite diagram of $\infty$-categories, a pro-object is
constant if and only if it is constant at each stage.
Let $K$ be a finite simplicial set, and let $F\colon K \to \mathrm{Cat}_\infty$ be a functor
into the $\infty$-category $\mathrm{Cat}_\infty$ of $\infty$-categories. Suppose that each
$F(k)$ has finite limits and each edge in $K$ is taken to a functor which
respects finite limits.
In this case, we obtain a natural functor
\begin{equation}\label{rkan} \mathrm{Pro} \left( \varprojlim_K F(k) \right)
\to \varprojlim_K \mathrm{Pro}( F(k)), \end{equation}
which respects all limits.
\begin{proposition}
The functor
$ \mathrm{Pro} \left( \varprojlim_K F(k) \right)
\to \varprojlim_K \mathrm{Pro}( F(k))$ is fully
faithful.
\end{proposition}
\begin{proof}
In fact, the functors $F(k) \to \mathrm{Pro}(F(k))$ are fully faithful for each $k \in
K$, so that
\[ \varprojlim_K F(k) \to \varprojlim_K \mathrm{Pro}( F(k)) \]
is fully faithful and respects finite limits.
In order for the right Kan extension
\eqref{rkan} to be fully faithful, it follows by \cite[Section 5.3]{HTT} that it suffices
for the embedding
$\varprojlim_K F(k) \to \varprojlim_K \mathrm{Pro}( F(k))$ to land in the
\emph{cocompact} objects. However, over a finite diagram of $\infty$-categories, an
object is cocompact if and only if it is cocompact pointwise, because finite
limits commute with filtered colimits in spaces.
\end{proof}
\begin{corollary}
\label{constantfinpro}
Let $K$ be a finite simplicial set and let $F\colon K \to \mathrm{Cat}_\infty$ be a functor as
above. Then a pro-object in
$\varprojlim_K F(k)$ is constant if and only if its evaluation in $\mathrm{Pro}( F(k))$
is constant for each vertex $k \in K$.
\end{corollary}
\begin{proof}
We have a commutative diagram
\[ \xymatrix{
\varprojlim_K F(k) \ar[d] \ar[r]^{\simeq} & \varprojlim_K F(k) \ar[d] \\
\mathrm{Pro}( \varprojlim_K F(k)) \ar[r] & \varprojlim_K \mathrm{Pro}(F(k))
},\]
where the bottom arrow is fully faithful. Given an object in $\mathrm{Pro}(
\varprojlim_K F(k))$, it is constant if and only if the image in $\varprojlim_K
\mathrm{Pro}(F(k))$ belongs to $\varprojlim_K F(k)$. Since each $F(k) \to \mathrm{Pro}(F(k))$
is fully faithful, this can be checked pointwise.
\end{proof}
\begin{remark}
The functor \eqref{rkan} is usually not essentially surjective; consider (with
$\mathrm{Ind}$-objects) for
instance the
failure of essential surjectivity in \Cref{modclosed}.
\end{remark}
\subsection{Descendable algebra objects}
Let $(\mathcal{C}, \otimes, \mathbf{1})$ be a 2-ring or a stable homotopy theory.
In this subsection, we will describe a definition of a commutative algebra object
in $\mathcal{C}$ which ``admits descent'' in a very strong sense, and prove
some basic properties.
We start by recalling a basic definition.
\begin{definition}
If $\mathcal{E}$ is a stable $\infty$-category, we will say that a full subcategory
$\mathcal{D} \subset \mathcal{E}$ is \textbf{thick} if $\mathcal{D}$ is closed
under finite limits and colimits and under retracts. In particular,
$\mathcal{D}$ is stable. Further, if $\mathcal{E}$ is given a symmetric
monoidal structure, then $\mathcal{D}$ is a \textbf{thick
$\otimes$-ideal} if in addition it is a $\otimes$-ideal.
Given a collection of objects in $\mathcal{E}$, the thick subcategory (resp.
thick $\otimes$-ideal) that they \textbf{generate} is defined to be the smallest
thick subcategory (resp. thick $\otimes$-ideal) containing that collection.
\end{definition}
The theory of thick subcategories, introduced in \cite{DHS, HS}, has played an important role in making
``descent'' arguments in proving the basic structural results of chromatic
homotopy theory. Thus, it is not too surprising that the following definition
might be useful.
This notion has been independently studied under the name \emph{nil-faithfulness} by Balmer
\cite{balmersep}.
\begin{definition} \label{admitd}
Given $A \in \mathrm{CAlg}(\mathcal{C})$, we will say that $A$ \textbf{admits descent}
or is \textbf{descendable}
if the thick $\otimes$-ideal generated by $A$ is all of $\mathcal{C}$.
More generally, in a stable homotopy theory $(\mathcal{C}, \otimes,
\mathbf{1})$, we will say that a morphism $A \to B$ in $\mathrm{CAlg}(\mathcal{C})$
\textbf{admits descent} if $B$, considered as a commutative algebra object in
$\mathrm{Mod}_{\mathcal{C}}(A)$, admits descent in the above sense.
\end{definition}
\newcommand{\mathrm{CB}^\bullet}{\mathrm{CB}^\bullet}
\newcommand{\mathrm{CB}_{\mathrm{aug}}^\bullet}{\mathrm{CB}_{\mathrm{aug}}^\bullet}
We now prove a few basic properties of the property of ``admitting descent,''
for instance the (evidently desirable) claim that an analog of \Cref{luried}
goes through. Here is the first observation.
\begin{proposition}
\label{faithful}
If $A \in \mathrm{CAlg}(\mathcal{C})$ admits descent, then $A$ is faithful: if $M \in
\mathcal{C}$, and $M \otimes A \simeq 0$, then $M$ is contractible.
\end{proposition}
\begin{proof}
Consider the collection of all objects $N \in \mathcal{C}$ such that $M \otimes
N \simeq 0$. This is clearly a thick $\otimes$-ideal. Since it contains $A$, it
must contain $\mathbf{1}$, so that $M$ is contractible.
\end{proof}
Given $A \in \mathrm{CAlg}(\mathcal{C})$, one can form the \emph{cobar resolution}
\[ A \rightrightarrows A \otimes A \triplearrows \dots, \]
which is a cosimplicial object in $\mathrm{CAlg}(\mathcal{C})$, receiving an
augmentation from $\mathbf{1}$.
Call this cosimplicial object $\mathrm{CB}^\bullet(A)$ and the augmented version
$\mathrm{CB}_{\mathrm{aug}}^\bullet(A)$.
\begin{proposition}
\label{constpro}
Given $A \in \mathrm{CAlg}(\mathcal{C})$, $A$ admits descent if and only if
the cosimplicial diagram $\mathrm{CB}^\bullet(A)$ defines a constant pro-object on
the level of towers $\left\{\mathrm{Tot}_n \mathrm{CB}^\bullet(A)\right\}_{n \geq 0}$ which
converges to $\mathbf{1}$ (i.e., $\mathrm{CB}_{\mathrm{aug}}^\bullet(A)$ is a limit diagram).
\end{proposition}
\begin{proof}
Suppose $A$ admits descent.
Consider the collection $\mathcal{C}_{\mathrm{good}}$ of $M \in \mathcal{C}$ such that the augmented
cosimplicial diagram $\mathrm{CB}_{\mathrm{aug}}^\bullet(A) \otimes M$ is a limit diagram, and such that
the induced $\mathrm{Tot}$ tower converging to $M$ defines a constant
pro-object. Our goal is to show that $\mathbf{1} \in
\mathcal{C}_{\mathrm{good}}$.
Note first that $A \in \mathcal{C}_{\mathrm{good}}$: in fact, the augmented
cosimplicial diagram $\mathrm{CB}_{\mathrm{aug}}^\bullet(A) \otimes A$ is \emph{split} and so is a limit
diagram and defines a constant pro-object (\Cref{splitconst}). Moreover, $\mathcal{C}_{\mathrm{good}}$ is a
thick $\otimes$-ideal.
The collection of pro-objects which are constant is thick, and the tensor
product of a constant pro-object with any object of $\mathcal{C}$ is constant (and the
limit commutes with the tensor product). Since $A \in \mathcal{C}_{\mathrm{good}}$, it
follows that $\mathbf{1} \in \mathcal{C}_{\mathrm{good}}$, which completes the
proof in one direction.
Conversely, if $\mathrm{CB}_{\mathrm{aug}}^\bullet(A)$ is a limit diagram, and $\mathrm{CB}^\bullet(A)$ defines a constant
pro-object,
it follows that $\mathbf{1}$ is a retract of $\mathrm{Tot}_n \mathrm{CB}^\bullet(A)$, for $n
\gg 0$. However, $\mathrm{Tot}_n \mathrm{CB}^\bullet(A)$ clearly lives in the thick
$\otimes$-ideal generated by $A$, which shows that $A$ admits descent.
\end{proof}
In other words, thanks to \Cref{constpro}, $A$ admits descent if and only if the unit object $\mathbf{1}$ can be
obtained as a retract of a finite colimit of a diagram in $\mathcal{C}$ consisting of
objects, each of which admits the structure of a module over $A$.
One advantage of the purely categorical (and finitistic) definition of
admitting descent is that it is preserved under base change. The next result
follows from \Cref{constpro}.
\begin{corollary}
Let $F\colon \mathcal{C} \to \mathcal{C}'$ be a symmetric monoidal functor between
symmetric monoidal, stable $\infty$-categories. Given $A \in
\mathrm{CAlg}(\mathcal{C})$, if $A$ admits descent, then $F(A)$ does as well.
\end{corollary}
\begin{proposition} \label{easydesc}
Let $\mathcal{C} $ be a stable homotopy theory.
Let $A \in \mathrm{CAlg}(\mathcal{C})$ admit descent. Then the adjunction
\[ \mathcal{C} \rightleftarrows \mathrm{Mod}_{\mathcal{C}}(A), \]
given by tensoring with $A$ and forgetting, is comonadic. In particular, the
natural functor from $\mathcal{C}$ to the totalization
\[ \mathcal{C} \to \mathrm{Tot}\left( \mathrm{Mod}_{\mathcal{C}}(A) \rightrightarrows
\mathrm{Mod}_{\mathcal{C}}(A \otimes A) \triplearrows \dots \right) \]
is an equivalence.
\end{proposition}
\begin{proof}
We need to check that the hypotheses of the Barr-Beck-Lurie theorem go through.
We refer to \cite[Th. 4.7.6.2]{higheralg} for the connection between
comonadicity and the totalization of $\infty$-categories considered above,
which is an $\infty$-categorical generalization of the classical
Beck-B{\'e}nabou-Roubaud theorem \cite{BRB}.
By \Cref{faithful}, tensoring with $A$ is conservative.
Now, fix a cosimplicial object $X^\bullet\colon \Delta \to \mathcal{C}$ such that $A
\otimes X^\bullet$ is split. We need to show
that the map
\[ A \otimes \mathrm{Tot}(X^\bullet) \to \mathrm{Tot}(A \otimes X^\bullet) \]
is an equivalence.
This will follow if the pro-object defined by $X^\bullet$ (i.e., by the
$\mathrm{Tot}$ tower) is constant. To see that, consider the collection of
objects $M \in \mathcal{C}$ such that $M \otimes X^\bullet$ defines a constant
pro-object. By assumption (and \Cref{splitconst}), this collection contains
$A$, and it is a thick $\otimes$-ideal. It follows that $X^\bullet$ itself defines
a constant pro-object, so we are done.
\end{proof}
\begin{remark}
We have used the fact that we have a symmetric monoidal functor $\mathcal{C}
\to \mathrm{Pro}( \mathcal{C})$, which embeds $\mathcal{C}$ as a full subcategory of
$\mathrm{Pro}( \mathcal{C})$: in particular, the tensor product of two constant
pro-objects in $\mathrm{Pro}(\mathcal{C})$ is constant.
\end{remark}
Finally, we prove a few basic permanence properties for admitting descent.
\begin{proposition} \label{permanence}
Suppose $\mathcal{C}$ is a stable homotopy theory.
Let $A \to B \to C$ be maps in $\mathrm{CAlg}(\mathcal{C})$.
\begin{enumerate}
\item If $A \to B$ and $B \to C$ admit descent, so does $A \to C$.
\item If $A \to C$ admits descent, so does $A \to B$.
\end{enumerate}
\end{proposition}
\begin{proof}
Consider the first claim.
Suppose $A \to B$ and $B \to C$ admit descent.
Then, via the cobar construction, we find that $B$ belongs to the thick subcategory of $\mathrm{Mod}_{\mathcal{C}}(B)$ generated by
the $C$-modules. It follows that $B$ belongs to the thick subcategory of
$\mathrm{Mod}_{\mathcal{C}}(A)$ generated by the $C$-modules, and therefore every $B$-module
belongs to the thick $\otimes$-ideal in $\mathrm{Mod}_{\mathcal{C}}(A)$ generated by $C$.
Since $A \to B$ admits descent, we find that the thick $\otimes$-ideal that $C$
generates in $\mathrm{Mod}_{\mathcal{C}}(A)$ contains $A$.
For the second claim, we note simply that a $C$-module is in particular a
$B$-module: the thick $\otimes$-ideal that $B$ generates contains any $B$-module,
for instance $C$.
\end{proof}
\begin{proposition}
\label{descfinloc}
Let $K$ be a finite simplicial set and let $p\colon K \to \mathrm{CAlg}( \mathrm{Pr}^L_{\mathrm{st}})$ be a diagram. Then
a commutative algebra object $A \in \mathrm{CAlg}( \varprojlim_K p)$ admits descent if
and only if its ``evaluations'' in $\mathrm{CAlg}( p(k))$ admit descent for each $k \in K$.
\end{proposition}
\begin{proof}
Admitting descent is preserved under symmetric monoidal, exact functors, so one
direction is evident. For the other, if $A \in \mathrm{CAlg}( \varprojlim_K p)$ has the
property that its image in each $\mathrm{CAlg}( p(k))$ admits descent, then consider the
cobar construction $\mathrm{CB}^\bullet(A)$. It defines a constant pro-object after evaluating
at each $k \in K$, and therefore, by \Cref{constantfinpro}, it defines a
constant pro-object in $\varprojlim_K p$ too. The inverse limit is necessarily
the unit (since this is true at each vertex), so $A$ admits descent.
\end{proof}
\subsection{Nilpotence}
In this subsection, we present a slightly different formulation of the
definition of admitting descent, which makes clear the connection with nilpotence.
Let $(\mathcal{C}, \otimes, \mathbf{1})$ be a stable homotopy theory and let
$A \in \mathcal{C}$ be any object.
Given a map $f\colon X \to Y$ in $\mathcal{C}$, we say that $f$ is \emph{$A$-zero}
if $A \otimes X \xrightarrow{1_A \otimes f} A \otimes Y$ is nullhomotopic (as
a morphism in $\mathcal{C}$).
The collection of all $A$-zero maps forms what is classically called a
\emph{tensor ideal} in the triangulated category $\mathrm{Ho}(\mathcal{C})$.
The main
result of this subsection is that a \emph{commutative algebra} object $A$ admits descent if and only if this ideal
is nilpotent, in a natural sense.
\begin{definition}
A collection $\mathcal{I}$ of maps in $\mathrm{Ho}(\mathcal{C})$
is a \textbf{tensor ideal} if the following hold:
\begin{enumerate}
\item
For each $X, Y$, the collection of homotopy classes of maps $X \to Y$ that
belong
to $\mathcal{I}$ is a subgroup.
\item Given $f\colon X \to Y, g\colon Y \to Z, h \colon Z \to W$, then if $g \in
\mathcal{I}$, we have $h \circ g \circ f \in \mathcal{I}$.
\item Given $g\colon Y \to Z$ in $\mathcal{I}$ and any other object $T \in
\mathcal{C}$, the tensor product $g \otimes 1_T\colon Y \otimes T \to Z \otimes T$
belongs to $\mathcal{I}$.
\end{enumerate}
\end{definition}
For any $A \in \mathcal{C}$, the collection of $A$-zero maps is clearly a
tensor ideal $\mathcal{I}_A$. Given two tensor
ideals $\mathcal{I}, \mathcal{J}$, we will define the product
$\mathcal{I}\mathcal{J}$ to be the smallest tensor ideal containing all
composites $g \circ f$ where $ f\in \mathcal{J}$ and $ g \in \mathcal{I}$.
\begin{proposition} \label{descnilp}
Let $A \in \mathrm{CAlg}(\mathcal{C})$ be a commutative algebra object.
Then the following are equivalent:
\begin{enumerate}
\item There exists $s \in \mathbb{N}$ such that the composite of $s$ consecutive $A$-zero
maps is zero.
\item $\mathcal{I}_A^s = 0$ for some $s \in
\mathbb{Z}_{\geq 0}$.
\item $A$ admits descent.
\end{enumerate}
\end{proposition}
This result is essentially \cite[Proposition 3.15]{balmersep}.
\begin{proof}
Suppose first $A$ admits descent. We want to show that $\mathcal{I}_A^s = 0$
for some $s \gg 0$. Now, $\mathcal{I}_\mathbf{1} =0$, so our strategy is to use
a thick subcategory argument.
We make the following three claims:
\begin{enumerate}
\item
If $M, N \in \mathcal{C}$, then $\mathcal{I}_M \subset \mathcal{I}_{M \otimes
N}$.
\item If $N$ is a retract of $M$, then $\mathcal{I}_M \subset \mathcal{I}_N$.
\item Given a cofiber sequence
\[ M' \to M \to M'' \]
in $\mathcal{C}$, we have
\[ \mathcal{I}_{M'}\mathcal{I}_{M''} \subset \mathcal{I}_M. \]
\end{enumerate}
Of these, the first and second are obvious. For the third, it suffices to show
that the composite of an $M'$-null map and an $M''$-null map is $M$-null.
Suppose $f\colon X \to Y$ is $M''$-null and $g\colon Y \to Z$ is $M'$-null. We want to
show that $g \circ f$ is $M$-null.
We have a diagram
\[ \xymatrix{
X \otimes M' \ar[d] \ar[r] & Y \otimes M' \ar[d] \ar[r] & Z \otimes M' \ar[d] \\
X \otimes M \ar[d] \ar[r] & Y \otimes M \ar[d] \ar[r] & Z \otimes M \ar[d] \\
X \otimes M'' \ar[r] & Y \otimes M'' \ar[r] & Z \otimes M''
}.\]
Here the vertical arrows are cofiber sequences. Chasing through this diagram,
we find that $X \otimes M \to Y \otimes M$ factors through $X \otimes M \to Y
\otimes M'$, so that the composite $X \otimes M \to Z \otimes M$ factors
through $X \otimes M \to Y \otimes M' \stackrel{0}{\to} Z \otimes M' \to Z
\otimes M$ and is thus nullhomotopic.
It thus follows (from the above three items) that if $M \in \mathcal{C}$ is arbitrary, then for any
$\overline{M} \in
\mathcal{C}$ belonging to the thick $\otimes$-ideal generated by $M$, we have
\[ \mathcal{I}_M^s \subset \mathcal{I}_{\overline{M}}, \]
for some integer $s \gg 0$. If $\mathbf{1} \in \mathcal{C}$ belongs
to this thick $\otimes$-ideal, that forces $\mathcal{I}_M$ to be nilpotent.
Conversely, suppose there exists $s \in \mathbb{Z}_{\geq 0}$ such that the composite of $s$ consecutive
$A$-zero maps is zero. We will show that $A$ admits descent.
Given an object $M \in \mathcal{C}$, we want to show that $M$ belongs to the
thick $\otimes$-ideal generated by $A$.
For this, consider the functor
\[ F_1(X) = \mathrm{fib}(X \to X \otimes A); \]
we have a natural map
\( F_1(X) \to X , \) which is $A$-zero, and whose cofiber belongs to the thick
$\otimes$-ideal generated by $A$. Iteratively define $F_n(X) = F_1(F_{n-1}(X))$ for
$n > 0$. We get a tower
\[ \dots \to F_n(M) \to F_{n-1}(M) \to \dots \to F_1(M) \to M, \]
where all the successive cofibers of $F_i(M) \to F_{i-1}(M)$ belong to the
thick $\otimes$-ideal generated by
$A$. By chasing cofiber sequences, this means that
the cofiber of each $F_i(M) \to M$ belongs to the thick $\otimes$-ideal generated
by $A$.
Moreover, each of the maps in this tower is $A$-zero.
It follows that $F_s(M) \to M$ is zero. Thus the cofiber of $F_s(M) \to M$ is
$M \oplus \Sigma F_s(M)$, which belongs to the thick $\otimes$-ideal generated by
$A$. Therefore, $M$ belongs to this thick $\otimes$-ideal, and we are done.
\end{proof}
\subsection{Local properties of modules}
In classical algebra, many properties of modules are local for the \'etale (or
flat) topology. These statements can be generalized to the setting of
$\e{\infty}$-ring
spectra, where
one considers morphisms $R \to R'$ of $\e{\infty}$-rings that are \'etale (or flat, etc.) on the
level of $\pi_0$ and such that the natural map $\pi_0 R' \otimes_{\pi_0 R}
\pi_* R \to \pi_* R'$ is an isomorphism.
Our next goal is to prove a couple of basic results in our setting
for
descendable morphisms.
\begin{proposition}
\label{compactdesc}
Let $A \to B$ be a descendable morphism of $\e{\infty}$-rings.
Let $M$ be an $A$-module such that $B \otimes_A M$ is a perfect $B$-module.
Then $M$ is a perfect $A$-module.
\end{proposition}
\begin{proof}
Consider a filtered category $\mathcal{I}$ and a functor $\iota\colon \mathcal{I}
\to \mathrm{Mod}(A)$. We then need to show that
\[ \varinjlim \hom_{A}(M, M_\iota) \to \hom_{A}(M, \varinjlim M_{\iota}) , \]
is an equivalence.
Consider the collection $\mathcal{U}$ of $A$-modules $N$ such that
\[ \varinjlim \hom_{A}(M, M_\iota \otimes_{A} N) \to \hom_{A}(M, \varinjlim M_{\iota}
\otimes_{A} N) , \]
is a weak equivalence; we would like to show that it contains
$A$ itself. The collection $\mathcal{U}$ clearly forms a thick subcategory.
Observe that it contains $N = B$ using the adjunction relation
\[ \hom_A(P, P' \otimes_A B) \simeq \hom_{B}(P \otimes_A B , P' \otimes_A B), \]
valid for $P, P' \in \mathrm{Mod}(A)$,
and the assumption that $M \otimes_A B$ is compact in $\mathrm{Mod}(B)$. More generally,
this implies that
every tensor product $B \otimes_A \dots \otimes_A B$ belongs to $\mathcal{U}$. Since $A$
is a retract of a finite limit of copies of such $A$-modules, via the cobar
construction, it follows that
$A \in \mathcal{C}$ and that $M$ is compact or perfect in $\mathrm{Mod}(A)$.
\end{proof}
\begin{remark}
More generally, the argument of \Cref{compactdesc} shows that if $\mathcal{C}$ is an $A$-linear
$\infty$-category, and $M \in \mathcal{C}$ is an object that becomes compact after
tensoring with $B$ (as an object of $\mathrm{Mod}_{\mathcal{C}}(B)$), then $M$ was compact
to begin with. \Cref{compactdesc} itself could have also been proved by observing
that $\mathrm{Mod}(A) $ is a totalization $\mathrm{Tot}\left(\mathrm{Mod}(B) \rightrightarrows \mathrm{Mod}(B \otimes_A B)
\triplearrows\right)$
by \Cref{easydesc}
and an $A$-module is thus dualizable (equivalently, compact) if
and only if its base-change to $\mathrm{Mod}(B)$ is, as dualizability in an inverse limit
of symmetric monoidal $\infty$-categories can be checked vertexwise (cf.
\cite[Prop. 4.6.1.11]{higheralg}).
\end{remark}
\begin{proposition}
Let $A \to B$ be a descendable morphism of $\e{\infty}$-rings. Let $M$ be an
$A$-module. Then $M$ is invertible if and only if $M \otimes_A B$ is invertible.
\end{proposition}
\begin{proof}
Observe first that $M \otimes_A B$ is perfect (since it is invertible), so
$M$ is also perfect via \Cref{compactdesc}. The evaluation map $M
\otimes_A M^{\vee} \to A$ has the property
that it becomes an equivalence after tensoring up to $B$, since the formation
of $M \mapsto M^{\vee}$ commutes with base extension for $M$ perfect. It
follows that $M \otimes_A M^{\vee} \to A$ is itself an equivalence, so that $M$
is invertible.
\end{proof}
Let $M$ be an $A$-module. If $A \to B$ is a descendable morphism of
$\e{\infty}$-rings such that $M \otimes_A B$ is a finite direct sum of copies
of $B$, the $A$-module $M$ itself need
not
look anything like a free module. (The finite covers explored in this paper are examples.)
However, such ``locally free'' $A$-modules seem to have interesting
and quite restricted properties.
\subsection{First examples}
In the following section, we will discuss more difficult examples of the
phenomenon of admitting descent, and try to give a better feel for it. Here, we describe
some relatively ``formal'' examples of maps which admit descent.
We start by considering the evident faithfully flat case.
In general, we \emph{do not know} if a faithfully flat map $A \to B$ of
$\e{\infty}$-ring spectra (i.e., such that $\pi_0(A) \to \pi_0(B)$ is
faithfully flat and such that $\pi_*(A) \otimes_{\pi_0(A)} \pi_0(B) \to
\pi_*(B)$ is an isomorphism) necessarily admits descent, even in the case of
discrete $\e{\infty}$-rings. This would have some implications. For example, if $A$ and $B$ are discrete commutative rings, it would imply that if $M$ is an $A$-module
and $\gamma \in \mathrm{Ext}^n_A(M, M)$ is a class whose image in
$\mathrm{Ext}^n_{B}(M \otimes_A B, M \otimes_A B)$ vanishes, then $\gamma$ is
nilpotent.
Nonetheless, one has:
\begin{proposition}
\label{ffdesc}
Suppose $A \to B$ is a faithfully flat map of $\e{\infty}$-rings such that
$\pi_*(A)$ is countable. Then $A \to B$ admits descent.
\end{proposition}
\begin{proof}
We can use the criterion of \Cref{descnilp}. We claim that we can take $s = 2$.
That is, given composable maps $M \to M' \to M''$ of $A$-modules each of which
becomes
nullhomotopic after tensoring up to $B$, the \emph{composite} is nullhomotopic.
To see this, we observe that any $B$-zero map in $\mathrm{Mod}(A)$ is \emph{phantom}. In
other words, if $M \to M'$ is $B$-zero, then any composite
\[ P \to M \to M', \]
where $P$ is a perfect $A$-module, is already nullhomotopic. To see this, note
that $P \to M'$ is $B$-zero, but to show that it is already nullhomotopic, we
can dualize and consider
\[ \pi_* ( \mathbb{D}P \otimes_A M') \to \pi_* ( \mathbb{D}P \otimes_A M'
\otimes_A B), \]
which is injective since $B$ is faithfully flat over $A$ on the level of
homotopy groups. The injectivity of this map forces any $B$-zero map $P \to M'$
to be automatically zero to begin with.
Finally, we can conclude if we know that the composite of two phantom maps in
$\mathrm{Mod}(A)$ is
zero. This claim is \cite[Theorem 4.1.8]{axiomatic}; we need countability of
$\pi_*(A)$ to conclude that homology theories on $A$-modules are representable
(by \cite[Theorem 4.1.5]{axiomatic}).
\end{proof}
Without the countability hypothesis, the result about phantom maps is known to
be false.
It is, however, possible to strengthen \Cref{ffdesc} using
more recent techniques of \emph{transfinite} Adams representabililty \cite{RM}. We are grateful to Oriol Ravent{\'os} for
explaining the following to us.
\begin{proposition}
Let $ A \to B$ be a faithfully flat morphism of $\e{\infty}$-rings such that
$\pi_*(A)$ has cardinality at most $\aleph_k$ for some $k \in \mathbb{N}$. Then
$A \to B$ admits descent.
\end{proposition}
\begin{proof}
As above, it suffices to show that the composite of $k + 2$ phantom maps of $A$-modules
is necessarily nullhomotopic.
Consider the class $\mathcal{C} = \mathrm{Perf}(A)$ of perfect $A$-modules, which
at most $\aleph_\kappa$ isomorphism classes of objects.
Consider the
category $\mathrm{Mod}(\mathcal{C})$ of functors
$\mathcal{C}^{op} \to \mathrm{Ab}$ which preserve finite coproducts.
Given any object $X \in \mathrm{Mod}(A)$, the Yoneda lemma gives an object $h_X \in
\mathrm{Mod}(\mathcal{C})$. Note that $h_X$ is a filtered colimit of functors
representable by objects in $\mathcal{C}$.
Taking $\alpha = \aleph_0$, we apply \cite[Prop. 2.13]{RM},
we find that $h_X$ for any $X \in \mathcal{C}$ has projective dimension $\leq
k+1$. By \cite[Cor. 6.3.5]{RM}, we find that $X$ is $(k+2)-\mathcal{C}$-cellular in the
sense of \cite[Def. 6.1.5]{RM}. Since $X$ was arbitrary, we find by \cite[Prop.
6.1.6]{RM} that the composite of $(k+2)$ phantom maps is zero.
\end{proof}
Since descendability is preserved under base change, we obtain:
\begin{corollary}
Let $A \to B$ be a faithfully flat map of $\e{\infty}$-rings such that
$\pi_0(B)$ has a presentation $\pi_0(A)$-algebra with at most $\aleph_k$
generators and relations for some $k \in \mathbb{N}$. Then $A \to B$
admits descent.
\end{corollary}
For example, a finitely presented faithfully flat map of discrete rings is
descendable. For a finitely presented map $A \to B$ of noetherian
rings, Bhatt and Scholze have shown \cite[Th. 5.26]{BhSch} that $A \to B$ is
admits descent if and only if $\mathrm{Spec}(B) \to \mathrm{Spec}(A)$ is an
$h$-cover, which is significantly weaker.
In addition to faithfully flat maps which are not too large, there are examples
of descendable maps of $\e{\infty}$-rings which look more like (relatively
mild) quotients.
\begin{proposition}
Suppose $A$ is an $\e{\infty}$-ring which is connective and such that $\pi_i A
= 0 $ for $i \gg 0$. Then the map $A \to \pi_0 A$ admits descent.
\end{proposition}
\begin{proof}
Given an $A$-module $M$ such that $\pi_*(M)$ is concentrated in one degree, it
admits the structure of a $\pi_0 A$-module (canonically) and thus belongs to
the thick $\otimes$-ideal generated by $\pi_0 A$. However, $A$ admits a
finite resolution by such $A$-modules, since one has a finite Postnikov
decomposition of $A$ in $\mathrm{Mod}(A)$ whose successive cofibers have a single
homotopy group, and therefore belongs to the thick $\otimes$-ideal generated by
$\pi_0 A$.
\end{proof}
\begin{proposition}
Let $R$ be a discrete commutative ring. Let $I \subset R$ be a nilpotent ideal.
Then the map $R \to R/I$ of discrete commutative rings, considered as a map of
$\e{\infty}$-rings, admits descent.
\end{proposition}
\begin{proof}
For $k \gg 0$, we have a finite filtration of $R$ in the world of discrete $R$-modules
\[ 0 = I^k \subset I^{k-1} \subset \dots \subset I \subset R, \]
whose successive quotients are $R/I$-modules. This implies that $R/I$ generates all of $\mathrm{Mod}(R)$ as a thick $\otimes$-ideal.
\end{proof}
There are also examples of descendable morphisms where the condition on the
thick $\otimes$-ideals follows from a defining limit diagram.
\begin{proposition}
Let $R$ be an $\e{\infty}$-ring and let $X$ be a finite connected CW complex. Then the
map $C^*(X; R) \to R$ given by evaluating at a basepoint $\ast \in X$ admits
descent.
\end{proposition}
\begin{proof}
In fact, the $\e{\infty}$-ring $C^*(X; R)$ is a finite limit (indexed by $X$) of copies of $R$ by definition.
That is, $C^*(X; R) \simeq \varprojlim_X R$.
\end{proof}
\begin{proposition}
Let $R $ be an $\e{\infty}$-ring and let $x \in \pi_0 R$. Then the map $R \to
R[x^{-1}] \times \widehat{R}_x$ (where $\widehat{R}_x$ is the $x$-adic
completion) admits descent.
\end{proposition}
\begin{proof}
This follows from the arithmetic square
\[ \xymatrix{
R \ar[d] \ar[r] & R[x^{-1}] \ar[d] \\
\widehat{R}_x \ar[r] & \widehat{R}_x[x^{-1}]
}.\]
All three of the terms in the fiber product here are $R[x^{-1}] \times
\widehat{R}_x$-modules, so $R$ belongs to the thick subcategory generated by the
$R[x^{-1}] \times
\widehat{R}_x$-modules and we are done.
\end{proof}
Next we include a deeper result, which will imply (for example) that the faithful Galois
extensions considered by \cite{rognes} admit descent; this will be very
important in the rest of the paper.
The theory of nilpotence with respect to a dualizable algebra object
has been treated in more detail in \cite{MNNequiv}.
\begin{theorem}
\label{cptdescent}
Let $\mathcal{C}$ be a stable homotopy theory.
Suppose $\mathbf{1} \in \mathcal{C}$ is compact, and suppose $A \in
\mathrm{CAlg}(\mathcal{C})$ is dualizable and faithful (i.e., tensoring with $A$ is
conservative). Then $A$ admits descent.
\end{theorem}
\begin{proof}
Consider the cobar construction $\mathrm{CB}^\bullet(A)$ on $A$. The first claim is that it
converges to $\mathbf{1}$: that is, the augmented cosimplicial construction
$\mathrm{CB}_{\mathrm{aug}}^\bullet(A)$ is a limit diagram. To see this, we can apply the Barr-Beck-Lurie
theorem to $A$. Since $A$ is dualizable, we have
for $X, Y \in \mathcal{C}$,
\[ \hom_{\mathcal{C}}(Y, A \otimes X) \simeq \hom_{\mathcal{C}}( \mathbb{D}A
\otimes Y, X), \]
and in particular tensoring with $A$ commutes with all limits in $\mathcal{C}$.
Since tensoring with $A$ is conservative, we find that the hypotheses of the
Barr-Beck-Lurie theorem go into effect (cf. also \cite[2.6]{banerjee}). In particular, $\mathrm{CB}^\bullet(A)$ converges to
$\mathbf{1}$ and, moreover, for any $M \in \mathcal{C}$, $\mathrm{CB}^\bullet(A) \otimes M $
converges to $M$.
We need to show that the induced pro-object is \emph{constant}, though. This
will follow from the next lemma.
\end{proof}
\begin{lemma}
\label{dualthing}
Let $(\mathcal{C}, \otimes, \mathbf{1})$ be a stable homotopy
theory where $\mathbf{1}$ is compact.
Let $I$ be a cofiltered category, and let $F\colon I \to \mathcal{C}$ be a functor.
Suppose that for each $i \in I$, $F(i) \in \mathcal{C}$ is dualizable. Then
$F$ defines a constant pro-object (or is \emph{pro-constant}) if and only if the following are satisfied.
\begin{enumerate}
\item $\varprojlim_I F(i)$ is a dualizable object.
\item For each object $C \in \mathcal{C}$, the natural map
\begin{equation} \label{thismap} ( \varprojlim_I F(i)) \otimes C \to
\varprojlim_I (F(i) \otimes C) \end{equation}
is an equivalence.
\end{enumerate}
\end{lemma}
\begin{proof}
Let $\mathbb{D}$ be the duality functor (of internal hom into $\mathbf{1}$); it
induces a contravariant auto-equivalence
on the subcategory $\mathcal{C}^{\mathrm{dual}}$ of dualizable objects in $\mathcal{C}$.
To say that $F$ defines a constant pro-object in $\mathcal{C}$ (or,
equivalently,
$\mathcal{C}^{\mathrm{dual}}$)
is to say that
$\mathbb{D}F$, which is an \emph{ind}-object of
$\mathcal{C}^{\mathrm{dual}}$, defines a constant ind-object. In other words, we
have a commutative diagram
of $\infty$-categories,
\[ \xymatrix{
\mathcal{C}^{\mathrm{dual}} \ar[d]^{\subset} \ar[r]_{\simeq}^{\mathbb{D}} &
\mathcal{C}^{\mathrm{dual, \ op}} \ar[d]^{\subset} \\
\mathrm{Pro}(\mathcal{C}^{\mathrm{dual}}) \ar[d]^{\subset}\ar[r]_{\simeq}^{\mathbb{D}} &
\mathrm{Ind}(\mathcal{C}^{\mathrm{dual}})^{\mathrm{op}} \\
\mathrm{Pro}(\mathcal{C})
}.\]
Now, since $\mathcal{C}^{\mathrm{dual}} \subset \mathcal{C}$ consists of compact
objects (since $\mathbf{1} \in \mathcal{C}$ is compact), we know that
there is a fully faithful inclusion $\mathrm{Ind}( \mathcal{C}^{\mathrm{dual}})
\subset \mathcal{C}$, which sends an ind-object to its colimit. If $\mathcal{C}$ is generated by dualizable objects, this
is even an equivalence, but we do not need this.
As a result, to show that $\mathbb{D}F \in \mathrm{Ind}(
\mathcal{C}^{\mathrm{dual}})$ defines a constant ind-object, it is sufficient to
show that its colimit in $\mathcal{C}$ actually belongs to
$\mathcal{C}^{\mathrm{dual}}$.
Let $X = \varprojlim_I F(i) \in \mathcal{C}$; by hypothesis, this is a
dualizable object.
We have a natural map (in $\mathcal{C}$)
\[ \varinjlim_I \mathbb{D} F(i) \to \mathbb{D} X, \]
and if we can prove that this is an equivalence, we will have shown that
$\varinjlim_I \mathbb{D} F(i)$ is a dualizable object and thus the ind-system
is constant. In other words, we must show that if $C \in \mathcal{C}$ is
arbitrary, then the natural map
of spectra
\[ \hom_{\mathcal{C}}(\mathbb{D}X, C) \to \varprojlim_I
\hom_{\mathcal{C}}(\mathbb{D} F(i), C) \]
is an equivalence. But this map is precisely
$\hom_{\mathcal{C}}(\mathbf{1}, \cdot)$ applied to \eqref{thismap}, so we are done.
\end{proof}
\begin{remark}
This result requires $\mathbf{1}$ to be compact. If $\mathcal{C}$
is the stable homotopy theory of $p$-adically complete chain complexes of
abelian groups (i.e., the localization of $D(\mathbb{Z})$ at
$\mathbb{Z}/p\mathbb{Z}$), then $\mathbb{Z}/p\mathbb{Z}$ is a
dualizable, faithful commutative
algebra object, but the associated pro-object is not constant, or the
$p$-adic integers $\mathbb{Z}_p$ would be torsion.
\end{remark}
\begin{remark}
One can prove the same results (e.g., \Cref{cptdescent}) if $A \in \mathcal{C}$ is given an
\emph{associative} (or $\e{1}$) algebra structure, rather than an
$\e{\infty}$-algebra structure. However, the symmetric monoidal structure on
$\mathcal{C}$ itself is crucial throughout.
\end{remark}
\subsection{Application: descent for linear $\infty$-categories}
In fact, the definition of descent considered here gives a more
general result than \Cref{easydesc}. Let
$\mathcal{C}$ be an $A$-linear $\infty$-category in the sense of \cite{DAGss}.
In other words, $\mathcal{C}$ is a presentable, stable $\infty$-category which
is a \emph{module} in the symmetric monoidal $\infty$-category $\mathrm{Pr}^L$ of presentable,
stable $\infty$-categories over $\mathrm{Mod}(A)$. This means that there is a bifunctor, which preserves colimits in each variable,
\[ \otimes_A\colon \mathrm{Mod}(A) \times \mathcal{C} \to \mathcal{C} , \quad (M, C) \mapsto M \otimes_A
{C} \]
together with additional compatibility data: for instance, equivalences $A \otimes_A M
\simeq M$ for each $M \in \mathcal{C}$.
Given such a $\mathcal{C}$, one can study, for any $A$-algebra $B$, the
$\infty$-category $\mathrm{Mod}_{\mathcal{C}}(B)$ of $B$-modules \emph{internal to $\mathcal{C}$}: this is the
``relative tensor product'' in $\mathrm{Pr}^L$
\[ \mathrm{Mod}_{ \mathcal{C}}(B) = \mathcal{C} \otimes_{\mathrm{Mod}(A)} \mathrm{Mod}(B). \]
Useful references for this, and for the tensor product of presentable
$\infty$-categories, are \cite{gaitsnotes} and \cite{BFN}.
Informally, $\mathrm{Mod}_{\mathcal{C}}(B)$ is the target of an $A$-bilinear functor
\[ \otimes_A\colon \mathcal{C} \times \mathrm{Mod}(B) \to \mathrm{Mod}_{\mathcal{C}}(B), \quad (X, M) \mapsto X
\otimes_A M,\]
which is colimit-preserving in each variable, and it is universal for such.
As in the case $\mathcal{C} = \mathrm{Mod}(A)$, one has an adjunction
\[ \mathcal{C} \rightleftarrows \mathrm{Mod}_{\mathcal{C}}(B), \]
given by ``tensoring up'' and forgetting the $B$-module structure.
One can then ask whether descent holds in $\mathcal{C}$, just as we studied
earlier for $A$-modules. In other words, we can ask whether
$\mathcal{C}$ is equivalent to the $\infty$-category of
$B$-modules in $\mathcal{C}$ equipped with analogous ``descent data'':
equivalently, whether the ``tensoring up'' functor
$\mathcal{C} \to \mathrm{Mod}_{\mathcal{C}}(B)$ is comonadic.
Stated another way,
we are asking whether, for any $\mathrm{Mod}(A)$-module
\emph{$\infty$-category} $\mathcal{C}$, we have an equivalence
of $A$-linear $\infty$-categories
\begin{equation}\label{Alineardescent} \mathcal{C} \simeq \mathrm{Tot}\left( \mathcal{C} \otimes_{\mathrm{Mod}(A)}
\mathrm{Mod}(B)^{\otimes (\bullet+1)}\right). \end{equation}
In fact, the proof of \Cref{easydesc} applies and we get:
\begin{corollary}
\label{proconstdescentC}
Suppose $A \to B$ is a descendable morphism of $\e{\infty}$-rings.
Then $A \to B$ satisfies descent for any $A$-linear $\infty$-category
$\mathcal{C}$ in that
the functor
from
$\mathcal{C} $
to ``descent data''
is an equivalence.
\end{corollary}
\begin{proof}
By the Barr-Beck-Lurie theorem, we need to see that tensoring with $B$ defines a conservative functor
$\mathcal{C} \to \mathrm{Mod}_{\mathcal{C}}(B)$ which respects $B$-split totalizations.
Conservativity can be proved as in \Cref{faithful}. Given $R \in \mathcal{C}$,
the collection of $A$-modules $M$ such that $M \otimes_A R \simeq 0$ is a thick
$\otimes$-ideal in $\mathrm{Mod}(A)$. If $B$ belongs to this thick $\otimes$-ideal, so must $A$, and $R$
must be zero.
Let $X^\bullet\colon \Delta \to \mathcal{C}$ be a cosimplicial object which becomes
split after tensoring with $B$. As in \Cref{easydesc}, it suffices to show that
the pro-object that $X^\bullet$ defines is constant in $\mathcal{C}$.
This follows via the same thick subcategory argument: one considers the
collection of $M \in \mathrm{Mod}(A)$ such that $X^\bullet \otimes_A M$ defines a
constant pro-object, and observes that $M$ is a thick $\otimes$-ideal containing
$B$, thus containing $A$.
Thus $X^\bullet$ defines a constant pro-object.
\end{proof}
We note that the argument via pro-objects yields a mild strengthening of the
results in the DAG series.
In particular, it shows that if $A \to B$ is a morphism
of $\e{\infty}$-rings which is faithfully flat and presented by at most
$\aleph_k$ generators and relations (for some $k \in \mathbb{N}$), it satisfies descent for any $A$-linear
$\infty$-category. In the DAG series, this is proved assuming
\emph{\'etaleness}
\cite[Th. 5.4]{DAGdesc}
or for faithfully flat morphisms assuming existence of a
$t$-structure \cite[Th. 6.12]{DAGss}. In fact, this idea of descent via thick subcategories seems to be the
right setting for considering the above questions, in view of the following
result, which was explained to us by Jacob Lurie:
\begin{proposition}
Let $A \to B$ be a morphism of $\e{\infty}$-rings such that, for any $A$-linear
$\infty$-category, descent holds, i.e., we have an equivalence \eqref{Alineardescent}.
Then $A \to B$ admits descent.
\end{proposition}
\begin{proof}
Suppose $A \to B$ does not admit descent. We will look for a counterexample
to \eqref{Alineardescent}.
We will exhibit an $A$-linear presentable $\infty$-category $\mathcal{D}$ and an object $X
\in \mathcal{D}$ such that the totalization of the cobar construction $\mathrm{CB}^\bullet(B)
\otimes_A X$ is not equivalent to $X$.
The idea is to take $\mathcal{D} = \mathrm{Pro}( \mathrm{Mod}(A))$ and $X = A$.
Consider the cobar construction $B \rightrightarrows
B \otimes_A B\triplearrows \dots$. The totalization of the cobar construction in $\mathrm{Pro}(\mathrm{Mod}(A))$ is
\emph{precisely} the cobar construction considered as a pro-object via the
$\mathrm{Tot}$ tower. In particular, if $A \to B$ fails to admit
descent, the cobar construction does not converge to $A$ in $\mathrm{Pro}(\mathrm{Mod}(A))$.
In order to make this argument precise, we have to address the fact that $\mathrm{Pro}(
\mathrm{Mod}(A))$ is not really an $A$-linear $\infty$-category: it is not, for example,
presentable.
Choose a regular cardinal $\kappa$ such that $B$ is $\kappa$-compact as an
$A$-module.
Choose a small subcategory $\mathcal{C} \subset \mathrm{Pro}( \mathrm{Mod}(A))$ which contains
the constant object $A$ and is closed under $\kappa$-small colimits and
countable limits.
Then $\mathcal{C}$ is tensored over the $\infty$-category $\mathrm{Mod}^\kappa(A)$
of $\kappa$-compact $A$-modules, so the presentable
$\infty$-category $\mathcal{D} = \mathrm{Ind}_\kappa(\mathcal{C})$ is tensored over $\mathrm{Mod}(A)$
in a compatible manner. Moreover, in this $\infty$-category the totalization of
the cobar construction $B \rightrightarrows B \otimes_A B \triplearrows \dots$
does not converge to $A$ as that does not happen in $\mathcal{C}$.
\end{proof}
Finally, we note a ``categorified'' version of
descent, which, while likely far from the strongest possible, is already of interest in
studying the Brauer group of $\e{\infty}$-rings such as $\mathrm{TMF}$.
This phenomenon has been extensively studied (under the name ``1-affineness'')
in \cite{gaits}. We will only consider a very simple and special case of this question.
The idea is that instead of considering descent for modules over
a ring spectrum $R$ (possibly internal to a linear $\infty$-category), we will
consider descent for the linear $\infty$-categories themselves, which we
will call \emph{2-modules},
meaning modules \emph{over} the presentable, symmetric monoidal
$\infty$-category $\mathrm{Mod}( R)$.
\newcommand{\operatorname{2-Mod}}{\operatorname{2-Mod}}
\begin{definition}
Given an $\e{\infty}$-ring $R$, there is a symmetric monoidal $\infty$-category
$\operatorname{2-Mod}(R)$
of $R$-linear
$\infty$-categories with the $R$-linear tensor product. In other words, $\operatorname{2-Mod}(R)$ consists of modules (in the
symmetric monoidal $\infty$-category of presentable, stable
$\infty$-categories) over $\mathrm{Mod}(R)$.
\end{definition}
For a useful reference, see \cite{gaitsnotes, AntieauGepner}.
We now record:
\begin{proposition}
\label{2descformal}
Let $A \to B$ be a descendable morphism of $\e{\infty}$-rings. Then $\operatorname{2-Mod}$ satisfies descent along $A \to B$.
\end{proposition}
As noted in \cite{gaits} and \cite{DAGdesc}, this is a formal consequence of
descent in linear $\infty$-categories (that is, \Cref{proconstdescentC}), but we recall the proof for convenience.
\begin{proof}
Recall that we have the adjunction
\[ (F, G) = \left( \otimes_{\mathrm{Mod}(A)} \mathrm{Mod}(B), \ \mathrm{forget}\right) \colon \quad \operatorname{2-Mod}(A) \rightleftarrows \operatorname{2-Mod}(B) , \]
where $G$ is the forgetful functor from $B$-linear $\infty$-categories to
$A$-linear $\infty$-categories, and where $F$ is ``tensoring up.''
The assertion of the proposition is that this adjunction is comonadic.
By the Barr-Beck-Lurie theorem, it suffices to show now that $F$ is
conservative and preserves certain totalizations.
But $F$ is conservative
because any $\mathcal{C}$-linear $\infty$-category can be recovered from its
``descent data'' after tensoring up to $B$ (\Cref{proconstdescentC}).
Moreover, $F$ commutes with all limits. In fact, $F$ sends an $A$-linear
$\infty$-category $\mathcal{C}$ to the collection of $B$-module objects in
$\mathcal{C}$, and this procedure is compatible with limits.
\end{proof}
It would be interesting to give conditions under which one could show that a
2-module over $R$ admitted a compact generator if and only if it did so locally
on $R$ in some sense. This would yield a type of descent for the \emph{Brauer
spectrum} of $R$ (see for instance
\cite{AntieauGepner}),
whose $\pi_0$ consists of equivalence classes of invertible 2-modules that
admit a compact generator. Descent for compactly generated $R$-linear
$\infty$-categories is known to hold in the \emph{usual} \'etale
topology on $\e{\infty}$-rings \cite[Theorem 6.1]{DAGdesc}, although the proof is long and
complex. Descent also holds for the finite covers considered in this paper
which are \emph{faithful}. It would be interesting to see if it held for $L_n S^0 \to
E_n$, possibly in some $K(n)$-local sense.
\label{lindesc}
\section{Nilpotence and Quillen stratification}
Let $(\mathcal{C}, \otimes, \mathbf{1})$ be a stable homotopy theory.
Let $A \in \mathrm{CAlg}(\mathcal{C})$ be a commutative algebra object in $\mathcal{C}$.
In general, we might hope that (for whatever reason) phenomena in
$\mathrm{Mod}_{\mathcal{C}}(A)$ might be simpler to understand than phenomena in
$\mathcal{C}$. For example, if $\mathcal{C} = \sp$, we do not know the homotopy
groups of the sphere spectrum, but there are many $\e{\infty}$-rings whose
homotopy groups we do know completely: for instance, $H \mathbb{F}_p$ and $MU$.
We might then try to use our knowledge of $A$ and some sort of descent to
understand phenomena in $\mathcal{C}$. For instance, we might attempt to
compute the homotopy groups of an object $M \in \mathcal{C}$ by constructing
the cobar resolution
\[ M \to \left( M \otimes A \rightrightarrows M \otimes A \otimes A
\triplearrows \dots \right), \]
and hope that it converges to $M$. This method is essentially the \emph{Adams
spectral sequence}, which, in case $\mathcal{C} = \sp$, is one of the most
important tools one has for calculating
and understanding the stable homotopy groups of spheres.
In the previous section, we introduced a type of commutative algebra object $A
\in \mathrm{CAlg}(\mathcal{C})$ such that, roughly, the above descent method converged
very efficiently --- much more efficiently, for instance, than the classical
Adams or Adams-Novikov spectral sequences. One can see this at the level of descent spectral sequences in the
existence of \emph{horizontal vanishing lines} that occur at finite stages.
In particular, in this situation, one can understand phenomena in $\mathcal{C}$
from phenomena in $\mathrm{Mod}_{\mathcal{C}}(A)$ and $\mathrm{Mod}_{\mathcal{C}}(A \otimes A)$
``up to (bounded) nilpotence.'' We began discussing this in \Cref{descnilp}. The purpose
of this section is to continue that discussion and to describe several
fundamental (and highly non-trivial) examples of commutative algebra
objects that admit descent.
These ideas have also been explored in \cite{balmersep}, and we learned of the
connection with Quillen stratification from there.
\subsection{Descent spectral sequences}
Let $\mathcal{C}$ be a stable homotopy theory.
Let $A \in \mathrm{CAlg}(\mathcal{C})$ and let $M \in \mathcal{C}$. As usual, we can try
to study $M$ via the $A$-module $M \otimes A$ and, more generally, the cobar
construction $M \otimes \mathrm{CB}^\bullet(A)$.
In this subsection, we will describe the effect of descendability on
the resulting spectral sequence.
\begin{definition}
The $\mathrm{Tot}$ tower of the cobar construction $M \otimes \mathrm{CB}^\bullet(A)$ is called
the \textbf{Adams tower} $\{T_n(A, M)\}$ of $M$.
The induced spectral sequence converging to $\pi_* \varprojlim ( M \otimes
\mathrm{CB}^\bullet(A))$ is called the \textbf{Adams spectral sequence} for $M$ (based on $A$).
\end{definition}
The Adams tower has the property
that it comes equipped with maps
\[ \xymatrix{
& \vdots \ar[d] \\
& T_2(A, M) \ar[d] \\
& T_1(A, M) \ar[d] \\
M \ar[ru] \ar[ruu] \ar[r] & T_0(A, M) \simeq A \otimes M
}.\]
In other words, it is equipped with a map from the \emph{constant} tower at
$M$. We let the cofiber of this map of towers be $\left\{U_n(A, M)\right\}_{n
\geq 0}$.
The tower $\left\{U_n(A, M)\right\}$ has the property that the cofiber of any map $U_n(A, M)
\to U_{n-1}(A, M)$ admits the structure of an $A$-module. Moreover, each map
$U_n(A, M) \to U_{n-1}(A, M)$ is null after tensoring
with $A$.
Suppose now that $A$ \emph{admits descent.} In this case, the towers we are
considering have particularly good properties.
\newcommand{\mathrm{Tow}}{\mathrm{Tow}}
\begin{definition}[\cite{HPS, thick}]
Let $\mathrm{Tow}(\mathcal{C}) = \mathrm{Fun}( \mathbb{Z}_{\geq 0}^{\mathrm{op}},
\mathcal{C})$ be the $\infty$-category
of towers in $\mathcal{C}$.
We shall say that a tower $\left\{X_n\right\}_{n
\geq 0}$ is \textbf{nilpotent} if
there exists $N$ such that $X_{n+N} \to X_n$ is null for each $n \in
\mathbb{Z}_{\geq 0}$.
It is shown in \cite{HPS} that the collection of nilpotent towers is a thick
subcategory of $\mathrm{Tow}(\mathcal{C})$. We shall say that a tower is
\textbf{strongly constant} if it belongs to the thick subcategory of
$\mathrm{Tow}(\mathcal{C})$ generated by the nilpotent towers and the constant towers.
\end{definition}
Observe that a nilpotent tower is pro-zero, and a strongly constant tower is
pro-constant. In general, nilpotence of a tower is \emph{much} stronger than
being pro-zero. For example, a tower $\left\{X_n\right\}$ is pro-zero if there is a
cofinal set of integers $i$ for which the $X_i$ are contractible. This does not
imply nilpotence.
We now recall the following fact about strongly constant towers:
\begin{proposition}[\cite{HPS}] Let $\{X_n\}_{n \geq 0} \in \mathrm{Tow}(\mathcal{C})$ be a strongly
constant tower. Then, for $Y \in \mathcal{C}$, the spectral sequence for $\pi_* \hom(Y, \varprojlim X_n)$
has a horizontal vanishing line at a finite stage.
\end{proposition}
In fact, in \cite{HPS}, it is shown that admitting such horizontal vanishing
lines is a \emph{generic} property of objects in $\mathrm{Tow}(\mathcal{C})$: that is,
the collection of objects with that property is a thick subcategory. Moreover,
this property holds for nilpotent towers and for constant towers.
\begin{corollary}
Let $A \in \mathrm{CAlg}(\mathcal{C})$ admit descent. Then the Adams tower
$\left\{T_n(A, M)\right\}$ is strongly constant.
In particular, the Adams spectral sequence converges with a horizontal
vanishing line at a finite stage (independent of $M$).
\end{corollary}
\begin{proof}
In fact, by \Cref{descnilp}, it follows that the tower $\left\{U_n(A,
M)\right\}$ is nilpotent, since all the successive maps in the tower are
$A$-zero, so the tower $\left\{T_n(A, M)\right\}$ is therefore strongly constant.
\end{proof}
It follows from this that we can get a rough global description of the
graded-commutative ring $\pi_*
\mathbf{1}$ if we have a description of $\pi_* A$. This is the description that
leads, for instance, to the description of various group cohomology rings ``up
to nilpotents.''
\begin{theorem} \label{Fiso}
Let $A \in \mathrm{CAlg}(\mathcal{C})$ admit descent.
Let $R_*$ be the equalizer of $\pi_*(A) \rightrightarrows \pi_*(A \otimes A)$.
There is a map $\pi_* ( \mathbf{1}) \to R_*$ with the following properties:
\begin{enumerate}
\item The kernel of $\pi_*(\mathbf{1} ) \to R_*$ is a nilpotent ideal.
\item Given an element $x \in R_*$ with $Nx = 0$, then $x^{N^k}$ belongs to the
image of $\pi_* ( \mathbf{1}) \to R_*$ for $k \gg 0$ (which can be chosen
uniformly in $N$).
\end{enumerate}
\end{theorem}
In the examples arising in practice, one already has a complete or
near-complete picture \emph{rationally}, so the torsion information is the
most interesting. For example, if $p $ is nilpotent in $\pi_* (\mathbf{1} )$,
then the map that one gets is classically called a \emph{uniform
$F$-isomorphism}.
\begin{proof}
In fact, $R_*$ as written is the zero-line (i.e., $s = 0$) of the $E_2$-page of
the $A$-based Adams spectral sequence converging to the homotopy groups of $\mathbf{1}$.
The map that we have written down is precisely the edge homomorphism in the
spectral sequence. We know that anything of positive filtration at $E_\infty$
must be nilpotent of bounded order because of the horizontal vanishing line.
That implies the first claim.
For the second claim, let $x \in E_2^{0, t}$ be
$N$-torsion. We want to show that $x^{N^k}$ survives the spectral sequence for
some $k$ (which can be chosen independently of $x$).
In fact, $x^N$ can support no $d_2$ by the Leibnitz rule. Similarly, $x^{N^2}$
can support no $d_3$ and survives until $E_4$. Since the spectral sequence
collapses at a finite stage, we conclude that some $x^{N^k}$ must survive, and
$k$ depends only on the finite stage at which the spectral sequence collapses.
\end{proof}
\begin{remark}
One can obtain an analog of \Cref{Fiso} for any commutative algebra object in
$\mathcal{C}$ replacing $\mathbf{1}$.
\end{remark}
\subsection{Quillen stratification for finite groups}
Let $G$ be a finite group, and let $R$ be a (discrete) commutative ring.
Consider the $\infty$-category $\mathrm{Mod}_G(R) \simeq \mathrm{Fun}(BG, \mathrm{Mod}(R))$ of $R$-module spectra with a
$G$-action (equivalently, the $\infty$-category of module spectra over the
\emph{group ring}), which is symmetric monoidal under the $R$-linear tensor product.
Given a subgroup $H \subset G$, we have a natural symmetric monoidal functor
\[ \mathrm{Mod}_G(R) \to \mathrm{Mod}_H(R), \]
given by restricting the $G$-action to $H$.
As in ordinary algebra, we can identify this with a form of tensoring
up: we can identify $\mathrm{Mod}_H(R)$ with the $\infty$-category
of modules over the commutative algebra object $\prod_{G/H} R \in \mathrm{Mod}_G(R)$,
with $G$ permuting the factors.
We state this formally as a proposition (compare \cite{balmerstack, BDAS}).
\begin{proposition}
Consider the commutative algebra object
$\prod_{G/H} R \in \mathrm{CAlg}( \mathrm{Mod}_G(R))$, with $G$-action permuting the factors.
Then the forgetful functor identifies $\mathrm{Mod}_H(R)$ with the symmetric monoidal
$\infty$-category of modules in $\mathrm{Mod}_G(R)$ over $\prod_{G/H} R$.
\end{proposition}
We can interpret this in the following algebro-geometric manner as well.
The $\infty$-category
$\mathrm{Mod}_G(R)$ can be described as the $\infty$-category of quasi-coherent
complexes on the classifying stack $BG$ of the discrete group $G$, over the base
ring $R$. Similarly, $\mathrm{Mod}_H(R)$ can be described as the $\infty$-category of
quasi-coherent sheaves on $BH$. One has an affine map $\phi\colon BH \to BG$ (in fact, a
finite \'etale cover), so that quasi-coherent complexes on $BH$ can be
identified with quasi-coherent complexes on $BG$ with a module action by
$\pi_*(\mathcal{O}_{BH})$, which corresponds to $\prod_{G/H} R$.
In particular, we can attempt to perform ``descent'' along the restriction
functor $\mathrm{Mod}_G(R) \to \mathrm{Mod}_H(R)$, or descent with the commutative algebra object
$\prod_{G/H} R$, or descent for quasi-coherent sheaves along the cover $BH
\to BG$. If $R$ contains $\mathbb{Q}$ or, more generally, if $|G|/|H|$ is invertible
in $R$, there are never any problems, because the $G$-equivariant
\emph{norm map} $\prod_{G/H}R \to R$ will exhibit $R$ as a retract of the
object
$\prod_{G/H} R$, so that the commutative algebra object $\prod_{G/H} R$ is descendable.
The
question is much more subtle in modular characteristic. For example, given a finite group
$G$ and a field $k$ of characteristic $p$ with $p \mid |G|$, the group
cohomology $H^*(G; k)$ is always infinite-dimensional, which prevents the
commutative algebra object $\prod_G k$ from being descendable. Nonetheless, one
has the following result. Recall that a group is called \emph{elementary
abelian} if it is of the form $(\mathbb{Z}/p)^n$ for some prime number $p$.
\begin{theorem}[Carlson \cite{carlson}, Balmer \cite{balmersep}] \label{BC}
Let $G$ be a finite group, and let $\mathcal{A}$ be a collection of elementary
abelian subgroups of $G$ such that every maximal elementary abelian
subgroup of $G$ is conjugate to an element of $\mathcal{A}$. Then the
commutative algebra object $\prod_{H \in \mathcal{A}}\prod_{G/H} R$ admits
descent in $\mathrm{Mod}_G(R)$. \end{theorem}
In other words, there is a strong theory of descent
along the map $\bigsqcup_{A \in \mathcal{A}} BA \to BG$ of stacks.
If $p$ is invertible in $R$ and $H$ is an elementary
abelian $p$-group, then $\prod_{G/H} R \in \mathrm{Mod}_G(R)$ is a retract of $\prod_{G}
R$.
To translate to our terminology, we note that \cite[Theorem 2.1]{carlson}
states that there is a finitely generated $\mathbb{Z}[G]$-module $V$ with the
property that there exists a
finite filtration $0 = V_0 \subset \dots \subset V_k = \mathbb{Z} \oplus V$
such that the successive quotients are all \emph{induced}
$\mathbb{Z}[G]$-modules from elementary abelian subgroups of $G$. Given an
object of $\mathrm{Mod}_G(\mathbb{Z})$ which is induced from $H \subset G$, we observe
that it is naturally a module in $\mathrm{Mod}_G(\mathbb{Z})$ over $\prod_{G/H}
\mathbb{Z}$.
Note moreover that the map
\begin{equation} \label{ss} \bigsqcup_{A \in \mathcal{A}} BA \to BG,
\end{equation}
which we have identified as having a good theory of descent, is explicit enough
that we can also write down the relative fiber product
$\left(\bigsqcup_{A \in \mathcal{A}} BA \right) \times_{BG}
\left(\bigsqcup_{A \in \mathcal{A}} BA\right)$ via a double coset decomposition.
Stated another way, the tensor products of commutative algebra objects of the
form $\prod_{G/H} R$, which appear in the cobar construction, can be described explicitly.
From this, and \Cref{Fiso} (and the immediately following remark), one obtains the following corollary, which is known to modular
representation theorists and is a generalization of the description by
Quillen \cite{equiv} of the cohomology ring of a finite group up to
$F$-isomorphism.
\begin{corollary}
Let $R$ be an $\e{2}$-algebra in $\mathrm{Mod}(\mathbb{Z})$ with an action of the finite
group $G$. Suppose $p$ is nilpotent in $R$.
Let $\mathcal{A}$ be the collection of all elementary abelian $p$-subgroups of
$G$.
Then the map
\[ R^{hG} \to \prod_{A \in \mathcal{A}} R^{hA}, \]
has nilpotent kernel in $\pi_*$. The image, up to uniform $F$-isomorphism, consists of all
families which are compatible under restriction and conjugation.
\end{corollary}
A family $(a_A \in \pi_* R^{hA})_{A \in \mathcal{A}}$ is compatible under
retriction and conjugation if, whenever $g \in G$ conjugates $A $ into $A'$,
then the induced map $R^{hA} \simeq R^{hA'}$ carries $a_{A}$ into $a_{A'}$;
and, furthermore, whenever $B \subset A$, then the map $R^{hA} \to R^{hB}$
carries $a_A$ into $a_B$. These compatible families form the $E_2$-page of the
descent spectral sequence for the cover \eqref{ss}.
When $R = \mathbb{F}_p$ (as was considered by Quillen), the above corollary is extremely useful
since the cohomology rings of elementary abelian groups are entirely known
and easy to work with.
Given a connected space $X$ with $\pi_1 X$ finite, one could also apply it to
the $\pi_1$-action on $C^*(\widetilde{X}; \mathbb{F}_p)$ where $\widetilde{X}$
is the universal cover.
We will use this picture extensively in the future, in particular for the
\emph{stable module $\infty$-categories.}
For now, we note a simple example of one of its consequences.
\begin{corollary}
The inclusion $\mathbb{Z}/p \subset \mathbb{Z}/p^k$ induces a descendable map
of $\e{\infty}$-rings
\[ \mathbb{F}_p^{h \mathbb{Z}/p^k} \to \mathbb{F}_p^{h \mathbb{Z}/p}, \]
for each $k > 0$.
\end{corollary}
\begin{proof}
Consider the $\infty$-category $\mathrm{Mod}_{\mathbb{Z}/p^k}(\mathbb{F}_p)$ of
$\mathbb{F}_p$-module spectra with a $\mathbb{Z}/p^k$-action. Inside here we
have the commutative algebra object $\prod_{ \mathbb{Z}/p^{k-1}} \mathbb{F}_p$
which, by \Cref{BC}, admits descent.
Note that,
as in
\eqref{reppgroup}, the subcategory $\mathrm{Mod}^\omega_{\mathbb{Z}/p^k}(
\mathbb{F}_p)$ of perfect $\mathbb{F}_p$-modules with a $\mathbb{Z}/p^k$-action
is symmetric monoidally equivalent to the $\infty$-category of perfect $\mathbb{F}_p^{h
\mathbb{Z}/p^k}$-modules. Thus, if we show that
$\prod_{ \mathbb{Z}/p^{k-1}} \mathbb{F}_p$ generates the unit $\mathbb{F}_p$ itself as a
thick $\otimes$-ideal in
$\mathrm{Mod}^\omega_{\mathbb{Z}/p^k}(
\mathbb{F}_p)$ (rather than the larger $\infty$-category $\mathrm{Mod}_{\mathbb{Z}/p^k}(
\mathbb{F}_p)$), we will be done. But this extra claim comes along for free,
since we can use the cobar construction. The cobar construction on
$\prod_{\mathbb{Z}/p^{k-1}} \mathbb{F}_p$ is constant as a pro-object either way, and that means
that $\mathbb{F}_p$ belongs to the thick $\otimes$-ideal generated by
$\prod_{ \mathbb{Z}/p^{k-1}} \mathbb{F}_p$ in the smaller $\infty$-category.
\end{proof}
We refer to \cite{MNNequiv, MNNequiv2} for many further examples of these phenomena in
equivariant homotopy theory (e.g., when $R$ is replaced by a ring spectrum)
and analogs of $F$-isomorphism and induction theorems.
\subsection{Stratification for Hopf algebras}
Let $k$ be a field of characteristic $p$, and let $A$ be a
finite-dimensional commutative Hopf algebra over $k$.
One may attempt to obtain a similar picture in the derived $\infty$-category of
$A$-comodules.
This has been considered by several authors, for example in \cite{palmieri,
wilkerson, FP}.
The case of the previous subsection was $A = \prod_G k$ when $G$ is
a finite group, given the coproduct dual to the multiplication in $k[G]$.
In this subsection, which will not be used in the sequel, we describe the
connection between some of this work and the notion of descent theory
considered here.
In this subsection, we assume that all Hopf algebras $A$ that occur are \emph{graded connected}, i.e.,
$A = \bigoplus_{i \in \mathbb{Z}_{\geq 0}} A_i$ with $A_0 = k$ and the Hopf
algebra structure respects the grading.
The Hopf algebra $A$ defines a \emph{finite group scheme} $G =
\mathrm{Spec} A$ over $k$, and we are interested in the $\infty$-category of quasi-coherent
complexes on the classifying stack $B G$ and in understanding descent in here.
For every closed subgroup $H \subset G$, we obtain a morphism of stacks
\[ f_H\colon BH \to BG, \]
which is \emph{affine}, even finite: in particular, quasi-coherent sheaves on $BH$ can be
identified with modules in $\mathrm{QCoh}(BG)$ over $(f_H)_*(\mathcal{O}_{BH}) \in
\mathrm{CAlg}( BG)$. One might hope that a certain collection of (proper) subgroup schemes $H
\subset G$ would have the property that the commutative algebra objects $(f_H)_*(\mathcal{O}_{BH})$
jointly generate, as a thick $\otimes$-ideal, all of $\mathrm{QCoh}( BG)$.
When $G$ is constant (although this is not covered by our present graded
connected setup), then the Quillen stratification theory (i.e.,
\Cref{BC}) identifies such a collection of subgroups. The key step is to show
that if $G$ is not elementary abelian, then the collection of
$(f_H)_*(\mathcal{O}_{BH})$
as $H$ ranges over \emph{all} proper
subgroups of $G$ jointly satisfy descent.
The picture is somewhat more complicated for finite group schemes.
\begin{definition}[Palmieri \cite{palmieri}] A group scheme $G$ is \textbf{elementary}
if it is commutative and satisfies the following
condition. Let $\mathcal{O}(G)^{\vee}$ be the ``group algebra,'' i.e., the dual to the
ring $\mathcal{O}(G)$ of functions on $G$. Then for every $x$ in the augmentation ideal of
$\mathcal{O}(G)^{\vee}$, we have $x^p = 0$.
Dualizing, this is equivalent to the condition that the
\emph{Verschiebung} should annihilate $G$.
\end{definition}
\begin{remark}
The
``group algebra'' $\mathcal{O}(G)^{\vee}$
plays a central role here because $\mathrm{QCoh}(BG)$, if we forget the symmetric
monoidal structure, is simply $\mathrm{Mod}( \mathcal{O}(G)^{\vee})$; the Hopf algebra
structure on $\mathcal{O}(G)^{\vee}$ gives rise to the symmetric monoidal
structure.
\end{remark}
In \cite{palmieri}, Palmieri also defines a weaker notion of
\emph{quasi-elementarity} for finite group schemes $G$, in terms of the
vanishing of certain products of Bocksteins.
It is this more complicated condition that actually ends up intervening.
Consider first a group scheme $G$ of rank $p$ over $k$ (which is necessarily
commutative), arising as the spectrum of a graded connected Hopf algebra. Then
the underlying algebra $\mathcal{O}(G)^{\vee}$ is isomorphic to $k[x]/x^p$.
In particular, there is a basic generating class $\beta \in H^2( BG ) \simeq
\mathrm{Ext}^2_{\mathcal{O}(G)^{\vee}}(k, k)$ called the \emph{Bockstein}
$\beta_G$. The Bockstein, considered as a map $\mathbf{1} \to
\Sigma^2\mathbf{1}$ in $\mathrm{QCoh}(BG)$, has the property
that
the \emph{cofiber} of $\beta$ belongs to the thick subcategory generated by the
``regular representation'' $\mathcal{O}(G)^{\vee}$, in view of the exact
sequence of $\mathcal{O}(G)^{\vee} \simeq k[x]/x^p$-modules
\[ 0 \to k \to \mathcal{O}(G)^{\vee} \to \mathcal{O}(G)^{\vee} \to k \to 0, \]
which exhibits the two-term complex $\mathcal{O}(G)^{\vee} \to
\mathcal{O}(G)^{\vee}$ as the cofiber of $\beta$ (up to a shift).
Since the map $\mathcal{O}(G)^{\vee} \to \mathcal{O}(G)^{\vee}$ is nilpotent
(it is given by multiplication by $x$), it follows that the thick subcategory
generated by the cofiber of $\beta$ is equal to that generated by the standard
representation.
\begin{definition} \label{quasi}
A group scheme $G$ arising from a graded connected Hopf algebra is \textbf{quasi-elementary} if the product $\prod_{\phi\colon G
\twoheadrightarrow G'} \phi^*( \beta_{G'})$ for all surjections $\phi\colon G
\twoheadrightarrow G'$ for $G'$ a group scheme of rank $p$ (always respecting
the grading), is not nilpotent in
the cohomology of $BG$. \end{definition}
\begin{remark}
Let $G = \mathrm{Spec} A$ be a nontrivial group scheme arising from a graded connected Hopf algebra.
Then there is always a surjective map $G \twoheadrightarrow G'$ with $G'$ of
rank $p$
(respecting the grading). To see this, we observe that there is a nontrivial
primitive element $x \in A_i$ for $i > 0$ and, replacing $x$ with a suitable
power, we may assume that $x^p = 0$. This defines the map to a graded version
of $\alpha_p$.
\end{remark}
For finite groups, it is a classical theorem of Serre that quasi-elementarity is
equivalent to being elementary abelian: if $G$ is a finite $p$-group which is not
elementary abelian, then there are nonzero classes $\alpha_1, \dots, \alpha_n \in
H^1(G; \mathbb{Z}/p)$ such that the product of the Bocksteins $\prod \beta
(\alpha_i)$ vanishes. Serre's result is, as explained in \cite{carlson,
balmersep}, at the source of the Quillen stratification theory for finite
groups, in particular \Cref{BC}.
\begin{proposition}[{Cf. \cite[Th. 1.2]{palmieri}}]
Let $G$ be a finite group scheme arising from a graded connected Hopf
algebra over $k$. Then
$G$ is not quasi-elementary if and only if the
objects $(f_{H})_*(\mathcal{O}_{BH}) \in \mathrm{CAlg}( \mathrm{QCoh}(BG))$, for $H \subset G$ a proper
normal subgroup scheme (respecting the grading), generate the unit as
a thick $\otimes$-ideal.
\end{proposition}
\begin{proof}
Suppose $\kappa$ is nilpotent.
For each rank $p$ quotient $\phi\colon G \twoheadrightarrow G'$, we have a map
$\mathbf{1} \to \Sigma^2\mathbf{1}$ in $\mathrm{QCoh}(BG')$ whose cofiber is in the thick subcategory of
$\mathrm{QCoh}(BG')$
generated by the pushforward of the structure sheaf via $\ast \to BG'$. Pulling
back, we get, for each rank $p$ quotient $\phi\colon G \twoheadrightarrow G'$ with
kernel $H_{\phi}$, a map $\beta_\phi\colon \mathbf{1} \to \mathbf{1}[2]$ in $\mathrm{QCoh}(BG)$ whose cofiber is in the
thick subcategory generated by $(f_{H_\phi})_*(\mathcal{O}_{BH_\phi})$ where
$f_{H_\phi}\colon BH_\phi \to BG$ is the natural map.
It follows in particular that the cofiber of each $\beta_{\phi}$ belongs to the
thick subcategory $\mathcal{C} \subset \mathrm{QCoh}( BG)$ generated by the
$\{ (f_H)_*(\mathcal{O}_{BH}) \}$
for $ H
$ a proper normal subgroup scheme of $G$.
Therefore, using the octahedral axiom, the cofiber of each \emph{composite} of a finite string of
$\beta_{\phi}$'s (e.g., $\kappa$ and its powers)
belongs to $\mathcal{C}$.
It follows finally that, by nilpotence of $\kappa$, the unit object itself
belongs to $\mathcal{C}$.
Conversely, suppose that the $\{(f_{H})_* ( \mathcal{O}_{BH})\}$ generate the
unit as a thick $\otimes$-ideal: that is, descent holds. In this case, we show
that the product of Bocksteins
$\kappa = \prod_{\phi\colon G
\twoheadrightarrow G'} \phi^*( \beta_{G'})$ in \Cref{quasi}
is forced to be nilpotent.
In fact, we observe that for every
proper normal subgroup $H \subset G$, there exists a morphism from $G/H $ to a
rank $p$ group scheme $Q$. The pull-back of the Bockstein $\beta_Q$ to $H^2(BG)$ restricts to
zero on $H$; in particular, $\kappa$ restricts to zero on each normal subgroup
scheme of $G$. By descent, it follows that $\kappa$ is nilpotent.
\end{proof}
By induction, one gets:
\begin{corollary}
Let $G$ be a group scheme over $k$ arising from a graded connected Hopf algebra. Then the commutative algebra
objects $(f_H)_*(\mathcal{O}_{BH}) \in \mathrm{CAlg}( \mathrm{QCoh}(BG))$, as $H \subset G$
ranges over all the quasi-elementary subgroup schemes (respecting the grading), admits descent.
\end{corollary}
Unfortunately, it is known that quasi-elementarity and elementarity are not equivalent for
general finite group schemes \cite{wilkerson}. There is, however, one important case when this
is known.
Let $p = 2$.
Consider the
dual Steenrod algebra $\mathcal{A} \simeq \mathbb{F}_2[\xi_1, \xi_2, \dots ]$. This is a graded, connected, and
commutative (but not cocommutative) Hopf algebra over $\mathbb{F}_2$.
The object
$\mathrm{Spec} \mathcal{A}$, which is now an (infinite-dimensional) group scheme,
admits an elegant algebro-geometric interpretation as the
automorphism group scheme of the formal additive group $\widehat{\mathbb{G}_a}$.
Let $A$ be a finite-dimensional graded Hopf algebra quotient of the dual Steenrod
algebra, so that $G = \mathrm{Spec} A$ is a finite group scheme inside the group scheme of
automorphisms of $\widehat{\mathbb{G}_a}$.
\begin{theorem}[Wilkerson \cite{wilkerson}] Let $A$ be as above, and let $\mathcal{B}$ range
over all the elementary subgroup schemes $H \subset G$ (respecting the grading). Then the map
\( \bigsqcup_{H \in \mathcal{B}} BH \to B G, \)
admits descent, in the sense that the commutative algebra object $\prod_{H \in
\mathcal{B}} (f_H)_{*}(\mathcal{O}_{BH}) \in \mathrm{CAlg}(\mathrm{QCoh}(BG))$ does.
\end{theorem}
In particular, it is known that for subgroup schemes of $\mathrm{Spec}
\mathcal{A}$ (cut out by homogeneous ideals), elementarity and quasi-elementarity are equivalent. Related ideas
have been used by Palmieri \cite{palmieriquillen} to give a complete
description of the cohomology of such Hopf
algebras up to $F$-isomorphism at the prime 2.
\subsection{Chromatic homotopy theory}
Thick subcategory ideas were originally introduced in chromatic homotopy theory.
Let $E_n$ denote a Morava $E$-theory of height $n$; thus $\pi_0(E_n) \simeq
W(k)[[v_1, \dots,v_{n-1}]]$ where $W(k)$ denotes the Witt vectors on a perfect
field $k$ of characteristic $p$.
Moreover, $\pi_*(E_n) \simeq \pi_0(E_n)[t_2^{\pm 1}]$ and $E_n$ is thus
\emph{even periodic}; the associated formal group is the Lubin-Tate universal
deformation of a height $n$ formal group over the field $k$.
By a deep theorem of Goerss-Hopkins-Miller, $E_n$ has the (canonical) structure
of an $\e{\infty}$-ring.
Let $L_n $ denote the functor of localization at $E_n$.
The basic result is the following:
\begin{theorem}[{Hopkins-Ravenel \cite[Chapter 8]{ravenelorange}}]
\label{HR}
The map $L_n S^0 \to E_n$ admits descent.
\end{theorem}
In other words, the $E_n$-based Adams-Novikov spectral sequence degenerates
with a horizontal vanishing line at a finite stage, for any spectrum.
This degeneration does \emph{not} happen at the $E_2$-page (e.g., for the sphere) and
usually implies that a great many differentials are necessary early on.
\Cref{HR}, which implies that $E_n$-localization is \emph{smashing}, is
fundamental to the global structure of the stable homotopy category and its
localizations.
As in the finite group case, one of the advantages of results such as \Cref{HR}
is that $E_n$ is much simpler algebraically than is $L_n S^0$.
The Hopkins-Ravenel result is a basic finiteness property of the $E_n$-local
stable homotopy category. It implies, for instance, that many homotopy limits
that one takes (such as the homotopy fixed points for the $\mathbb{Z}/2$-action
on $KU$) behave much more like finite homotopy limits than infinite ones.
\begin{example}
Let $R$ be an $\e{2}$-ring spectrum
which is $L_n$-local. Then it follows that the map from $\pi_*(R)$ to the
zero-line of the
$E_2$-page of the Adams-Novikov spectral sequence for $R$ is an $F$-isomorphism.
Indeed, we know that the map from $\pi_*(R)$ to the
zero-line at $E_2$ is a rational isomorphism and, moreover, everything above
the $s =0$ line vanishes at $E_2$. (This comes from the algebraic fact that
rationally, the moduli stack of formal groups is a $B \mathbb{G}_m$ and has no
higher cohomology.)
\end{example}
\begin{example}
Let $R$ be an $L_n$-local ring spectrum. Then any class in $\pi_*(R)$ which
maps to zero in $(E_n)_*(R)$ is nilpotent. This is a very special case of the
general (closely related) nilpotence theorem of \cite{DHS, HS}.
For an $\e{\infty}$-ring, by playing with power operations, one can actually
prove a stronger result \cite{MNN}: any \emph{torsion} class is
automatically nilpotent.
\end{example}
\part{The Galois formalism}
\section{Axiomatic Galois theory}
Let $(X, \ast)$ be a pointed, connected topological space.
A basic and useful invariant of $(X, \ast)$ is the \emph{fundamental group}
$\pi_1(X, \ast)$, defined as the group of homotopy classes of paths $\gamma\colon
[0, 1] \to X$ with $\gamma(0) = \gamma(1) = \ast$.
This definition has the disadvantage, at least from the point of view of an
algebraist, of intrinsically using the unit
interval $[0, 1]$ and the topological structure of the real numbers
$\mathbb{R}$. However, the fundamental group also has another incarnation that
makes no reference to the theory of real numbers, via the theory of
\emph{covering spaces}.
\begin{definition} \label{defcov}
A map $p \colon Y \to X$ of topological spaces is a \textbf{covering space} if, for
every $x \in X$, there exists a neighborhood $U_x$ of $x$ such that in the
pullback
\[ \xymatrix{
Y \times_X U_x\ar[d] \ar[r] & Y \ar[d] \\
U_x \ar[r] & X
},\]
the map $Y \times_X U_x \to U_x$ has the form $\bigsqcup_S U_x \to U_x$ for a
set $S$.
\end{definition}
The theory of covering spaces makes, at least a priori,
no clear use of $[0, 1]$. Moreover, understanding the theory of covering
spaces of $X$ is
essentially equivalent to
understanding the group $\pi_1(X, \ast)$. If $X$ is locally contractible, then one has
the following basic result:
\begin{theorem} \label{coveringspaces}
Suppose $X$ is path-connected and locally contractible.
Let $\mathrm{Cov}_X$ be the category of maps $Y \to X$ which are covering spaces.
Then, we have an equivalence of categories $\mathrm{Cov}_X \simeq
\mathrm{Set}_{\pi_1(X, \ast)}$, which sends a cover $p\colon Y \to X$ to the fiber
$p^{-1}(\ast)$ with the monodromy action of $\pi_1(X, \ast)$.
\end{theorem}
The fundamental group $\pi_1(X, \ast)$ can, in fact, be \emph{recovered} from
the structure of the category $\mathrm{Cov}_X$.
This result suggests that the theory of the fundamental group should be more
primordial than its definition might suggest; at least, it might be expected to have
avatars in other areas of mathematics in which the notion
of a covering space makes sense.
Grothendieck realized, in \cite{sga1}, that there is a purely algebraic notion
of a \emph{finite cover} for a scheme (rather than a topological space): that
is, given a scheme $X$, one can define a version of $\mathrm{Cov}_X$ that corresponds
to the topological notion of a finite cover. When $X$ is a variety over the
complex numbers $\mathbb{C}$, the algebraic notion turns out to be equivalent
to the topological notion of a finite cover of the complex points
$X(\mathbb{C})$ with the analytic topology. As a result, in \cite{sga1}, it was possible to define a
\emph{profinite group} classifying these finite covers of schemes. Grothendieck
had to prove a version of \Cref{coveringspaces} without an a priori definition
of the fundamental group, and did so by \emph{axiomatizing} the properties that
a category would have to satisfy in order to arise as the category of finite
sets equipped with a continuous action of a profinite group. He could then
\emph{define} the group in terms of the category of finite covers. The main objective
of this paper is to obtain similar categories from stable homotopy theories.
The categories
that appear in this setting are called \emph{Galois categories}, and the
theory of Galois categories will be
reviewed in this section.
We will, in particular, describe a version of Grothendieck's Galois theory
that does not require a fiber functor, relying primarily on versions
of descent theory.
\subsection{The fundamental group}
To motivate the definitions, we begin by quickly reviewing how the classical
\'etale fundamental group of \cite{sga1} arises.
\begin{definition}
Let $f\colon Y \to X$ be a finitely presented map of schemes. We say that $f\colon Y \to X$ is
\textbf{\'etale} if $f$ is flat and the sheaf $\Omega_{Y/X}$ of relative
K\"ahler differentials vanishes.
\end{definition}
\'Etaleness is the algebro-geometric analog of being a ``local homeomorphism''
in the complex analytic topology.
Given it, one can define
the analog of a (finite) covering space.
\begin{definition}
A map $f\colon Y \to X$ is a \textbf{finite cover} (or finite covering space) if $f$
is finite and \'etale. The collection of all finite covering spaces of $X$ forms a
category $\mathrm{Cov}_X$, a full subcategory of the category of schemes over $X$.
\end{definition}
The basic example of a finite \'etale cover is the map $\bigsqcup_S X \to X$.
If $X$ is connected, then a map $Y \to X$ is a finite cover if and only if it
\emph{locally} has this form with respect to the flat topology. In other
words, a map $Y \to X$ is a finite cover if and only if there exists a finitely
presented, faithfully flat map $X' \to X$ such that the pull-back
\[ \xymatrix{
X' \times_X Y \ar[d] \ar[r] & Y \ar[d] \\
X' \ar[r] & X
},\]
is of the form $\bigsqcup_S X' \to X'$ where $S$ is a finite set; if $X$ is
not connected, the number of sheets may vary over $X$. In other
words, one has an analog of \Cref{defcov}, where ``locally'' is replaced by ``locally
in the flat topology.'' This strongly suggests that the
algebro-geometric definition
of a finite cover is a good analog of the conventional topological one.
\begin{example} \label{galpt}
Suppose $X = \mathrm{Spec} k$ where $k$ is an algebraically closed field. In this case,
there is a canonical equivalence of categories
\[ \mathrm{Cov}_X \simeq \mathrm{FinSet} , \]
where $\mathrm{FinSet}$ is the category of finite sets,
which sends an \'etale cover $Y \to X$ to its set of connected components.
\end{example}
Fix a geometric point $\overline{x} \to X$, and assume that $X$ is a
\emph{connected} scheme.
Grothendieck's idea is to extract the fundamental group $\pi_1(X,
\overline{x})$ directly from the structure of the
\emph{category} $\mathrm{Cov}_X$.
In particular, as in \Cref{coveringspaces}, the category $\mathrm{Cov}_X$ will be
equivalent to the
category of representations (in finite sets) of a certain (profinite) group
$\pi_1(X, \overline{x})$.
\begin{definition}
The \textbf{fundamental group} $\pi_1(X, \overline{x})$ of the pair $(X,
\overline{x})$ is given by the
automorphism group of the forgetful functor
\[ \mathrm{Cov}_X \to \mathrm{FinSet}, \]
which consists of the composite
\[ \mathrm{Cov}_X \to \mathrm{Cov}_{\overline{x}} \simeq \mathrm{FinSet}, \]
where the first functor is the pull-back and the second is the equivalence of
\Cref{galpt}.
\end{definition}
The automorphism group of such a functor naturally acquires the structure of a
\emph{profinite} group, and the forgetful functor above naturally lifts to a
functor
$\mathrm{Cov}_X \to \mathrm{FinSet}_{\pi_1(X, \overline{x})}$, where $\mathrm{FinSet}_{\pi_1(X,
\overline{x})}$ denotes the category of finite sets equipped with a
continuous action of the profinite group
$\pi_1(X,
\overline{x})$.
Then, one has:
\begin{theorem}[Grothendieck \cite{sga1}]
\label{etalecorr}
The above functor $\mathrm{Cov}_X \to \mathrm{FinSet}_{\pi_1(X, \overline{x})}$ is an
equivalence of categories.
\end{theorem}
Grothendieck proved \Cref{etalecorr} by \emph{axiomatizing} the properties
that a category would have to satisfy in order to be of the form $\mathrm{FinSet}_{G}$
for $G$ a profinite group, and checking that any $\mathrm{Cov}_X$ is of this form.
We review the axioms here.
Recall that, in a category $\mathcal{C}$, a map $X \to Y$ is a \emph{strict
epimorphism} if the natural diagram
\[ X \times_Y X \rightrightarrows X \to Y, \]
is a coequalizer.
\begin{definition}[{Grothendieck \cite[Exp. V, sec. 4]{sga1}}] \label{defgalcat}
A \textbf{classical Galois category} is a category $\mathcal{C}$ equipped with a
\textbf{fiber functor} $F\colon \mathcal{C} \to \mathrm{FinSet}$ satisfying the following
axioms:
\begin{enumerate}
\item $\mathcal{C} $ admits finite limits and $F$ commutes
with finite limits.
\item $\mathcal{C}$ admits finite coproducts and $F$ commutes with finite
coproducts.
\item $\mathcal{C}$ admits quotients by finite group actions, and $F$ commutes
with those.
\item $F$ is conservative and preserves strict epimorphisms.
\item Every map $ X \to Y$ in $\mathcal{C}$ admits a factorization $X \to Y'
\to Y$ where $X \to Y'$ is a strict epimorphism and where $Y' \to Y$ is a
monomorphism, which is in addition an inclusion of a summand.
\end{enumerate}
\end{definition}
Let $\mathcal{C}$ be a classical Galois category with fiber functor $F\colon \mathcal{C} \to
\mathrm{FinSet}$.
Grothendieck's Galois theory shows that $\mathcal{C}$ can be recovered as the
category of finite sets equipped with a continuous action of a certain
profinite group.
\begin{definition}
The \textbf{fundamental (or Galois) group} $\pi_1(\mathcal{C})$ of a
classical Galois category
$(\mathcal{C}, F)$ in the sense of Grothendieck is the automorphism group of the functor $F\colon \mathcal{C} \to
\mathrm{FinSet}$.
\end{definition}
The fundamental group of $\mathcal{C}$ is naturally a profinite group, as a
(non-filtered)
inverse
limit of finite groups. Note that if $\mathcal{C}$ is a classical Galois
category with fiber functor $F$, if $\pi_1(\mathcal{C})$ is the
Galois group, then the fiber functor $\mathcal{C} \to \mathrm{FinSet}$ naturally lifts
to
\[ \mathcal{C} \to \mathrm{FinSet}_{\pi_1(\mathcal{C})}, \]
just as before.
\begin{proposition}[{Grothendieck \cite[Exp. V, Theorem 4.1]{sga1}}] \label{galcorconn}
If $(\mathcal{C}, F)$ is a classical Galois category, then the functor $\mathcal{C}
\to \mathrm{FinSet}_{\pi_1(\mathcal{C})}$ as above is an equivalence of categories.
\end{proposition}
Given a connected scheme $X$ with a geometric point $\overline{x} \to X$, then
one can show that the category $\mathrm{Cov}_X$ equipped with the above fiber functor
(of taking the preimage over $\overline{x}$ and taking connected components) is
a classical Galois category.
The resulting fundamental group is a very useful invariant of a scheme, and for
varieties over an algebraically closed fields of
characteristic zero can be computed by profinitely completing the topological
fundamental group (i.e., that of the $\mathbb{C}$-points).
In particular, \Cref{etalecorr} is a special case of \Cref{galcorconn}.
\subsection{Definitions}
In this section, we will give an exposition of Galois theory appropriate to the
nonconnected setting.
Namely, to a type of category which we will simply call a {Galois
category}, we will attach a \emph{profinite groupoid:} that is, a pro-object
in the $(2, 1)$-category of groupoids with finitely many objects and finite
automorphism groups. The advantage of this approach, which relies heavily on
descent theory, is that we will not start
by assuming the existence of a fiber functor, since we might not have one a
priori.
Axiomatic Galois theory in many forms has a voluminuous literature.
The original treatment, of course, is \cite{sga1}, reviewed in the previous
subsection. A textbook reference for some of these ideas is \cite{borceux}.
In \cite{GR}, an approach to Galois theory (in the connected
case) for almost rings is
given that does not assume a priori the existence of a fiber functor.
The use of profinite groupoids in Galois theory is well-known (e.g.,
\cite{cjf, Magid}), and the main
result below (\Cref{galequiv}) is presumably familiar to experts; we have included
a detailed exposition for lack of a precise reference and because our
$(2, 1)$-categorical approach may be of some interest.
Certain types of infinite Galois theory have been developed in the work of
Bhatt-Scholze \cite{BSpro} on the pro-{\'e}tale topology; we will not touch
on anything related to this here.
Finally, we note that forthcoming work of Lurie will treat an embedding from
the $\infty$-category of profinite spaces into that of $\infty$-topoi,
which provides a vast generalization of
these ideas.
We start by reviewing some category theory.
\begin{definition}
We say that an object $\emptyset$ in a category $\mathcal{C}$ is \textbf{empty}
if any map $x \to \emptyset$ is an isomorphism, and if $\emptyset$ is initial.
\end{definition}
For example, the empty set is an empty object in the category of sets. In the
\emph{opposite} to the category of commutative rings, the zero ring is empty.
\begin{definition}
Let $\mathcal{C}$ be a category admitting finite coproducts, such that the
initial object (i.e., the empty coproduct) is empty. We shall say that
$\mathcal{C}$ admits \textbf{disjoint coproducts}
if for any $x, y \in
\mathcal{C}$, the natural square
\[ \xymatrix{
\emptyset \ar[d] \ar[r] & x \ar[d] \\
y \ar[r] & x \sqcup y
},\]
is cartesian.
\end{definition}
The category of sets (or more generally, any topos) admits disjoint coproducts.
The \emph{opposite} of the category of commutative rings also admits disjoint
coproducts.
\begin{definition}
Let $\mathcal{C}$ be a category admitting finite coproducts and finite limits. We will say that
\textbf{coproducts are distributive} if for every $y \to x$ in $\mathcal{C}$,
the pullback functor
\( \mathcal{C}_{/x} \to \mathcal{C}_{/y} \)
commutes with finite coproducts.
\end{definition}
Similarly, the category of sets (or any topos) and the opposite to the category
of commutative rings satisfy this property and are basic examples to keep in
mind.
Suppose $\mathcal{C}$ admits disjoint and distributive coproducts. Then $\mathcal{C}$ acquires
the following very useful feature (familiar from \Cref{prode}). Given an object $x \simeq x_1 \sqcup x_2$ in
$\mathcal{C}$, then we have a natural equivalence
of categories,
\[ \mathcal{C}_{/x} \simeq \mathcal{C}_{/x_1} \times \mathcal{C}_{/x_2}, \]
which sends an object $y \to x$ of $\mathcal{C}_{/x}$ to the pair $(y \times_x
x_1 \to x_1, y \times_x x_2 \to x_2)$.
\begin{definition}
Let $\mathcal{C}$ be a category admitting finite limits. Given a map $y \to x$
in $\mathcal{C}$, we have an adjunction
\begin{equation} \label{adjn} \mathcal{C}_{/y} \rightleftarrows
\mathcal{C}_{/x}, \end{equation}
where the left adjoint sends $y' \to y$ to the composite $y' \to y \to x$, and
the right adjoint takes the pullback along $y \to x$.
We will say that $y \to x$ is an \textbf{effective descent morphism} if the above
adjunction is
monadic.
By the Beck-B\'enabou-Roubaud theorem that establishes the
connection between monads and descent \cite{BRB}, we can reformulate the
notion equivalently as follows. Form the bar construction
in $\mathcal{C}$,
\[ \dots \triplearrows y \times_x y \rightrightarrows y, \]
which is a simplicial object in $\mathcal{C}$ augmented over $x$.
Applying the pullback functor everywhere, we get a cosimplicial category
\[ \mathcal{C}_{/y} \rightrightarrows \mathcal{C}_{/y \times_x y}
\triplearrows \dots , \]
receiving an augmentation from $\mathcal{C}_{/x}$. Then $y \to x$ is an
effective descent morphism if the functor
\[ \mathcal{C}_{/x} \to \mathrm{Tot}\left( \mathcal{C}_{/y} \rightrightarrows \mathcal{C}_{/y \times_x y}
\triplearrows \dots \right),\]
is an equivalence of categories.
If $\mathcal{C}$ is an $\infty$-category, we can make the same definition.
\end{definition}
We note that whether or not a map $y \to x$ is an effective descent morphism can be
checked using the Barr-Beck theorem applied to the adjunction \eqref{adjn}.
Namely, the pullback along $y \to x$ needs to preserve reflexive coequalizers
which are split under pullback, and it needs to be conservative.
Finally, we are ready to define a Galois category.
\newcommand{\mathrm{GalCat}}{\mathrm{GalCat}}
\begin{definition} \label{galax}
A \textbf{Galois category} is a category $\mathcal{C}$ such that:
\begin{enumerate}
\item $\mathcal{C} $ admits finite limits and coproducts, and the initial
object $\emptyset$ is empty.
\item Coproducts are disjoint and distributive in $\mathcal{C}$.
\item Given an object $x$ in $\mathcal{C}$, there is an effective
descent morphism $x' \twoheadrightarrow \ast$ (where $\ast$ is the terminal object) and a decomposition $x' = x'_1 \sqcup \dots \sqcup x'_n$
such that
each map $x \times x'_i \to x'_i$ decomposes as the fold map $x \times x'_i \simeq
\bigsqcup_{S_i} x'_i \to x_i'$ for a finite set $S_i$.
\end{enumerate}
The collection of all Galois categories and functors between them
(which are required to preserve coproducts, effective descent morphisms, and finite
limits) can be organized into a $(2, 1)$-category $\mathrm{GalCat}$.
Given $\mathcal{C}, \mathcal{D} \in \mathrm{GalCat}$, we will let
$\mathrm{Fun}^{\mathrm{Gal}}(\mathcal{C}, \mathcal{D})$ denote the groupoid of functors
$\mathcal{C} \to \mathcal{D}$ in $\mathrm{GalCat}$.
\end{definition}
In other words, we might say that an object $x \in \mathcal{C}$ is in \emph{elementary form}
if $x \simeq \bigsqcup_S \ast$ for some finite set $S$. More generally,
if there exists a decomposition $\ast \simeq \ast_1 \sqcup \dots \sqcup \ast_n$, such
that, as an object of $\mathcal{C}_{} \simeq \prod_i \mathcal{C}_{/\ast_i}$,
each $y \times_{\ast} \ast_i \to \ast_i$ is in elementary form, we say that $y$ is in
\emph{mixed elementary form.} Then the \emph{defining} feature of a Galois category
is that, locally, every
object is in mixed elementary form.
Our first goal is to develop some of the basic properties of Galois categories.
First, we need a relative version of the previous paragraph.
\begin{definition}
Let $\mathcal{C}$ be a category satisfying the first two conditions of
\Cref{galax} (which we note are preserved by passage to $\mathcal{C}_{/x}$
for any $x \in \mathcal{C}$).
We say that a map $f\colon x \to y$ is
\emph{setlike} if there are finite sets $S, T$ such that $x \simeq \bigsqcup_S
\ast$, $y \simeq \bigsqcup_T \ast$ and the map $x \to y$ comes from a map of
finite sets $S \to T$.
This implies that $x \in \mathcal{C}_{/y}$ is in mixed elementary form.
\end{definition}
For example, if $y = \ast$, then $x \to y$ is setlike if and only if $x$ is in
elementary form.
Suppose $x, y$ are in elementary form, so that $x \simeq \bigsqcup_S \ast$ and
$y \simeq \bigsqcup_T \ast$. Then a map $x \to y$ is not necessarily setlike.
However, by the disjointness of coproducts, it follows that the map
$\bigsqcup_S \ast \to \bigsqcup_T \ast$ gives, for each $s \in S$, a decomposition of the terminal
object $\ast$ as a disjoint union of objects $\ast_{t}^{(s)}$ for each $t \in T$. It follows
that, refining these decompositions, there exists a decomposition $\ast \simeq \ast_1 \sqcup \dots \sqcup \ast_n$
such that the map $x \to y$ becomes setlike after pulling back along $\ast_i
\to \ast$. In particular, $x \to y$ is locally setlike. The same argument works
if $x, y$ are disjoint unions of summands of the terminal object.
More generally, we have:
\begin{proposition}
\label{locsetlike}
Let $f\colon x \to y$ be any map in the Galois category $\mathcal{C}$. Then there exists an effective
descent morphism $t \twoheadrightarrow \ast$ and a decomposition $t \simeq
\bigsqcup_{i=1}^n t_i$ such that the map $x \times t_i \to y \times t_i$ in
$\mathcal{C}_{/t_i}$ is setlike.
More generally, given any finite set of maps $f_j \colon x_j \to y_j$ we can
find such a decomposition such that each $f_j \times t_i$ is setlike.
\end{proposition}
\begin{proof}
We can choose $t$ such that $(x \sqcup y) \times t$ is in mixed elementary
form: in particular, we have a decomposition $t \simeq t_1 \sqcup \dots \sqcup
t_n$ such that $(x \sqcup y) \times t_i$ is a disjoint union of copies of
$t_i$ in $\mathcal{C}_{/t_i}$. It follows that $x \times t_i \to t_i$ and $y
\times t_i \to t_i$ are objects in $\mathcal{C}_{/t_i}$ which are disjoint
union of summands of copies of the terminal object $t_i \in
\mathcal{C}_{/t_i}$.
Using the previous discussion, it follows that we can refine the $t_i$ further
(by splitting into summands) to make $x \to y$ setlike on each summand.
A similar argument would work for any finite set of morphisms in $\mathcal{C}$.
\end{proof}
\begin{corollary}
Let $\mathcal{C}$ be a Galois category and let $x \in \mathcal{C}$. Then
$\mathcal{C}_{/x}$ is a Galois category.
\end{corollary}
\begin{proof}
The first two axioms are evident. For the third, fix a map $y \to x$ in
$\mathcal{C}$ (thus defining an object of $\mathcal{C}_{/x}$). By
\Cref{locsetlike}, we can find an
object $x' \in \mathcal{C}$ together with an effective descent morphism $x'
\twoheadrightarrow \ast$ such that $y \times x' \to x \times x'$ becomes, after
decomposing $x'$ into a disjoint union of summands, setlike in
$\mathcal{C}_{/x'}$. It follows that $y \times x' \to x' \times x$ is in mixed
elementary form as an object of $\mathcal{C}_{/x \times x'}$.
\end{proof}
The notion of an effective descent morphism is a priori not so well-behaved, which
might be a cause for worry. Our next goal is to show that this is not the case.
\begin{proposition} \label{colimdist}
A Galois category $\mathcal{C}$ admits finite colimits, which are
distributive over pullbacks.
\end{proposition}
\begin{proof}
Let $K$ be a finite category; choose a map $p\colon K \to
\mathcal{C}_{/x}$ for some object $x \in \mathcal{C}$. Since $\mathcal{C}_{/x}$
is itself a Galois category, we can replace $\mathcal{C}_{/x}$ with
$\mathcal{C}$ and show that if $y \in \mathcal{C}$ is arbitrary, then the
natural map
\begin{equation} \label{climeq} \varinjlim_K (y \times p(k) ) \to y \times \varinjlim_K p(k), \end{equation}
is an equivalence, and in particular the colimits in question exist.
There is one case in which the above would be automatic.
Since $\mathcal{C}$ has finite coproducts,
we
can define the product of a finite set with any object in $\mathcal{C}$.
Suppose there exists a
diagram $\overline{p}\colon K \to \mathrm{FinSet}$ and an object $u \in \mathcal{C}$ such
that $p = \overline{p} \times u$. For example, suppose that for every
morphism in $K$, the image in $\mathcal{C}$ is setlike; then this would happen. In this case, both sides of \eqref{climeq} are defined and are given by $y \times u \times \varinjlim_K
\overline{p}$, since finite coproducts distribute over pullbacks.
We will say that a diagram $p\colon K \to \mathcal{C}$ is \emph{good} if it
arises from a $\overline{p}\colon K \to \mathrm{FinSet}$ and an $u \in \mathcal{C}$; the
good case is thus straightforward.
If we have a finite decomposition of the terminal object $\ast =
\bigsqcup_{i=1}^n \ast_i$ such that the restriction $p \times_{\ast} \ast_i$ is
good, then we say that $p$ is \emph{weakly good}. In this case, using
$\mathcal{C} \simeq \prod_{i=1}^n \mathcal{C}_{/\ast_i}$, we conclude that
\eqref{climeq} is defined and holds.
We can reduce to the good (or weakly good) case via descent.
There exists an effective descent morphism $x \to \ast$ such that $p \times x\colon K \to
\mathcal{C}_{/x}$ is weakly good by \Cref{locsetlike}.
Using
the expression $\mathcal{C} \simeq \mathrm{Tot}\left( \mathcal{C}_{/x \times \dots
\times x}\right)$, it follows that \eqref{climeq} must be true at each stage in
the totalization, and the respective colimits are compatible with the coface
and coboundary maps, so that it is (defined and) true in the totalization.
\end{proof}
\begin{remark}
In the above argument, we have tacitly used the following fact. Consider a
category $I$ and an $I$-indexed family of categories (or $\infty$-categories) $(\mathcal{C}_i)_{i \in
I}$. Consider a functor $p\colon K \to \varprojlim_I \mathcal{C}_i$, where $K$ is
a fixed simplicial set. Suppose each
composite $K \stackrel{p}{\to} \varprojlim_I \mathcal{C}_i \to \mathcal{C}_{i_1}$
(for each $i_1 \in I$) admits a colimit and suppose these colimits are
preserved by the various maps in $I$. Then $p$ admits a colimit compatible with
the colimits in each $\mathcal{C}_i$.
\end{remark}
\begin{corollary}
The composite of two effective descent morphisms in a Galois category $\mathcal{C}$ is an
effective descent morphism.\footnote{Results on this question in more general
categories are contained in \cite{ST, RST}.} If $x \to y$ is any map in $\mathcal{C}$ and $y' \to y$
is an effective descent morphism, then $x \to y$ is an effective descent morphism if and
only if $x \times_y y' \to y'$ is one.
\end{corollary}
\begin{proof}
Since
(\Cref{colimdist})
a Galois category has finite colimits, which distribute over pull-backs,
it follows by the Barr-Beck theorem a map $x \to y$ is an effective descent morphism if and only if it
is conservative. This is preserved under compositions. The second statement is
proved similarly, since one only has to check conservativity locally.
\end{proof}
\begin{proposition}
Given a map $f\colon x \to y$ in the Galois category $\mathcal{C}$, the following are
equivalent:
\begin{enumerate}
\item $f$ is an effective descent morphism.
\item $f$ is a strict epimorphism.
\item For every $y' \to y$ with $y'$ nonempty, the pullback $x \times_y y'$ is
nonempty.
\end{enumerate}
\end{proposition}
\begin{proof}
All three conditions can be checked locally.
After base-change by an effective descent morphism $t \twoheadrightarrow \ast$ and
a decomposition $t \simeq t_1 \sqcup \dots \sqcup t_n$, we can assume that the
map $x \to y$ is setlike, thanks to \Cref{locsetlike}. In this case, the result
is obvious.
\end{proof}
We now discuss a few facts about functors between Galois categories.
These will be useful when we analyze $\mathrm{GalCat}$ as a 2-category in the next
section.
\begin{proposition}
Let $\mathcal{C}, \mathcal{D}$ be Galois categories. A functor $\mathcal{C} \to
\mathcal{D}$ in $\mathrm{GalCat}$ preserves finite colimits.
\end{proposition}
\begin{proof}
This is proved as in \Cref{colimdist}: any functor preserves colimits of
\emph{good} diagrams (in the terminology of the proof of \Cref{colimdist}), and
after making a base change one may reduce to this case.
\end{proof}
Next, we include a result that shows that $\mathrm{GalCat}$ (or, rather, its opposite) behaves, to some extent,
like a Galois category itself; at least, it satisfies a version of the first
axiom of \Cref{galax}.
\begin{definition}
\label{connectedgalois}
A Galois category $\mathcal{C}$ is \textbf{connected} if there exists no
decomposition $\ast \simeq \ast_1 \sqcup \ast_2$ with $\ast_1, \ast_2$
nonempty and if additionally $\emptyset \not\simeq \ast$.
\end{definition}
\begin{proposition} \label{prodgc}
Let $\mathcal{C}$ be a connected Galois category and let $\mathcal{C}_1,
\mathcal{C}_2$ be Galois categories. Then $\mathcal{C}_1 \times \mathcal{C}_2
\in \mathrm{GalCat}$ and we have an equivalence of groupoids
\[ \mathrm{Fun}^{\mathrm{Gal}}(\mathcal{C}_1 \times \mathcal{C}_2, \mathcal{C}) \simeq
\mathrm{Fun}^{\mathrm{Gal}}( \mathcal{C}_1, \mathcal{C}) \sqcup \mathrm{Fun}^{\mathrm{Gal}}(\mathcal{C}_2, \mathcal{C}),
\]
\end{proposition}
The above equivalence of groupoids is as follows.
Given a functor $\mathcal{C}_i \to \mathcal{C}$ for $i \in
\left\{1,2\right\}$, we obtain a functor $\mathcal{C}_1 \times \mathcal{C}_2
\to \mathcal{C}$ by composing with the appropriate projection.
\begin{proof}
The assertion that $\mathcal{C}_1 \times \mathcal{C}_2 \in \mathrm{GalCat}$ is easy to
check.
Consider a functor $F\colon \mathcal{C}_1 \times \mathcal{C}_2 \to \mathcal{C}$ in
$\mathrm{GalCat}$.
Note that every object
$(x,y) \in \mathcal{C}_1 \times \mathcal{C}_2$ decomposes as the disjoint union
$(x, \emptyset) \sqcup (\emptyset, y)$.
For example, in $\mathcal{C}_1 \times \mathcal{C}_2$, the terminal object $\ast
= (\ast, \ast)$
decomposes as the union $\ast_1 \sqcup \ast_2$ where $\ast_1$ is terminal in
$\mathcal{C}_1$ and empty in $\mathcal{C}_2$, and $\ast_2$ is terminal in
$\mathcal{C}_2$ and empty in $\mathcal{C}_1$.
It follows that $F(\ast_1) = \emptyset$ or $F(\ast_2) = \emptyset$ since
$\mathcal{C}$ is connected. If $F( \ast_1) = \emptyset$ and therefore
$F(\ast_2) = \ast$, then we have
for $x \in \mathcal{C}_1, y \in \mathcal{C}_2$,
\[ F((x,y)) \simeq F((x,y) \times \ast_2) \simeq F( (\emptyset, y)), \]
so that $F$ (canonically) factors through $\mathcal{C}_2$.
The other case is analogous.
\end{proof}
More generally, let $\mathcal{C}$ be an arbitrary Galois category, and fix
$\mathcal{C}_1, \mathcal{C}_2 \in \mathrm{GalCat}$. We find, by the same reasoning,
\begin{equation} \label{prodgcgen} \mathrm{Fun}^{\mathrm{Gal}}( \mathcal{C}_1 \times \mathcal{C}_2,
\mathcal{C}) \simeq \bigsqcup_{\ast = \ast_1
\sqcup \ast_2} \mathrm{Fun}^{\mathrm{Gal}}(\mathcal{C}_1, \mathcal{C}_{/\ast_1}) \times \mathrm{Fun}^{\mathrm{Gal}}(
\mathcal{C}_2, \mathcal{C}_{/\ast_2}), \end{equation}
where the disjoint union is taken over all decompositions of the terminal
object in $\mathcal{C}$.
This concludes our preliminary discussion of the basic properties of Galois categories.
In the next subsection, we will give another description of the $(2,
1)$-category of Galois categories. For now, though, we describe a basic method of extracting Galois
categories from other sources.
\begin{definition}
\label{galcontextdef}
A \textbf{Galois context} is an $\infty$-category $ \mathcal{C}$
satisfying the first two axioms of \Cref{galax} together with a class
$\mathcal{E} \subset \mathcal{C}$ of morphisms such that:
\begin{enumerate}
\item $\mathcal{E} $ is closed under composition and base change and contains
every equivalence.
\item Every morphism in $\mathcal{E}$ is an effective descent morphism.
\item Given a cartesian diagram
\[ \xymatrix{
x' \ar[d] \ar[r] & x \ar[d] \\
y' \ar[r] & y
},\]
where $y' \to y \in \mathcal{E}$, then $x \to y $ belongs to $\mathcal{E}$ if and
only if $x' \to y'$ does.
\item A map $x \to y \simeq y_1 \sqcup y_2$ belongs to $\mathcal{E}$ if and only if $x
\times_{y} y_1 \to y_1$ and $x \times_y y_2 \to y_2$ belong to $\mathcal{E}$.
\item For any object $x \in \mathcal{C}$ and any finite nonempty set $S$, the
fold map $\bigsqcup_S x \to x$ belongs to $\mathcal{E}$.
\end{enumerate}
Given Galois contexts $(\mathcal{C}, \mathcal{E})$ and $(\mathcal{D},
\mathcal{E}')$, a \textbf{functor of Galois contexts} $F \colon(\mathcal{C},
\mathcal{E}) \to (\mathcal{D}, \mathcal{E}')$ will mean a functor of
$\infty$-categories $\mathcal{C} \to \mathcal{D}$ which respects finite limits
and coproducts and which carries morphisms in $\mathcal{E}$ to morphisms in
$\mathcal{E}'$.
\end{definition}
\begin{definition}
Given a Galois context $(\mathcal{C}, \mathcal{E})$, we say that an object $x \in \mathcal{C}$ is \textbf{Galoisable} (or
$\mathcal{E}$-Galoisable) if there
exists a map $y \to \ast$ in $\mathcal{E}$ such that the pullback $x \times y
\to y$ is in mixed elementary form in $\mathcal{C}_{/y}$, as in the discussion
after \Cref{galax}. In
other words, we require that there is a decomposition $y \simeq y_1 \sqcup
\dots \sqcup y_n$ such that each $x \times y_i \to y_i$ decomposes as a finite
coproduct $\bigsqcup_{S_i} y_i \to y_i$.
\end{definition}
Given a category satisfying the first two axioms of \Cref{galax},
the following result enables us to extract a Galois category by considering
the Galoisable objects.
\begin{proposition} \label{galcontext}
Let $(\mathcal{C}, \mathcal{E})$ be a Galois context. Then the collection of Galoisable objects in $\mathcal{C}$
(considered as a full subcategory of $\mathcal{C}$) forms a Galois category.
\end{proposition}
\begin{proof}
Note first that the collection of Galoisable objects actually forms a
\emph{category} rather than an $\infty$-category: that is, the mapping space
between any two Galoisable objects is (homotopy) discrete. More precisely, if
$x \in \mathcal{C}$ is Galoisable and $x' \in \mathcal{C}$ is arbitrary, then
we claim that $\hom_{\mathcal{C}}(x', x)$ is discrete. To see this, we choose
an effective descent morphism $u_1 \sqcup \dots \sqcup u_n \twoheadrightarrow \ast$
such that each map $u_i \times x \to x$ is in elementary form. Using the
expression $\mathcal{C} \simeq \mathrm{Tot}( \mathcal{C}_{/u_1 \times \dots
\times u_n})$, one reduces to the case where $x$ is a (disjoint) finite
coproduct of copies
of the terminal object $\ast$. In this case, $\hom_{\mathcal{C}}(x',
\bigsqcup_S \ast)$
is the \emph{set} of all $S$-labeled decompositions of $x'$ as direct sums of
subobjects, using the expression $\mathcal{C}_{/\bigsqcup_S \ast} \simeq
\prod_S \mathcal{C}_{/\ast} \simeq \prod_S \mathcal{C}$.
Suppose $y \in \mathcal{C}$ is a Galoisable object. We need to show that there is
a Galoisable object $t'$ and an $\mathcal{E}$-morphism $t' \twoheadrightarrow
\ast$ such that the
pullback $y \times t' \to t'$ is in mixed elementary form. By assumption, we
know that we can do this with \emph{some} object $t \in \mathcal{C}$ with an
$\mathcal{E}$-morphism $t \twoheadrightarrow \ast$, but we do not have any
control of $t$.
We will find a \emph{Galoisable} choice of $t'$ by an inductive procedure.
Define the \emph{rank} of a
Galoisable object $y \in \mathcal{C}$ as follows. If $y$ is mixed elementary, with respect to a
decomposition $\ast \simeq \bigsqcup_{i=1}^n \ast_i$ (with the $\ast_i$
nonempty) and $y = \bigsqcup_{i=1}^n
\bigsqcup_{S_i} \ast_i$ for finite sets $S_i$, we define the rank to be $\sup_i
|S_i|$.
In general, we make a base change in $\mathcal{C}$ along some
$\mathcal{E}$-morphism $t \to \ast$ (by a not necessarily
Galoisable object)
to reduce to this case. In other words, to define the rank of $y$, we choose an
$\mathcal{E}$-morphism $t \twoheadrightarrow \ast$ such that $y \times t \to t$
is in mixed elementary form in $\mathcal{C}_{/t}$, and then consider the rank
of that.
If the rank is zero, then $y = \emptyset$.
We now use {induction} on the rank of $y$.
First, we claim that there is a decomposition $\ast \simeq \ast_1 \sqcup
\ast_2$ such that $y \to \ast$ factors through an $\mathcal{E} $-morphism
$ y \to \ast_1$. (Meanwhile, $y \times_{\ast} \ast_2 = \emptyset$.) To see
this decomposition and claim, we can work locally on $\mathcal{C} \simeq \mathrm{Tot}( \mathcal{C}_{/t
\times \dots \times t})$ to reduce to the case in which $y$ is already in mixed
elementary form, for which the assertion is evident.
Thus we can reduce to the case where $y \to \ast$ is an $\mathcal{E}$-morphism.
Now consider the pullback $y \times y \to y$.
This admits a section, so we have $y \times y \simeq y \sqcup c$ where $c$ is
another Galoisable object in $\mathcal{C}_{/y}$; to see that $c$ exists, one works locally using
$t$ to reduce to the mixed elementary case. However, by working locally again, one sees that the rank
of $c $ is one less than the rank of $y $. We can reduce
the rank one by one, splitting off pieces, to get down to the case where $y =
\emptyset$.
\end{proof}
In fact, the above argument shows that if $x \in \mathcal{C}$ is Galoisable,
there exists a Galoisable $y \in \mathcal{C}$ together with a morphism $y
\twoheadrightarrow \ast$ which belongs to $\mathcal{E}$ such that $x \times y
\to y$ is in mixed elementary form.
\begin{corollary}
Let $(\mathcal{C}, \mathcal{E})$ be a Galois context. Then a map $x \to y$
between Galoisable objects in $\mathcal{C}$ is an effective descent morphism in the
category of Galoisable objects if and only if it belongs to $\mathcal{E}$.
Therefore, a functor of Galois contexts induces a functor of Galois categories.
\end{corollary}
\begin{proof}
Working locally (because of the local nature of belonging to $\mathcal{E}$,
and in view of the preceding remark), we may assume the map $x \to y$ is setlike, in which case it
is evident.
\end{proof}
\subsection{The Galois correspondence}
The Galois correspondence for groupoids gives an alternate description of the
$(2, 1)$-category $\mathrm{GalCat}$. To see this, we describe the building
blocks in $\mathrm{GalCat}$.
\begin{example} \label{gpgal}
Let $G$ be a finite group. Then the category $\mathrm{FinSet}_G$ of finite $G$-sets is a Galois
category. Only the last axiom requires verification. In fact, given any finite $G$-set $T$, we have an effective
descent morphism $G \to \ast$ such that $T \times G$, as a $G$-set, is a disjoint
union of copies of $G$ (since it is free).
This Galois category enjoys a convenient universal property, following
\cite{cjf}.
\begin{definition}
Let $\mathcal{C}$ be a Galois category and let $G$ be a finite group. A
\textbf{$G$-torsor} in $\mathcal{C}$ consists of an object $x \in \mathcal{C}$
with a $G$-action such that there exists an effective descent morphism $y
\twoheadrightarrow \ast$ such that $y \times x \in \mathcal{C}_{/y}$, as an
object with a $G$-action, is given by
\[ y \times x \simeq \bigsqcup_G y, \]
where $G$ acts on the latter by permuting the summands.
For instance, $x$ could be $\bigsqcup_G \ast$.
The collection of $G$-torsors forms a full subcategory
$\mathrm{Tors}_G(\mathcal{C})
\subset \mathrm{Fun}(BG, \mathcal{C})$.
\end{definition}
The Galois category $\mathrm{FinSet}_G$ has a natural example of a $G$-torsor: namely,
$G$ itself. The next result states that it is \emph{universal} with respect to
that property.
\begin{proposition}
\label{torsors}
If $\mathcal{C}$ is a Galois category, there is a natural equivalence between
$\mathrm{Fun}^{\mathrm{Gal}}(\mathrm{FinSet}_G, \mathcal{C})$ and the category
$\mathrm{Tors}_G(\mathcal{C})$ of $G$-torsors in
$\mathcal{C}$.
\end{proposition}
\begin{proof}
Any functor of Galois categories preserves torsors for any finite group.
In particular, given a functor $F\colon \mathrm{FinSet}_G \to \mathcal{C}$ in $\mathrm{GalCat}$, one gets a natural
choice of $G$-torsor in $\mathcal{C}$ by considering $F(G)$. Since everything
in $\mathrm{FinSet}_G$ is a colimit of copies of $G$, the choice of $F(G)$ determines
everything else. Together with the Yoneda lemma, this implies that the functor from $\mathrm{Fun}^{\mathrm{Gal}}(\mathrm{FinSet}_G,
\mathcal{C})$ to $G$-torsors is fully faithful.
It remains to argue that, given a $G$-torsor in $\mathcal{C}$,
one can construct a corresponding functor $\mathrm{FinSet}_G \to \mathcal{C}$ in
$\mathrm{GalCat}$.
In other words, we want to show that the fully faithful functor
\[ \mathrm{Fun}^{\mathrm{Gal}}( \mathrm{FinSet}_G, \mathcal{C}) \to \mathrm{Tors}_G(\mathcal{C}) , \]
is essentially surjective.
However, writing $\mathcal{C}$ as a
totalization of $\mathcal{C}_{/x \times \dots \times x}$, one may assume
the $G$-torsor is trivial, in which case the claim is evident.
\end{proof}
\end{example}
More generally, we can build Galois categories from finite groupoids.
This will be very important from a 2-categorical point of view.
\begin{definition}
We say that a groupoid $\mathscr{G}$ is \textbf{finite} if
$\mathscr{G}$ has finitely many isomorphism classes of objects and, for each object $x
\in \mathscr{G}$, the automorphism group $\mathrm{Aut}_{\mathscr{G}}(x)$ is finite.
The collection of all finite groupoids, functors, and natural transformations is naturally organized into a (2,
1)-category $\mathrm{Gpd}_{\mathrm{fin}}$.
\end{definition}
In other words, a finite groupoid is a 1-truncated homotopy type such that
$\pi_0$ is finite, as is $\pi_1$ with any choice of basepoint.
Given a finite groupoid $\mathscr{G}$, the category $\mathrm{Fun}(\mathscr{G}, \mathrm{FinSet})$ of functors from
$\mathscr{G}$ into the category of finite sets forms a Galois category.
This is a generalization of \Cref{gpgal} and follows from it since the
categories $\mathrm{Fun}(\mathscr{G}, \mathrm{FinSet})$ are finite products of the Galois categories of
finite $G$-sets as $G$ varies over the automorphism groups.
If we interpret $\mathscr{G}$ as a 1-truncated homotopy type, then this is
precisely the category of finite \emph{covering spaces} of $\mathscr{G}$, or of local
systems of finite sets on $\mathscr{G}$.
It follows that we get a functor
of $(2, 1)$-categories
\[ \mathrm{Gpd}_{\mathrm{fin}}^{\mathrm{op}} \to \mathrm{GalCat}, \]
sending a finite groupoid $\mathscr{G}$ to the associated functor category $\mathrm{Fun}( \mathscr{G},
\mathrm{FinSet})$. Note that, for example, a
natural transformation between functors of finite groupoids gives a natural
transformation at the level of Galois categories.
In order to proceed further, we need a basic formal property of $\mathrm{GalCat}$:
\begin{proposition}
The $(2, 1)$-category $\mathrm{GalCat}$ admits filtered colimits, which are computed
at the level of the underlying categories: the colimit of a diagram of
Galois
categories and functors between them (which respect coproducts, finite limits,
and effective descent morphisms) in the $(2, 1)$-category of categories is again a
Galois category.
\end{proposition}
\begin{proof}
Let $F\colon I \to \mathrm{GalCat}$ be a filtered diagram of Galois categories. Our claim is
that the colimit $\varinjlim_I F$ is a Galois category and the natural
functors $F(j) \to \varinjlim_I F$ respect the relevant structure. We first
observe that $\varinjlim_I F$ has all finite limits and colimits, and
the functors $F(j) \to \varinjlim_I F$ respect those. This holds for any
filtered diagram of $\infty$-categories and functors preserving finite limits
(resp. colimits) as a formal consequence of the commutation of finite limits
and filtered colimits in the $\infty$-category of spaces. For example, every
finite diagram in $\varinjlim_I F$ factors through a finite stage.
From this, the first two axioms of \Cref{galax} follow.
Next, we want to claim that the functors $F(j) \to \varinjlim_I F$ respect
effective descent morphisms. Once we have shown this, the last axiom of \Cref{galax}
will follow, since we know it at each stage $F(j)$.
In fact, let $x \to y$ be an effective descent morphism in $F(j)$.
Then, we need to check that pull-back along $x \to y$ is conservative and
respects finite colimits in $\varinjlim_I F$; however, this follows since it
holds in each $F(j')$, since finite colimits and pullbacks are preserved under
$F(j') \to \varinjlim_I F$.
Finally, it follows from the previous paragraph that since every object in each $F(j)$ is locally in mixed
elementary form, with respect to effective descent morphisms in $F(j)$, the same is
true in $\varinjlim_I F$, since every object in the colimit comes from a
finite stage.
\end{proof}
It follows that we get a natural functor
\[ \mathrm{Pro}( \mathrm{Gpd}_{\mathrm{fin}})^{\mathrm{op}} \simeq \mathrm{Ind}( \mathrm{Gpd}_{\mathrm{fin}}^{\mathrm{op}}) \to \mathrm{GalCat} , \]
i.e., a \emph{contravariant} functor from the $(2, 1)$-category
$ \mathrm{Pro}( \mathrm{Gpd}_{\mathrm{fin}})^{\mathrm{op}}$ into the $(2,
1)$-category of Galois categories.
We give this a name.
\begin{definition}
A \textbf{profinite groupoid} is an object of $\mathrm{Pro}( \mathrm{Gpd}_{\mathrm{fin}}^{\mathrm{op}})$.
\end{definition}
We will describe some features of the $(2, 1)$-category of profinite groupoids
in the next subsection.
In the meantime, the main result can now be stated as follows.
\begin{theorem}[The Galois correspondence] \label{galequiv}
The functor $\mathrm{Pro}( \mathrm{Gpd}_{\mathrm{fin}})^{\mathrm{op}} \to \mathrm{GalCat}$ is an equivalence of
2-categories.
\end{theorem}
\begin{proof}
We first check that the functor is fully faithful. To do this, first fix
\emph{finite} groupoids $\mathscr{G}, \mathscr{G}'$. We want to compare
the categories of functors $\mathrm{Fun}( \mathscr{G}, \mathscr{G}')$ and $\mathrm{Fun}^{\mathrm{Gal}}( \mathrm{Fun}(\mathscr{G}', \mathrm{FinSet}), \mathrm{Fun}(\mathscr{G}, \mathrm{FinSet}))$.
In particular, we want to show that
\begin{equation} \label{agalmap} \mathrm{Fun}( \mathscr{G}, \mathscr{G}') \to \mathrm{Fun}^{\mathrm{Gal}}(
\mathrm{Fun}(\mathscr{G}', \mathrm{FinSet}), \mathrm{Fun}(\mathscr{G}, \mathrm{FinSet})),\end{equation}
is an equivalence of groupoids.
We can reduce to the case where $\mathscr{G}$ has one isomorphism class of
objects, since both sides of \eqref{agalmap} send coproducts in $\mathscr{G}$ to
products of groupoids. We can also reduce to the case where
$\mathscr{G}'$ has a single connected component, since if $\mathscr{G}$ is connected, then both sides of
\eqref{agalmap} take coproducts in $\mathscr{G}'$ to coproducts.
This is clear for the left-hand-side. For the right-hand-side, note that
coproducts in $\mathscr{G}'$ go over to \emph{products} in $\mathrm{GalCat}$ for $\mathrm{Fun}( \mathscr{G}',
\mathrm{FinSet})$. Now use \Cref{prodgc} to describe the corepresented functor for a product
in $\mathrm{GalCat}$.
In order to show that \eqref{agalmap} is an equivalence when $\mathscr{G}, \mathscr{G}'$ are
finite groupoids, it thus suffices to work with \emph{groups}.
We can do this extremely explicitly.
In the case of \emph{finite groups}, given any two such $G, G'$, the groupoid
of maps between the associated groupoids has connected components given by the
conjugacy classes of homomorphisms $G \to G'$. Given any $f\colon G \to G'$, the
automorphism group of $f$ is the centralizer of the image $f(G)$.
To understand $\mathrm{Fun}^{\mathrm{Gal}}(\mathrm{FinSet}_{G'}, \mathrm{FinSet}_G)$, we can use \Cref{torsors}. We
need to describe the category of $G'$-torsors in $\mathrm{FinSet}_G$.
Any such gives a $G'$-torsor in $\mathrm{FinSet}$ by forgetting, so a $G'$-torsor in
$\mathrm{FinSet}_G$ yields in particular a copy of $G'$ with $G$ acting
$G'$-equivariantly (i.e., $G$ acts by right multiplication by various elements of $G'$). It follows that any torsor arises by considering a
homomorphism $\phi\colon G \to G'$ and using that to equip the $G$-torsor $G' \in \mathrm{FinSet}_{G'}$ with
the structure of a $G$-set.
A natural transformation of functors, or a morphism of torsors, is
given by a conjugacy in $G'$ between two homomorphisms $G \to G'$: an
automorphism of the torsor comes from right multiplication by an element of
$G'$ which centralizes the image of $G \to G'$.
This verifies full faithfulness for finite groupoids, i.e., that
\eqref{agalmap} is an equivalence if $\mathscr{G}, \mathscr{G}'$ are finite.
Finally, we need to check that the full faithfulness holds for all
\emph{profinite} groupoids. That is a formal consequence of the fact that
$\mathrm{Fun}( \mathscr{G}, \mathrm{FinSet})$ is a \emph{compact} object in $\mathrm{GalCat}$ for $\mathscr{G}$ a finite
groupoid. If $\mathscr{G}$ is connected, this is a consequence of the universal
property, \Cref{torsors}, since a torsor involves a finite amount of data. In general, the observation follows from the
connected case together with \Cref{prodgc} (and the remarks immediately
following, in particular \eqref{prodgcgen}).
To complete the proof, we need to show that the functor is essentially surjective: that is, every
Galois category arises from a profinite groupoid.
For this, we need another lemma on the formal structure of $\mathrm{GalCat}$.
\begin{lemma}
\label{finlimgal}
$\mathrm{GalCat}$ admits finite limits, which are preserved under $\mathrm{GalCat} \to \mathrm{Cat}_\infty$.
\end{lemma}
\begin{proof}
Since $\mathrm{GalCat}$ has a terminal object (the terminal category), it suffices to
show that given a diagram
\[ \xymatrix{
& \mathcal{C}' \ar[d] \\
\mathcal{C}'' \ar[r] & \mathcal{C}
},\]
in $\mathrm{GalCat}$, the category-theoretic fiber product is still a Galois category.
Of the axioms in \Cref{galax}, only the third needs checking.
Note first that a map $x \to y$ in $\mathcal{C}' \times_{\mathcal{C}} \mathcal{C}''$ is
an effective descent morphism if it is one in $\mathcal{C}'$ and
$\mathcal{C}''$. This follows from
the fact that the formation of overcategories and totalizations are compatible
with fiber products of categories.
Let $x$ be an object of the fiber product. We want to show that $x$ is locally
in mixed elementary form. As before, we can perform induction on the
\emph{rank} of $x$ (defined as the maximum of the ranks of the images in
$\mathcal{C}', \mathcal{C}''$).
The natural map $x \to \ast$ has the property that
$\ast \simeq \ast_1 \sqcup \ast_2$ where $x \to \ast$ factors through an
effective descent morphism $x \twoheadrightarrow \ast_1$. In fact, we can construct
these on $\mathcal{C}', \mathcal{C}''$ and they have to match up on
$\mathcal{C}$. So, we can assume that $x \to \ast$ is an effective
descent morphism. Now after base-change along $x \to \ast$, we can find a section
of $x \times x \to x$ and thus obtain a splitting of $x \times x $ (since we
can in $\mathcal{C}', \mathcal{C}''$). Using induction on the rank, we can
conclude as before.
\end{proof}
\begin{remark}
\label{limgalcat}
The same logic shows that $\mathrm{GalCat}$ admits arbitrary limits, although they are
no longer preserved under the forgetful functor $\mathrm{GalCat} \to \mathrm{Cat}_\infty$; one has to
take the subcategory of the categorical limit consisting of objects whose rank
is bounded.
\end{remark}
Let $\mathcal{C}$ be any Galois category, which we want to show lies in the
image of the fully faithful functor $\mathrm{Pro}( \mathrm{Gpd}_{\mathrm{fin}})^{\mathrm{\mathrm{op}}} \to \mathrm{GalCat}$. In
order to do this, we will write $\mathcal{C}$ as a filtered colimit of
subcategories which do belong to the image.
Let $\mathcal{C}$ be a Galois category. Then, if $\mathcal{C}$ is not the
terminal category (i.e., if the map $\emptyset \to \ast$ in $\mathcal{C}$ is
not an isomorphism),
there is a faithful functor $\mathrm{FinSet} \to \mathcal{C}$ which sends a finite set
$S$ to $\bigsqcup_S \ast$. This is a functor in $\mathrm{GalCat}$ and defines, for
every nonempty Galois category $\mathcal{C}$, a (non-full) Galois subcategory
$\mathcal{C}_{\mathrm{triv}}$.
In other words, we take the objects which are in elementary form and the
setlike maps between them.
More generally, if $\ast$ decomposes as $\ast =
\ast_1 \sqcup \dots \sqcup \ast_n$, we can define a subcategory
$\mathcal{C}_{\mathrm{triv}}^{\mathrm{loc}} \subset \mathcal{C}$ by writing
$\mathcal{C} \simeq \prod_{i=1}^n \mathcal{C}_{/\ast_i}$ and taking the
subcategory $\mathcal{C}^{\mathrm{loc}}_{\mathrm{triv}} = \prod_{i=1}^n
({\mathcal{C}_{/\ast_i}})_{\mathrm{triv}}$.
Let $y\twoheadrightarrow \ast$ be an effective
descent morphism and let $y \simeq y_1 \sqcup \dots \sqcup y_n$ be a decomposition
of $y$. We define a map $f\colon x \to x'$ in $\mathcal{C}$ to be \emph{split} with respect to $y$
and the above decomposition if $f \times y_i \in \mathcal{C}_{/y_i}$ is setlike for each $i = 1, 2,
\dots, n$.
Via descent theory, we can write this subcategory as
\[ \mathcal{C}' = \mathrm{Tot}\left( \prod_{i=1}^n \mathcal{C}^{\mathrm{triv}}_{/y_i}
\rightrightarrows \prod_{i, j = 1}^n \mathcal{C}^{\mathrm{triv}}_{y_i \times
y_j} \triplearrows \dots \right).
\]
In other words, this subcategory of $\mathcal{C}$ arises as an inverse limit
(indexed by a cosimplicial diagram) of products of copies of $\mathrm{FinSet}$. Any
such is the category of finite covers of a finite CW complex (presented by
3-skeleton of the dual
simplicial set\footnote{We recall that the 3-truncation of the above
totalization is sufficient to compute the totalization.}) and is thus in the image of $\mathrm{Pro}( \mathrm{Gpd}_{\mathrm{fin}})^{\mathrm{op}}$. However, $\mathcal{C}$ is the filtered union over all such
subcategories as we consider effective descent morphisms $y_1 \sqcup \dots y_n
\twoheadrightarrow \ast$ with the $\left\{y_i\right\}$ varying.
It follows that $\mathcal{C}$ is the filtered colimit in $\mathrm{GalCat}$ of objects
which belong to the image of $\mathrm{Pro}( \mathrm{Gpd}_{\mathrm{fin}})^{\mathrm{op}} \to \mathrm{GalCat}$, and is therefore in the
image of $\mathrm{Pro}( \mathrm{Gpd}_{\mathrm{fin}})^{\mathrm{op}}$ itself.
\end{proof}
\Cref{galequiv} enables us to make the following fundamental definition.
\begin{definition}
Given a Galois category $\mathcal{C}$, we define the \textbf{fundamental
groupoid} or \textbf{Galois groupoid} $\pi_{\leq 1}\mathcal{C}$ of $\mathcal{C}$ as the associated
profinite groupoid under the correspondence of \Cref{galequiv}.
\end{definition}
We next use the Galois correspondence to obtain a few technical results on
torsors.
\begin{corollary}
\label{torsorenough}
The Galois categories $\mathrm{FinSet}_G$
jointly detect equivalences: given a functor in $\mathrm{GalCat}$, $F\colon \mathcal{C} \to
\mathcal{D}$, if $F$ induces an equivalence on the categories of $G$-torsors
for each finite group $G$, then $F$ is an equivalence. In other words, if
the map
\begin{equation} \label{tmap} \mathrm{Tors}_G(\mathcal{C})\to
\mathrm{Tors}_G(\mathcal{D}) \end{equation}
is an equivalence of groupoids for each $G$, then $F$ is an equivalence.
\end{corollary}
\begin{proof}
By \eqref{prodgcgen}, it follows that if
\eqref{tmap} is always an equivalence, then the map
\[ \hom_{\mathrm{GalCat}}( \mathrm{Fun}( \mathscr{G}, \mathrm{FinSet}), \mathcal{C}) \to \hom_{\mathrm{GalCat}}( \mathrm{Fun}(
\mathscr{G}, \mathrm{FinSet}), \mathcal{D}), \]
is an equivalence for each finite \emph{groupoid} $\mathscr{G}$. Dualizing,
and using the Galois correspondence, we
find that the map $\pi_{\leq 1} \mathcal{D} \to \pi_{\leq 1} \mathcal{C}$ of
profinite groupoids has the property that
\[ \hom_{\mathrm{Pro}( \mathrm{Gpd}_{\mathrm{fin}})}( \pi_{\leq 1} \mathcal{C}, \mathscr{G}) \to
\hom_{\mathrm{Pro}( \mathrm{Gpd}_{\mathrm{fin}})}( \pi_{\leq 1} \mathcal{D}, \mathscr{G})
\]
is always an equivalence, for every finite groupoid $\mathscr{G}$.
However, we know that finite groupoids generate
$\mathrm{Pro}( \mathrm{Gpd}_{\mathrm{fin}})$ under cofiltered limits, so we are done.
\end{proof}
\begin{corollary}
\label{splitbytorsor}
Let $\mathcal{C}$ be a Galois category and $x \in \mathcal{C}$ be an object.
Then there exists a $G$-torsor $y$ in $\mathcal{C}$ for some finite group
$G$ such that $x \times y \to y$ is in mixed elementary form in
$\mathcal{C}_{/y}$.
\end{corollary}
\begin{proof}
We can reduce to the case where $\mathcal{C} = \mathrm{Fun}( \mathscr{G}, \mathrm{FinSet})$ for
$\mathscr{G}$ a finite groupoid, since $\mathcal{C}$ is a filtered colimit of
such. Let $\mathscr{G}$ have objects $x_1, \dots , x_n$ up to isomorphism with
automorphism groups $G_1, \dots, G_n$. Then, there is a natural $G_1 \times
\dots \times G_n$-torsor $y$ on $\mathscr{G} \simeq \bigsqcup_{i=1}^n BG_i$
(which on the $i$th summand is the universal cover times the trivial $\prod_{j
\neq i} G_j$-torsor) such that any object $x$ in $\mathcal{C}$
has the property that $y \times x$ is in mixed elementary form.
\end{proof}
\subsection{Profinite groupoids}
Given \Cref{galequiv}, it behooves us to discuss the 2-category $\mathrm{Pro}(\mathrm{Gpd}_{\mathrm{fin}})$ of
profinite groupoids in more detail. We begin by studying connected components.
We have a natural functor $\pi_0 \colon \mathrm{Gpd}_{\mathrm{fin}} \to \mathrm{FinSet}$ sending a groupoid to its
set of isomorphism classes of objects. Therefore, we get a functor
$\pi_0 \colon \mathrm{Pro}( \mathrm{Gpd}_{\mathrm{fin}}) \to \mathrm{Pro}( \mathrm{FinSet})$ which
is uniquely determined by the properties that it recovers the old $\pi_0$ for
finite groupoids and that it commutes with cofiltered limits.
Recall that the
category $\mathrm{Pro}(\mathrm{FinSet})$ is the category of compact, Hausdorff, and totally
disconnected topological spaces, under the
realization functor which sends a profinite set to its inverse limit (in the
category of sets) with the inverse limit topology.
It follows that the collection of ``connected
components'' of a profinite groupoid is one of these.
\begin{remark}
Note that $\pi_0\colon \mathrm{Gpd}_{\mathrm{fin}} \to \mathrm{FinSet}$ does not commute with finite inverse
limits, so that its right Kan extension to
$\mathrm{Pro}(\mathrm{Gpd}_{\mathrm{fin}})$ does not.
While the reader might object that there should be a $\lim^1$ obstruction to
the commutation of $\pi_0$ and cofiltered limits (of towers, say), we
remark that $\lim^1$-terms always vanish for towers of finite groups.
\end{remark}
In practice, we will mostly be concerned with
the case where the (profinite) set $\pi_0$ of connected components is a
singleton.
\begin{definition}
We say that a profinite groupoid is \textbf{connected} if its $\pi_0$ is a
singleton.
The collection of connected profinite groupoids spans a full subcategory $\mathrm{Pro}(
\mathrm{Gpd}_{\mathrm{fin}})^{\geq 0} \subset \mathrm{Pro}( \mathrm{Gpd}_{\mathrm{fin}})$.
\end{definition}
In general, it will thus be helpful to have an explicit description of this profinite set.
Recall that there is an algebraic description of $\mathrm{Pro}(\mathrm{FinSet})$ given by
\emph{Stone duality.}
Given a Boolean algebra $B$, the spectrum $\mathrm{Spec} B$ of prime ideals (with its Zariski topology) is
an example of a profinite set, i.e., it is compact, Hausdorff, and totally
disconnected.
Recall now:
\begin{theorem}[Stone duality] The functor $B \mapsto \mathrm{Spec} B$ establishes an
anti-equivalence $\mathrm{Bool}^{\mathrm{op}} \simeq \mathrm{Pro}( \mathrm{FinSet})$.
\end{theorem}
For a textbook reference on Stone duality, see \cite{Johnstone}.
The Galois correspondence in the form of \Cref{galequiv} can be thought of as a
mildly categorified version of Stone duality.
In particular, we can use Stone duality to describe
$\pi_0$ of a profinite groupoid.
\begin{proposition} \label{connectedigal}
Let $\mathcal{C}$ be a Galois category. Then $\pi_0( \pi_{\leq 1} \mathcal{C})$
corresponds, under Stone duality, to the Boolean algebra of subobjects $x
\subset \ast$.
\end{proposition}
Let $\mathcal{C}$ be a Galois category. Given two subobjects $x, y \subset
\ast$ of the terminal object,
we define their product to be the categorical product $x \times y$. Their sum
is the minimal subobject of $\ast$ containing both $x,y$: in other words, the
image of $x \sqcup y \to \ast$.
By working locally, it follows that this actually defines a Boolean algebra.
\begin{proof}
In fact, if $\mathcal{C}$ is a Galois category corresponding to a \emph{finite}
groupoid, the result is evident. Since the construction above sends filtered
colimits of Galois categories to filtered colimits of Boolean algebras, we can
deduce it for any Galois category in view of \Cref{galequiv}.
\end{proof}
In practice, the Galois categories that we will be considering will be
connected (in the sense of \Cref{connectedgalois}). By \Cref{connectedigal}, it
follows that a Galois category $\mathcal{C}$ is
connected if and only if $\pi_{\leq 1} \mathcal{C}$ is connected as a
profinite groupoid.
In our setting, this will amount to the condition that certain commutative
rings are free from idempotents.
With this in mind, we turn our attention to the \emph{connected} case.
Here we will be able to obtain a very strong connection with the (somewhat more
concrete) theory of \emph{profinite groups.}
The $2$-category $\mathrm{Pro}( \mathrm{Gpd}_{\mathrm{fin}})$ has a terminal object $\ast$, the
contractible profinite groupoid. Under the Galois correspondence, this
corresponds to the category $\mathrm{FinSet}$ of finite sets.
\begin{definition}
A \textbf{pointed profinite groupoid} is a profinite groupoid
$\mathscr{G}$ together with a
map $\ast \to \mathscr{G}$ in $\mathrm{Pro}( \mathrm{Gpd}_{\mathrm{fin}})$. The collection of pointed profinite groupoids forms
a $(2, 1)$-category, the undercategory $\mathrm{Pro}( \mathrm{Gpd}_{\mathrm{fin}})_{\ast/}$.
\end{definition}
\newcommand{\mathrm{FinGp}}{\mathrm{FinGp}}
For example, let $G$ be a profinite group, so that $G$ is canonically a pro-object in finite
groups. Applying the classifying space functor to this system, we obtain a
\emph{pointed} profinite groupoid $BG \in \mathrm{Pro}( \mathrm{Gpd}_{\mathrm{fin}})$ as the formal inverse
limit of the finite groupoids $ B(G/U)$ as $U \subset G$ ranges over the open
normal subgroups, since each $B(G/U)$ is pointed. By construction, the associated Galois category is
$\varinjlim_{U \subset G} \mathrm{FinSet}_{G/U}$, or equivalently, the category of
finite sets equipped with a \emph{continuous} $G$-action (i.e., an action which
factors through $G/U$ for $U$ an open normal subgroup).
We thus obtain a functor
\[ B\colon \mathrm{Pro}( \mathrm{FinGp}) \to \mathrm{Pro}( \mathrm{Gpd}_{\mathrm{fin}})_{\ast/}, \]
where $\mathrm{FinGp}$ is the category of finite groups and $\mathrm{Pro}(\mathrm{FinGp})$ is the category of
profinite groups.
Observe that this functor is \emph{fully faithful}, since the analogous functor
$B\colon \mathrm{FinGp} \to (\mathrm{Gpd}_{\mathrm{fin}})_{\ast/}$ is fully faithful, and each $BG$ for $G$
finite defines a cocompact object of $\mathrm{Pro}( \mathrm{Gpd}_{\mathrm{fin}})_{\ast/}$.
There is a rough inverse to this construction, given by taking the
``fundamental group.''
In
general, if $\mathcal{C}$ is an $\infty$-category with finite limits, and $C
\in \mathcal{C}$ is an object, then the natural functor
\[ \mathrm{Pro}( \mathcal{C}_{C/}) \to \mathrm{Pro}(\mathcal{C})_{C/} \]
is an equivalence of $\infty$-categories.
In the case of $\mathcal{C} = \mathrm{Gpd}_{\mathrm{fin}}$, we know that there is a functor
\begin{equation} \pi_1\colon (\mathrm{Gpd}_{\mathrm{fin}})_{\ast/} \to \mathrm{FinGp} , \label{p1}\end{equation}
to the category $\mathrm{FinGp}$ of finite groups, given by the usual fundamental group of
a pointed space, or more categorically as the automorphism group of the
distinguished point.
As above, let $\mathrm{Pro}( \mathrm{FinGp})$ be the category of profinite groups and continuous
homomorphisms.
\begin{definition}
We define a functor $\pi_1\colon \mathrm{Pro}( \mathrm{Gpd}_{\mathrm{fin}})_{\ast/} \to \mathrm{Pro}( \mathrm{FinGp})$ from
the $2$-category of pointed profinite groupoids to the category of profinite
groups given by right Kan extension of \eqref{p1}, so that $\pi_1$ agrees
with the old $\pi_1$ on pointed finite groupoids and commutes with filtered
limits.
\end{definition}
Given a pointed finite groupoid $\mathscr{G}$, we have a natural map
\begin{equation} \label{nattransp} B \pi_1 ( \mathscr{G}) \to \mathscr{G}, \end{equation}
and by general formalism, we have a natural transformation of the form
\eqref{nattransp} on $\mathrm{Pro}( \mathrm{Gpd}_{\mathrm{fin}})_{\ast/}$.
\begin{proposition}
\label{gppt}
Given an object $\mathscr{G} \in \mathrm{Pro}( \mathrm{Gpd}_{\mathrm{fin}})_{\ast/}$, the following
are equivalent:
\begin{enumerate}
\item $\mathscr{G}$ is connected, i.e., $\pi_0 \mathscr{G}$ is a singleton.
\item The map $B \pi_1 \mathscr{G} \to \mathscr{G}$ is an equivalence in
$\mathrm{Pro}( \mathrm{Gpd}_{\mathrm{fin}})_{\ast/}$.
\end{enumerate}
In particular, the functor $B\colon \mathrm{Pro}( \mathrm{FinGp}) \to \mathrm{Pro}( \mathrm{Gpd}_{\mathrm{fin}})_{\ast/}$ is fully
faithful with image consisting of the pointed connected profinite groupoids.
\end{proposition}
\begin{proof}
The second statement clearly implies the first: any $B G$ for $G$ a profinite
group is connected, as the inverse limit of connected profinite groupoids.
We have also seen that the functor $B$ is fully faithful, since it is fully
faithful on finite groups.
It remains to show that if $\mathscr{G}$ is a pointed, connected profinite
groupoid, then the map $B \pi_1 \mathscr{G} \to \mathscr{G}$ is an equivalence.
For this, we write $\mathscr{G}$ as a cofiltered limit $\varprojlim_I
\mathscr{G}_i$, where $I$ is a filtered partially ordered set indexing the $\mathscr{G}_i$ and each $\mathscr{G}_i$ is a
pointed finite groupoid. We know that $\mathscr{G}$ is connected, though each
$\mathscr{G}_i$ need not be. However, we obtain a new inverse system
$\left\{B \pi_1 \mathscr{G}_i\right\}$ equipped with a map to the inverse system
$\{\mathscr{G}_i\}$ and we want to show that the two inverse systems are
pro-isomorphic.
We need to produce an inverse map of pro-systems $\left\{\mathscr{G}_i\right\} \to
\left\{B \pi_1 \mathscr{G}_i\right\}$.
For this, we need to produce for each $i \in I$
an element $j \geq i$ and a map
\[ \mathscr{G}_j \to B \pi_1 \mathscr{G}_i. \]
These should define an element of $\varprojlim_i \varinjlim_j \hom(
\mathscr{G}_j, B \pi_1 \mathscr{G}_i)$.
In order to do this, we simply note that there exists $j \geq i$ such that the
map $\mathscr{G}_j \to \mathscr{G}_i$ lands inside the connected component $B
\pi_1 \mathscr{G}_i$ of $\mathscr{G}_i$ at the basepoint, because otherwise the
pro-system would not be connected as a filtered inverse limit of nonempty finite
sets is nonempty.
One checks easily that the two maps of pro-systems define an isomorphism
between $\left\{\mathscr{G}_i\right\}$ and $\left\{B
\pi_1\mathscr{G}_i\right\}$.
\end{proof}
Let $\mathscr{G} \in \mathrm{Pro}( \mathrm{Gpd}_{\mathrm{fin}})$ be a
\emph{connected} profinite groupoid.
This means that the space of maps $\ast \to \mathscr{G}$ in $\mathrm{Pro}( \mathrm{Gpd}_{\mathrm{fin}})$ is
connected, i.e., there is only one such map up to homotopy. (This is not
entirely immediate, but will be a special case of \Cref{mappingspaces} below.) Once we choose a
map, we point $\mathscr{G}$ and then the data is essentially equivalent to
that of a
profinite group
in view of \Cref{gppt}. If we do not point $\mathscr{G}$, then what we have is
essentially a profinite group ``up to conjugacy.''
\begin{proposition}
\label{mappingspaces}
Let $G, G'$ be profinite groups. Then the space $\hom_{\mathrm{Pro}( \mathrm{Gpd}_{\mathrm{fin}})}( BG, BG')$
is given as follows:
\begin{enumerate}
\item The connected components are in one-to-one correspondence with conjugacy
classes of continuous homomorphisms $f\colon G \to G'$.
\item The group of automorphisms of a given continuous homomorphism $f\colon G \to
G'$ is given by the centralizer in $G'$ of the image of $f$.
\end{enumerate}
\end{proposition}
In other words, if we restrict our attention to the subcategory $\mathrm{Pro}(
\mathrm{Gpd}_{\mathrm{fin}})^{\geq 0} \subset \mathrm{Pro}(
\mathrm{Gpd}_{\mathrm{fin}})$ consisting of \emph{connected} profinite groupoids, then it has a simple
explicit description as a 2-category where the objects are the profinite
groups, maps are continuous homomorphisms, and 2-morphisms are conjugations.
\begin{proof}
This assertion is well-known when $G, G'$ are finite groups: maps between $BG$
and $BG'$ in $\mathrm{Gpd}_{\mathrm{fin}}$ are as above.
The general case follows by passage to cofiltered limits.
Let $G = \varprojlim_U G/U, G' = \varprojlim_V G'/V$ where $U$ (resp. $V$)
ranges over the open normal subgroups of $G$ (resp. $G'$).
In this case, we have
\[ \hom_{\mathrm{Pro}( \mathrm{Gpd}_{\mathrm{fin}})}(BG, BG') \simeq \varprojlim_V \varinjlim_U \hom_{\mathrm{Gpd}_{\mathrm{fin}}}(
B(G/U), B(G/V)), \]
and passing to the limit, we can conclude the result for $G, G'$ profinite, if
we observe that the set of conjugacy classes of continuous homomorphisms $G \to G'$
is the inverse limit of the sets of conjugacy classes of continuous
homomorphisms $G \to G'/V$ as $V \subset G$ ranges over open normal subgroups.
The assertion about automorphisms, or conjugacies, is easier.
To see this in turn,
suppose given continuous homomorphisms $\phi_1, \phi_2\colon G \to G'$ such that,
for every continuous map $\psi\colon G' \to G''$ where $G''$ is finite, the
composites $\psi \circ \phi_1, \psi \circ \phi_2$ are conjugate. We claim that
$\phi_1, \phi_2$ are conjugate. The collection of all surjections $\psi \colon G'
\to G''$ with $G''$ finite forms a filtered system, and for each $\psi$, we consider
the (finite) set $F_{\psi} \subset G''$ of $x \in G''$ such that $\psi
\circ \phi_2 = x ( \psi \circ \phi_1 ) x^{-1}$. Since by hypothesis each
$F_{\psi}$ is nonempty, it follows that the inverse limit is nonempty, so that
$\phi_1, \phi_2$ are actually conjugate as homomorphisms $G \to G'$.
Conversely, suppose given for each $\psi\colon G' \to G''$ with $G''$ finite a \emph{conjugacy class}
of continuous maps $\phi_{\psi}\colon G \to G''$, and suppose these are compatible with one
another; we want to claim that there exists a conjugacy class of continuous
homomorphisms $\phi\colon G \to G'$ that lifts all the $\phi_{\psi}$. For this, we
again consider the \emph{finite} nonempty sets $G_{\psi}$ of all continuous
homomorphisms $G \to G''$ in the conjugacy class of $\phi_{\psi}$, and observe
the inverse limit of these is nonempty. Any point in the inverse limit gives a
continuous homomorphism $G \to G''$ with the desired property.
\end{proof}
\section{The Galois group and first computations}
Let $(\mathcal{C}, \otimes, \mathbf{1})$ a stable homotopy theory. In this
section, we will make the main definition of this paper, and describe two candidates for the \emph{Galois group} (or, in
general, groupoid) of
$\mathcal{C}$. Using the descent theory described in
\Cref{sec:descent}, we will
define a category of \emph{finite covers} in the
$\infty$-category $\mathrm{CAlg}(\mathcal{C})$
of commutative algebra objects in $\mathcal{C}$. Finite covers will be
those commutative algebra objects which ``locally'' look like direct factors of
products of copies of the unit. There are two possible definitions of
``locally,'' which lead to slightly different Galois groups.
We will show that these $\infty$-categories of finite covers are actually
Galois categories in the sense of \Cref{galax}. Applying the Galois correspondence,
we will obtain a profinite groupoid.
The rest of this paper will be devoted to describing the Galois group in certain
special instances.
In this section, we will begin that process by showing that the Galois group is
entirely algebraic in two particular instances: connective $\e{\infty}$-rings
and even periodic $\e{\infty}$-rings with regular $\pi_0$. In
either of these cases, one has various algebraic tricks to study modules via
their homotopy groups.
The
associated $\infty$-categories of modules turn out to be extremely useful
building blocks for a much wider range of stable homotopy theories.
\subsection{Two definitions of the Galois group}
Let $(\mathcal{C}, \otimes, \mathbf{1})$ be a stable homotopy theory, as before.
We will describe two possible analogs of ``finite \'etaleness'' appropriate to
the categorical setting.
\newcommand{\clg^{\mathrm{cov}}}{\mathrm{CAlg}^{\mathrm{cov}}}
\newcommand{\clg^{\mathrm{w.cov}}}{\mathrm{CAlg}^{\mathrm{w.cov}}}
\begin{definition}
\label{deffinitecover}
An object $A \in \mathrm{CAlg}(\mathcal{C})$ is a \textbf{finite cover} if there exists
an $A' \in \mathrm{CAlg}(\mathcal{C})$ such that:
\begin{enumerate}
\item $A'$ admits descent, in the sense of
\Cref{admitd}.
\item $A \otimes A' \in \mathrm{CAlg}( \mathrm{Mod}_{\mathcal{C}}(A'))$ is of
the form $\prod_{i=1}^n A'[e_i^{-1}]$, where for each $i$, $e_i $ is an
idempotent in $A'$.
\end{enumerate}
The finite covers span a subcategory $\clg^{\mathrm{cov}}(\mathcal{C}) \subset \mathrm{CAlg}(
\mathcal{C})$.
\end{definition}
\begin{definition}
\label{weakfincover}
An object $A \in \mathrm{CAlg}(\mathcal{C})$ is a \textbf{weak finite cover} if there exists
an $A' \in \mathrm{CAlg}(\mathcal{C})$ such that:
\begin{enumerate}
\item The functor $\otimes A'\colon \mathcal{C} \to \mathcal{C}$ commutes with all homotopy
limits.
\item The functor $\otimes A'$ is conservative.
\item
$A \otimes A' \in \mathrm{CAlg}( \mathrm{Mod}_{\mathcal{C}}(A'))$ is of
the form $\prod_{i=1}^n A'[e_i^{-1}]$, where for each $i$, $e_i $ is an
idempotent in $A'$.
\end{enumerate}
The weak finite covers span a subcategory $\clg^{\mathrm{w.cov}}(\mathcal{C}) \subset
\mathrm{CAlg}(\mathcal{C})$.
\end{definition}
Our goal is to show that both of these definitions give rise to Galois
categories in the sense of the previous section, which we will do using the
general machine of \Cref{galcontext}. Observe first that
$\mathrm{CAlg}(\mathcal{C})^{\mathrm{op}}$ satisfies the first two conditions of \Cref{galax}.
\begin{lemma}
Given $\mathcal{C}$ as above, consider the $\infty$-category
$\mathrm{CAlg}(\mathcal{C})^{\mathrm{op}}$ and the collection of morphisms $\mathcal{E}$ given
by the maps $A \to B$ which admit descent. Then $(\mathrm{CAlg}(\mathcal{C})^{\mathrm{op}},
\mathcal{E})$ is a Galois context in the sense of \Cref{galcontextdef}.
\end{lemma}
\begin{proof}
The composite of two descendable morphisms is descendable by \Cref{permanence},
descendable morphisms are effective descent morphisms by \Cref{easydesc}, and the locality
of descendability (i.e., the third condition of \Cref{galcontextdef}) follows from the second part of \Cref{permanence}.
The remaining conditions are straightforward.
\end{proof}
\begin{lemma}
Given $\mathcal{C}$ as above, consider the $\infty$-category
$\mathrm{CAlg}(\mathcal{C})^{\mathrm{op}}$ and the collection of morphisms $\mathcal{E}$ given
by the maps $A \to B$ such that the functor $\otimes_A B \colon \mathrm{Mod}_{\mathcal{C}} (A) \to
\mathrm{Mod}_{\mathcal{C}}(B)$ commutes with limits and is conservative.
Then $(\mathrm{CAlg}(\mathcal{C})^{\mathrm{op}},
\mathcal{E})$ is a Galois context in the sense of \Cref{galcontextdef}.
\end{lemma}
\begin{proof}
It is easy to see that $\mathcal{E}$ satisfies the first axiom of
\Cref{galcontextdef}, and we can apply Barr-Beck-Lurie to see comonadicity of
$\otimes_A B$ (i.e., the second axiom). The fourth and fifth axioms are straightforward.
Finally, suppose $A \to B$ is a morphism in $\mathrm{CAlg}(\mathcal{C})$ and $A \to A'$ belongs
to $\mathcal{E}$, i.e., tensoring $\otimes_A A'$ commutes with limits and is
conservative. Suppose $A' \to B' \stackrel{\mathrm{def}}{=}A' \otimes_A B$ has the same property. Then we
want to claim that $A \to B$ belongs to $\mathcal{E}$.
First, observe that $\otimes_A B$ is conservative. If $M \in
\mathrm{Mod}_{\mathcal{C}}(A)$ is such that $M \otimes_A B \simeq 0$, then $(M \otimes_A
A') \otimes_{A'} B'$ is zero, so that $M \otimes_A A'$ is zero as
$A' \to B'$ belongs to $\mathcal{E}$, and thus $M = 0$.
Finally, we need to check the claim about $\otimes_A B $ commuting with
limits. In other words, given $\left\{M_i\right\} \in \mathrm{Mod}_{\mathcal{C}}(A)$, we need to
show that the natural map
\[ B \otimes_A \prod M_i \to \prod (M_i \otimes_A B) \]
is an equivalence. We can do this after tensoring with $A'$, so we need to see that
\[ A' \otimes_A B \otimes_A \prod M_i \to A' \otimes_A \prod (M_i \otimes_A B) \]
is an equivalence. However, since tensoring with $A'$ commutes with limits, this map is
\[ B' \otimes_{A'} \prod( M_i \otimes_A A') \to \prod (M_i \otimes_A A')
\otimes_{A'} B', \]
which is an equivalence since $\otimes_{A'}B'$ commutes with limits by
assumption.
\end{proof}
The basic result of this section is the following.
\begin{theorem}
\label{basicgal}
Given $\mathcal{C}$, $\clg^{\mathrm{cov}}(\mathcal{C})^{\mathrm{op}}$ and $\clg^{\mathrm{w.cov}}(\mathcal{C})^{\mathrm{op}}$ are
Galois
categories, with $\clg^{\mathrm{cov}}(\mathcal{C}) \subset \clg^{\mathrm{w.cov}}(\mathcal{C})$.
If $\mathbf{1} \in \mathcal{C}$ is compact, then the two are the same.
\end{theorem}
\begin{proof}
This follows from \Cref{galcontext} if we take $\mathrm{CAlg}(\mathcal{C})^{\mathrm{op}}$ as our input
$\infty$-category.
As we checked above, we have two candidates for $\mathcal{E}$, both of which
yield Galois contexts. The Galoisable objects yield either the finite covers or
the weak finite covers.
Next, we need to note that a finite cover is actually a weak finite cover.
Note first that either a finite cover or a weak finite cover is dualizable,
since dualizability can be checked locally in a limit diagram of
symmetric monoidal $\infty$-categories. However, the
argument of \Cref{galcontext} (or the following corollary) shows that, given a finite cover $A \in
\mathrm{CAlg}(\mathcal{C})$, we can choose the descendable $A' \in \mathrm{CAlg}(\mathcal{C})$
such that $A \otimes A'$ is in mixed elementary form so that $A'$ itself is a
finite cover: in particular, so that $A'$ is dualizable. Therefore, we can
choose $A'$ so that $\otimes A'$ commutes with arbitrary homotopy limits.
Finally, we need to see that the two notions are equivalent in the case where
$\mathbf{1}$ is compact. For this, we use the reasoning of the previous paragraph to
argue that if $A \in \clg^{\mathrm{w.cov}}(\mathcal{C})$, then there exists an object $A' \in
\clg^{\mathrm{w.cov}}(\mathcal{C})$ such that the dual to $\mathbf{1} \to A'$ is a distinguished
effective descent morphism (i.e., tensoring with $A'$ is conservative and commutes with homotopy limits)
and such that $A' \to A \otimes A'$ is in mixed elementary form. However, in
this case, $A'$ is dualizable, as an element of $\clg^{\mathrm{w.cov}}(\mathcal{C})$, so it
admits descent in view of \Cref{cptdescent}.
Therefore, $A$ is actually a finite cover.
\end{proof}
\begin{proposition}
Let $F\colon \mathcal{C} \to \mathcal{D}$ be a morphism of stable homotopy theories,
so that $F$ induces a functor $\mathrm{CAlg}(\mathcal{C}) \to \mathrm{CAlg}(\mathcal{D})$. Then
$F$ carries $\clg^{\mathrm{cov}}(\mathcal{C})$ into $\clg^{\mathrm{cov}}(\mathcal{D})$ and
$\clg^{\mathrm{w.cov}}(\mathcal{C})$ into $\clg^{\mathrm{w.cov}}(\mathcal{D})$.
\end{proposition}
\begin{proof}
Let $A \in \clg^{\mathrm{w.cov}}(\mathcal{C})$. Then there exists $A' \in \clg^{\mathrm{w.cov}}(\mathcal{C})$,
which is a $G$-torsor for some finite group $G$,
such that $A \otimes A'$ is a finite product of localizations of $A'$ at
idempotent elements, in view of \Cref{splitbytorsor}.
Therefore, $F(A) \otimes F(A')$ is a finite product of localizations of $F(A')$ at
idempotent elements.
Now $F(A') \in \mathrm{CAlg}(\mathcal{D})$ is dualizable since $A'$ is, so tensoring with $F(A')$
commutes with limits in $\mathcal{D}$. If we can show that tensoring with $F(A')$
is \emph{conservative} in $\mathcal{D}$, then it will follow that $F(A)$
satisfies the conditions of \Cref{weakfincover}.
In fact, we will show that the smallest \emph{ideal} of $\mathcal{D}$ closed
under arbitrary colimits and containing $F(A')$ is all of $\mathcal{D}$. This implies
that any object $Y \in \mathcal{D} $ with $Y \otimes F(A') \simeq 0$ must
actually be contractible.
To see this, recall that $A'$ has a $G$-action. We have a \emph{norm map} (cf.
\cite[sec. 2.1]{DAGrat} for a general reference in this context)
\[ A'_{hG} \to A'^{hG} \simeq \mathbf{1} , \]
which we claim is an equivalence (\Cref{normmap} below). After applying $F$, we find that $F(A')_{hG}
\simeq \mathbf{1}$, which proves the claim and thus shows that tensoring with $F(A')$ is faithful.
If $A \in \clg^{\mathrm{cov}}(\mathcal{C})$, then we could choose the torsor $A'$ so that it
actually belonged to $\clg^{\mathrm{cov}}(\mathcal{C})$ as well. The image $F(A')$ thus
is a descendable commutative algebra object in $\mathcal{D}$ since
descendability is a ``finitary'' condition that does not pose any convergence
issues with infinite limits. So, by similar (but easier) logic, we find
that $F(A) \in \clg^{\mathrm{cov}}(\mathcal{D})$.
\end{proof}
\begin{lemma}
\label{normmap}
Let $\mathcal{C}$ be a stable homotopy theory and let $A \in
\clg^{\mathrm{w.cov}}(\mathcal{C})^{\mathrm{op}}$ be a $G$-torsor, where $G$ is a finite group. Then
the norm map $A_{hG}\to A^{hG} \simeq \mathbf{1}$ is an equivalence.
\end{lemma}
\begin{proof}
It suffices to prove this after tensoring with $A$; note that tensoring with
$A$ is conservative and commutes with all homotopy limits.
However, after tensoring with $A$, the $G$-action on $A$ becomes induced, so
the norm map is an equivalence.
\end{proof}
\newcommand{\pi_1^{\mathrm{weak}}}{\pi_1^{\mathrm{weak}}}
Finally, we can make the main definition of this paper.
\begin{definition} Let $(\mathcal{C}, \otimes, \mathbf{1})$ be a stable
homotopy theory.
The \textbf{Galois groupoid} $\pi_{\leq 1}(\mathcal{C})$ of $\mathcal{C}$ is the
Galois groupoid of the Galois category $\clg^{\mathrm{cov}}(\mathcal{C})^{\mathrm{op}}$. The \textbf{weak
Galois groupoid} $\pi_{\leq 1}^{\mathrm{weak}}(\mathcal{C})$
is the Galois groupoid of $\clg^{\mathrm{w.cov}}(\mathcal{C})^{\mathrm{op}}$.
When $\mathbf{1}$ has no nontrivial idempotents, we will write
$\pi_1(\mathcal{C}), \pi_1^{\mathrm{weak}}(\mathcal{C})$ for the \textbf{Galois group} (resp.
\textbf{weak
Galois group}) of $\mathcal{C}$ with the understanding that these groups are
defined ``up to conjugacy.''
\end{definition}
As above, we have an inclusion $\clg^{\mathrm{w.cov}}(\mathcal{C}) \subset \clg^{\mathrm{cov}}(\mathcal{C})$
of Galois categories.
In particular, we obtain a morphism of profinite groupoids
\begin{equation} \label{weakmap}\pi_{\leq 1}^{\mathrm{weak}} (\mathcal{C}) \to
\pi_{\leq 1}(\mathcal{C}). \end{equation}
The dual map on Galois categories is fully faithful. In particular, if
$\mathcal{C}$ is \emph{connected}, so that $\pi_1, \pi_1^{\mathrm{weak}}$ can be represented by
profinite groups, the map \eqref{weakmap} is \emph{surjective.}
Moreover, by \Cref{basicgal}, if $\mathbf{1}$ is compact, \eqref{weakmap} is
an equivalence.
In the following, we will mostly be concerned with the Galois groupoid, which
is more useful for
computational applications because of the rapidity of the descent. The weak
Galois groupoid is better behaved as a functor out of the $\infty$-category of
stable homotopy theories. We will
discuss some of the differences further below. The weak Galois groupoid
seems in particular useful for potential applications in $K(n)$-local homotopy theory where
$\mathbf{1}$ is not compact.
Note, however, that the Galois groupoid depends only on the 2-ring of
\emph{dualizable objects} in a given stable homotopy theory, because the
property of admitting descent (for a commutative algebra object which is
dualizable) is a finitary one. So, the Galois groupoid can be viewed as a
functor $\mathrm{2}\text{-}\mathrm{Ring} \to \mathrm{Pro}( \mathrm{Gpd}_{\mathrm{fin}})^{\mathrm{op}}$.
\begin{definition}
We will define the \textbf{Galois group(oid)} of an $\e{\infty}$-ring $R$ to be that
of $\mathrm{Mod}(R)$. Note that the weak Galois group(oid) and the Galois group(oid) of $\mathrm{Mod}(R)$
are canonically isomorphic, by \Cref{basicgal}.
\end{definition}
In any event, both the profinite groupoids of \eqref{weakmap} map to something
purely algebraic. Given a finite \'etale cover of the ordinary commutative ring
$R_0 =
\pi_0 \mathrm{End}_{\mathcal{C}}(\mathbf{1})$, we get a commutative algebra
object in $\mathcal{C}$.
\begin{proposition}
Let $R'_0$ be a finite \'etale $R_0$-algebra. The induced classically \'etale
object of $\mathrm{CAlg}( \mathcal{C})$ is a finite cover, and we have a fully faithful
embedding
\[ \mathrm{Cov}_{\mathrm{Spec} R_0} \subset \clg^{\mathrm{cov}}(\mathcal{C})^{\mathrm{op}}, \]
from the category $\mathrm{Cov}_{\mathrm{Spec} R_0}$ of schemes finite \'etale over
$\mathrm{Spec} R_0$ into the opposite to the category $\clg^{\mathrm{cov}}(\mathcal{C})$.
\end{proposition}
This was essentially first observed in \cite{BRrealiz}.
\begin{proof}
We can assume that $\mathcal{C} = \mathrm{Mod}(R)$ for $R$ an $\e{\infty}$-ring, because
if $R = \mathrm{End}_{\mathcal{C}}(\mathbf{1})$, we always have an embedding
$\mathrm{Mod}^{\omega}(R) \subset \mathcal{C}$ and everything here happens inside
$\mathrm{Mod}^\omega(R)$ anyway. It follows from \Cref{etaletopinv} that we have a fully
faithful embedding $\mathrm{Cov}_{\mathrm{Spec} R_0} \subset \mathrm{CAlg}(\mathcal{C})^{\mathrm{op}}$, so it
remains only to show that any classically \'etale algebra object coming from a
finite \'etale $R_0$-algebra $R'_0$ is in fact a finite cover. However, we know that
there exists a finite \'etale $R_0$-algebra $R''_0$ such that:
\begin{enumerate}
\item $R''_0$ is faithfully flat over $R_0$.
\item $R'_0 \otimes_{R_0} R''_0$ is the localization of $\prod_S R''_0$ at an
idempotent element, for some finite set $S$.
\end{enumerate}
We can realize $R'_0, R''_0$ topologically by $\e{\infty}$-rings $R', R''$
under $R$. Now $R''$ admits descent over $R'$, as a finite faithfully flat $R$-module, and
$R' \otimes_R R''$ is the localization of $\prod_S R''$ at an idempotent
element, so that $R' \in \clg^{\mathrm{cov}}(\mathrm{Mod}(R))$.
\end{proof}
The classically \'etale algebras associated to finite \'etale $R_0$-algebras give the ``algebraic'' part of the Galois group
and fit into a sequence
\begin{equation}\label{weakmap2} \pi_1^{\mathrm{weak}}(\mathcal{C}) \twoheadrightarrow \pi_1(\mathcal{C})
\twoheadrightarrow \pi_1^{\mathrm{et}} \mathrm{Spec} R_0. \end{equation}
\begin{definition}
We will say that the Galois theory of $\mathcal{C}$ is \textbf{algebraic} if
these maps are isomorphisms.
\end{definition}
It is an insight of \cite{rognes} that
the second map in \eqref{weakmap2}
is generally not an isomorphism: that is, there are examples of finite covers that are
genuinely topological and do not appear so at the level of homotopy groups.
We will review the connection between our definitions and Rognes's work in the next section.
\subsection{Rognes's Galois theory}
In \cite{rognes}, Rognes introduced the definition of a \emph{$G$-Galois
extension} of an $\e{\infty}$-ring $R$ for $G$ a finite group.
(Rognes also considered the case of a \emph{stably dualizable group}, which
will be discussed only incidentally in this paper.)
Rognes worked in the setting of $E$-local spectra for $E$ a
fixed spectrum. The same definition would work in a general stable homotopy
theory. In this subsection, we will connect Rognes's definition with ours.
\begin{definition}[Rognes] \label{defgalr}
Let $(\mathcal{C}, \otimes, \mathbf{1})$ be a stable homotopy theory.
An object $A \in \mathrm{CAlg}(\mathcal{C})$ with the action of a finite group $G$ (in
$\mathrm{CAlg}(\mathcal{C})$) is a \textbf{$G$-Galois extension} if:
\begin{enumerate}
\item The map $\mathbf{1} \to A^{hG}$ is an equivalence.
\item The map $A \otimes A \to \prod_G A $ (given informally by $(a_1, a_2)
\mapsto \{a_1 g(a_2)\}_{g \in G}$) is an equivalence.
\end{enumerate}
We will say that $A$ is a \textbf{faithful $G$-Galois extension} if further
tensoring with $A$ is conservative.
\end{definition}
General $G$-Galois extensions in this sense are outside the scope of this
paper. In general, there is no reason for a $G$-Galois extension to
be well-behaved at all with respect to descent theory. By an example of Wieland
(see \cite{Rognes2}), the map $C^*(B \mathbb{Z}/p; \mathbb{F}_p) \to \mathbb{F}_p$ given by
evaluating on a point is a $\mathbb{Z}/p$-Galois extension, but one cannot
expect to carry out descent along it in any manner.
However, one has:
\begin{proposition}
\label{rognesequiv}
A faithful $G$-Galois extension in $\mathcal{C}$ is equivalent to a $G$-torsor
in the Galois category $\clg^{\mathrm{w.cov}}(\mathcal{C})$.
\end{proposition}
This in turn relies on:
\begin{proposition}[{\cite[Proposition 6.2.1]{rognes}} ]
\label{galdual}
Any $G$-Galois extension $A$ of the unit is dualizable.
\end{proposition}
The proof in \cite{rognes} is stated for the $E$-localization of $\mathrm{Mod}(A)$ for
$A$ an $\e{\infty}$-ring, but it is valid in any such setting.
\begin{proof}[Proof of \Cref{rognesequiv}]
A $G$-torsor in $\clg^{\mathrm{w.cov}}(\mathcal{C})$ is, by definition, a commutative algebra
object $A$ with an action of $G$ such that there exists an $A' \in
\mathrm{CAlg}(\mathcal{C} )$ such that $\otimes A'$ is conservative and commutes with
limits, with $A' \otimes A \simeq \prod_G A'$ as an $A'$-algebra and
compatibly with the $G$-action.
This together with descent along $\mathbf{1} \to A'$ implies that the map
$\mathbf{1} \to A^{hG}$ is an equivalence. Similarly, the map $A \otimes A \to
\prod_G A $ is well-defined in $\mathcal{C}$ and becomes an equivalence after
base-change to $A'$ (by checking for the trivial torsor), so that it must have
been an equivalence to begin with.
Finally, if $\mathbf{1} \to A$ is a faithful $G$-Galois extension in the sense
of \Cref{defgalr}, then $A$ is dualizable by \Cref{galdual}, so that $\otimes
A$ commutes with limits. Moreover, $\otimes A$ is faithful by assumption. Since
$A \otimes A$ is in elementary form, it follows that $A \in
\clg^{\mathrm{w.cov}}(\mathcal{C})$ and is in fact a $G$-torsor.
\end{proof}
The use of $G$-torsors will be very helpful in making arguments.
For example, given a connected Galois category, any nonempty
object is a quotient of a $G$-torsor for some finite group $G$; in
fact, understanding the Galois theory is equivalent to understanding torsors
for finite groups.
\begin{corollary}
\label{Gtorsor}
A $G$-torsor in the Galois category $\clg^{\mathrm{cov}}(\mathcal{C})$ is equivalent to a
$G$-Galois extension $A \in \mathrm{CAlg}(\mathcal{C})$ such that $A$
admits descent.
\end{corollary}
\begin{proof}
Given a $G$-torsor in $\clg^{\mathrm{cov}}(\mathcal{C})$, it follows easily that
it generates all of $\mathcal{C}$ as a thick $\otimes$-ideal, since
descendability can be checked locally and since a trivial torsor is descendable. Conversely, if $A$
is a $G$-Galois extension with this property, then $A$ is a finite cover of the
unit: we can take as our descendable commutative algebra object (required
by \Cref{deffinitecover})
$A$ itself.
\end{proof}
\begin{corollary}
If $|G|$ is invertible in $\pi_0 \mathrm{End}( \mathbf{1})$, then a $G$-torsor in $\clg^{\mathrm{w.cov}}(\mathcal{C})$
actually belongs to $\clg^{\mathrm{cov}}(\mathcal{C})$. In particular, if $\mathbb{Q} \subset
\pi_0 \mathrm{End}( \mathbf{1})$, then the two fundamental groups are the same:
\eqref{weakmap2} is an isomorphism.
\end{corollary}
\begin{proof}
In any stable $\infty$-category $\mathcal{D}$ where $|G|$ is invertible (i.e.,
multiplication by $|G|$ is an isomorphism on each object), then for any object
$X \in \mathrm{Fun}(BG, \mathcal{C})$, $X^{hG}$ is a retract of $X$.
In fact, the composite
\[ X^{hG} \to X \to X_{hG} \stackrel{N}{\to} X^{hG}, \]
is an equivalence, where $N$ is the norm map.
In particular, given a $G$-torsor $A \in \clg^{\mathrm{w.cov}}(\mathcal{C})$,
we have $\mathbf{1} \simeq A^{hG}$, so that $\mathbf{1}$ is a retract of $A$:
in particular, the thick $\otimes$-ideal $A$ generates contains all of
$\mathcal{C}$, so that (by \Cref{Gtorsor}) it belongs to $\clg^{\mathrm{cov}}(\mathcal{C})$.
This proves the first claim of the corollary.
Finally, if $\mathbb{Q} \subset \pi_0 \mathrm{End}( \mathbf{1})$, then
fix a weak finite cover $B \in \clg^{\mathrm{w.cov}}(\mathcal{C})$. There is a $G$-torsor $A
\in \clg^{\mathrm{w.cov}}(\mathcal{C})$
for some finite group $G$
such that $A \otimes B$ is a localization of a product of copies of $A$ at
idempotent elements. Since the thick $\otimes$-ideal that $A$ generates contains
all of $\mathcal{C}$ by the above, it follows that $B$ is actually a finite cover.
\end{proof}
\subsection{The connective case}
The rest of this paper will be devoted to computations of Galois groups. These
computations are usually based on descent theory together with results stating
that we can identify the Galois theory in certain settings as entirely
algebraic. Our first result along these lines shows in particular that we can
recover the classical \'etale fundamental group of a commutative ring. More
generally, we can describe the Galois group of a connective $\e{\infty}$-ring
purely algebraically.
\begin{theorem}
\label{connectivegal}
Let $A$ be a connective $\e{\infty}$-ring.
Then the map $ \pi_1( \mathrm{Mod}(A)) \to \pi_1^{\mathrm{et}} \mathrm{Spec}
\pi_0 A$ is an equivalence; that is,
all finite covers or weak finite covers are classically \'etale.
\end{theorem}
\begin{remark}
This result, while not stated explicitly in \cite{rognes}, seems to be folklore.
One has the following intuition: a connective $\e{\infty}$-ring consists of its
$\pi_0$ (which is a discrete commutative ring) together with higher homotopy
groups $\pi_i, i > 0$ which can be thought of as ``fuzz,'' a generalized sort
of nilthickening. Since
nilpotents should not affect the \'etale site, we would expect the Galois theory
to be invariant under the map $A \to \tau_{\leq 0} A$ in this case.
\end{remark}
\begin{proof}
Let $A$ be a connective $\e{\infty}$-ring.
The argument was explained for $\pi_0 A$ noetherian in \cite[Example
5.5]{MM}, and the general case can be reduced to this using the commutation
of Galois theory and filtered colimits (\Cref{galcolim} below).
In fact, the $\infty$-category of connective $\e{\infty}$-rings is compactly
generated and any compact object has noetherian $\pi_0$.
Therefore, the result assuming $\pi_0 A$ noetherian implies it in general
since any connective $\e{\infty}$-ring is a filtered colimit of compact
objects.
\end{proof}
The above argument illustrates a basic technique one has: one tries, whenever
possible, to reduce to the case of $\e{\infty}$-rings which satisfy
\emph{K\"unneth isomorphisms}. In this case, one can attempt to study
$G$-Galois extensions using algebra.
\begin{example}[{Cf. \cite[Theorem 10.3.3]{rognes}}]
The Galois group of $\sp$ is trivial, since $\sp$ is the $\infty$-category of
modules over the sphere $S^0$, and the \'etale fundamental group of $\pi_0(S^0)
\simeq \mathbb{Z}$ is trivial by Minkowski's theorem that the discriminant of
a number field is always $> 1$ in absolute value.
\end{example}
\subsection{Galois theory and filtered colimits}
In this subsection, we will prove that Galois theory behaves well with respect
to filtered colimits.
\begin{theorem} \label{galcolim}
The functor $A \mapsto \clg^{\mathrm{cov}}( \mathrm{Mod}(A)), \mathrm{CAlg} \to \mathrm{Cat}_\infty$
commutes with filtered colimits. In particular, given a filtered diagram $I \to
\mathrm{CAlg}$, the map
\[ \pi_{\leq 1} \mathrm{Mod}({\varinjlim_I A_i})\to \varprojlim_{I}
\pi_{\leq 1} \mathrm{Mod}(A_i), \]
is an equivalence of profinite groupoids.
\end{theorem}
\Cref{galcolim} will be a
consequence of
some categorical technology together and is a form of ``noetherian descent.''
To prove it, we can work with $G$-torsors in view of \Cref{torsorenough}.
Given an $\e{\infty}$-ring $A \in \mathrm{CAlg}$, we let $\mathrm{Gal}_G(A)$ be the category of
faithful $G$-Galois extensions of $A$: that is, the category of $G$-torsors in
$\clg^{\mathrm{cov}}(A)$.
We need to show that
given a filtered diagram $\left\{A_i\right\}$ of $\e{\infty}$-rings, the functor
\[ \varinjlim \mathrm{Gal}_G(A_i) \to \mathrm{Gal}_G(\varinjlim A_i), \]
is an equivalence of categories: i.e., that it is fully faithful and
essentially surjective.
We start by showing that faithful Galois
extensions are compact $\e{\infty}$-algebras.
\begin{lemma}
Let $A \to B$ be a faithful $G$-Galois extension. Then $B$ is a compact
object
in the $\infty$-category $ \mathrm{CAlg}_{A/}$ of $\e{\infty}$-algebras over $A$.
Moreover, $\hom_{\mathrm{CAlg}_{A/}}(B, \cdot)$ takes values in homotopy discrete
spaces.
\end{lemma}
\begin{proof}
First, recall that if $A \to B$ is a \emph{classically \'etale} extension, then the result
is true. In fact, if $A \to B$ is classically \'etale, then for any $\e{\infty}$-$A$-algebra
$A'$, the natural map
\[ \hom_{\mathrm{CAlg}_{A/}}(B, A') \to \hom_{\mathrm{Ring}_{\pi_0 A/}}(\pi_0 B, \pi_0 A'), \]
is an equivalence.
Moreover, $\pi_0 B$, as an \'etale $\pi_0 A$-algebra, is finitely presented or
equivalently compact in $\mathrm{Ring}_{\pi_0 A/}$. The result follows for an \'etale
extension.
Now, a Galois extension need not be classically \'etale, but it becomes \'etale after an
appropriate base change, so we can use descent theory.
Recall that we have an equivalence
of symmetric monoidal $\infty$-categories
\[ \mathrm{Mod}(A) \simeq \mathrm{Tot} \left( \mathrm{Mod}(B) \rightrightarrows \mathrm{Mod}(B \otimes_A
B ) \triplearrows \dots \right). \]
Upon taking commutative algebra objects, we get an equivalence
of $\infty$-categories
\[ \mathrm{CAlg}_{A/} \simeq
\mathrm{Tot}\left( \mathrm{CAlg}_{B/} \rightrightarrows \mathrm{CAlg}_{B \otimes_A B /}
\triplearrows \dots \right)
. \]
The object $B \in \mathrm{CAlg}_{A/}$
becomes classically \'etale, thus compact, after base-change along $A \to B$.
We may
now apply the next sublemma to conclude.
\end{proof}
\begin{sublemma}
Let $\mathcal{C}^{-1} \in \mathrm{Pr}^L$ be a presentable $\infty$-category and $\mathcal{C}^\bullet$ a
cosimplicial object in $\mathrm{Pr}^L$ with an equivalence
of $\infty$-categories
\[ \mathcal{C}^{-1} \simeq \mathrm{Tot}( \mathcal{C}^\bullet). \]
Suppose that $x \in \mathcal{C}^{-1}$ is an object such that:
\begin{itemize}
\item The image $x^i$ of $x$ in $\mathcal{C}^i, i \geq 0$ is compact for each $i$.
\item There exists $n$ such that the image $x^i$ of $x$ in each $\mathcal{C}^i$ is $n$-cotruncated
in the sense that
\[ \hom_{\mathcal{C}^i}(x^i, \cdot)\colon \mathcal{C}^i \to \mathcal{S}\]
takes values in the subcategory $\tau_{\leq n} \mathcal{S} \subset \mathcal{S}$
of $n$-truncated spaces. (This follows once $x^0$ is $n$-cotruncated.)
\end{itemize}
Then $x$ is compact (and $n$-cotruncated) in $\mathcal{C}^{-1}$).
\end{sublemma}
\begin{proof}
Given objects $w, z \in \mathcal{C}^{-1}$,
the natural map
\[ \hom_{\mathcal{C}}(w, z) \to \mathrm{Tot} \hom_{\mathcal{C}^\bullet}(
w^\bullet, z^\bullet) \]
is an equivalence, where for each $i \geq 0$, $w^i, z^i$ are the objects
in $\mathcal{C}^i$ that are the images of $w, z$.
Therefore, it follows that $\hom_{\mathcal{C}^{-1}}(x, \cdot)\colon \mathcal{C}^{-1} \to \mathcal{S}$ is
the totalization of a cosimplicial functor $\mathcal{C}^{-1} \to \mathcal{S}$
given by $\hom_{\mathcal{C}^\bullet}(x^\bullet, \cdot^\bullet)$. Each of the
terms in this cosimplicial functor, by assumption, commutes with filtered
colimits and takes values in $n$-truncated spaces. The sublemma thus follows
because the totalization functor
\[ \mathrm{Tot}\colon \mathrm{Fun}( \Delta, \tau_{\leq n} \mathcal{S}) \to
\mathcal{S}, \]
lands in $\tau_{\leq n} \mathcal{S}$, and commutes with filtered colimits: a
totalization of $n$-truncated spaces can be computed by a partial
totalization, and finite limits and filtered colimits of spaces commute with
one another.
\end{proof}
Next, we prove a couple of general categorical lemmas about compact objects in
undercategories and filtered colimits.
\begin{lemma}
Let $\mathcal{C}$ be a compactly generated, presentable $\infty$-category and
let $\mathcal{C}^\omega$ denote the collection of compact objects.
Then, for each $x \in \mathcal{C}$, the undercategory $\mathcal{C}_{x/}$ is
compactly generated.
Moreover, the subcategory $(\mathcal{C}_{x/})^\omega$ is generated under finite
colimits and retracts by the morphisms of the form $x \to x \sqcup y$ for $y
\in \mathcal{C}^\omega$.
\end{lemma}
\begin{proof}
To prove this, recall that if $\mathcal{D}$ is any presentable
$\infty$-category and $\mathcal{E} \subset \mathcal{D}$ is a (small)
subcategory of
compact objects, closed under finite colimits, then there is induced a
map in $\mathrm{Pr}^L$
\[ \mathrm{Ind}( \mathcal{E}) \to \mathcal{D}, \]
which is an equivalence of $\infty$-categories precisely when
$\mathcal{E}$ \emph{detects equivalences}: that is, when a map $x \to y$ in
$\mathcal{D}$ is an equivalence when $\hom_{\mathcal{D}}(e, x) \to
\hom_{\mathcal{D}}(e, y)$ is a homotopy
equivalence for all $e \in \mathcal{E}$.
Indeed, in this case, it follows that $\mathrm{Ind} (\mathcal{E}) \to
\mathcal{D}$ is a fully faithful functor, which embeds
$\mathrm{Ind}(\mathcal{E})$ as a full subcategory of $\mathcal{D}$ closed under
colimits. But any fully faithful left adjoint whose right adjoint is
conservative is an equivalence of $\infty$-categories.
This argument is a very slight variant of Proposition 5.3.5.11 of \cite{HTT}.
Now, we apply this to $\mathcal{C}_{x/}$. Clearly, the objects $x \to x
\sqcup y$ in $\mathcal{C}_{x/}$, for $y \in \mathcal{C}^\omega$, are compact. Since
\[ \hom_{\mathcal{C}_{x/}}(x \sqcup y, z) = \hom_{\mathcal{C}}(y, z), \]
it follows from the above paragraph if $\mathcal{C}$ is compactly generated,
then the $x \to x \sqcup y$ in $\mathcal{C}_{x/}$ \emph{detect equivalences}
and thus generate $\mathcal{C}_{x/}$ under colimits. More precisely, if
$\mathcal{E} \subset \mathcal{C}_{x/}$ is the subcategory generated under
finite colimits by the $x \to x \sqcup y, y \in
\mathcal{C}^\omega$, then the natural functor $\mathrm{Ind}( \mathcal{E}) \to
\mathcal{C}_{x/}$ is an equivalence. Since
$(\mathrm{Ind}(\mathcal{E}))^{\omega}$ is the idempotent completion of
$\mathcal{E}$ (Lemma 5.4.2.4 of \cite{HTT}), the lemma follows.
\end{proof}
Let $\mathcal{C}$ be a compactly generated, presentable $\infty$-category.
We observe that the association $x \in \mathcal{C} \mapsto
(\mathcal{C}_{x/})^\omega$ is actually functorial in $x$.
Given a morphism $x \to y$, we get a functor
\[ \mathcal{C}_{x/} \to \mathcal{C}_{y/} \]
given by pushout along $x \to y$. Since the right adjoint (sending a map $y \to
z$ to the composite $x \to y \to z$) commutes with filtered colimits, it
follows that $\mathcal{C}_{x/} \to \mathcal{C}_{y/}$ restricts to a functor on
the compact objects.
We get a functor
\[ \Phi\colon \mathcal{C} \to \mathrm{Cat}_\infty, \quad x \mapsto
(\mathcal{C}_{x/})^\omega. \]
Our next goal is to show that $\Phi$ commutes with filtered colimits.
\begin{lemma} \label{fullfaithfulthing}
The functor $\Phi$ has the property that
for any filtered diagram $x\colon I \to \mathcal{C}$, the natural functor
\begin{equation} \label{phi} \varinjlim_{I} \Phi( x_i) \to \Phi( \varinjlim_I
x_i),\end{equation}
is an equivalence of $\infty$-categories. \end{lemma}
\begin{proof}
Full faithfulness of $\Phi$ is a formal consequence of the definition of a compact object.
In fact, an element of $\varinjlim_I \Phi(x_i)$ is represented by an object $i
\in I$ and a map $x_i \to y_i$ that belongs to $(\mathcal{C}_{x_i/})^\omega$.
We will denote this object by $(i, y_i)$.
This object is the same as that represented by $x_j \to y_i \sqcup_{x_i} x_j$
for any map $i \to j$ in $I$.
Given two such objects in $\varinjlim_I \Phi(x_i)$, we can represent them both
by objects $x_i \to y_i, x_i \to z_i$ for some index $i$. Then
\[ \hom_{\varinjlim_I \Phi(x_i)}( (i, y_i), (i, z_i)) =
\varinjlim_{j \in I_{i/}}\hom_{\mathcal{C}_{x_j/} }(
y_j, z_j), \]
where $y_j, z_j$ denotes the pushforwards of $y_i, z_i$ along $x_j \to z_j$.
Let $x = \varinjlim_I x_i$, and let $y, z$ denote the pushforwards of $y_i,
z_i$ all the way along $x_i \to x$. Then our claim is that the map
\[ \varinjlim_{j \in I_{i/}}\hom_{\mathcal{C}_{x_j/} }(
y_j, z_j) \to \hom_{\mathcal{C}_{x/}}(y, z)
\]
is an equivalence.
Now, we write
\begin{align*} \hom_{\mathcal{C}_{x/}}(y, z) & \simeq
\hom_{\mathcal{C}_{x_i/}}(y_i, z) \\
& \simeq
\hom_{\mathcal{C}_{x_i/}}(y_i, \varinjlim_{j \in I_{i/}} z_j ) \\
& \simeq
\varinjlim_{j \in I_{i/}}\hom_{\mathcal{C}_{x_i/}}(y_i, z_j ) \\
& \simeq
\varinjlim_{j \in I_{i/}}\hom_{\mathcal{C}_{x_j/}}(y_j, z_j ),
\end{align*}
and we get the equivalence as desired.
Finally, to see that \eqref{phi} establishes the right hand side as the idempotent
completion of the first, we use the description of compact objects in
$\mathcal{C}_{x/}$.
To complete the prooof, note now that a filtered colimit of idempotent complete $\infty$-categories is
itself idempotent complete \cite[Lemma 7.3.5.16]{higheralg}.
\end{proof}
\begin{corollary}
\label{0truncatedcolim}
Hypotheses as above, the functor $\Psi: x \mapsto (\mathcal{C}_{x/})^{\omega, \leq
0}$ sending $x$ to the category of 0-cotruncated, compact objects in
$\mathcal{C}_{x/}$ has the property that the natural functor
\( \varinjlim_I \Psi(x_i) \to \Psi( \varinjlim x_i) \)
is an equivalence.
\end{corollary}
This follows from the previous lemma, because 0-cotruncatedness of an object
$y$ is equivalent to the claim that the map $S^1 \otimes y \to y$ is an
equivalence.
\begin{proof}[Proof of \Cref{galcolim}]
For $A$ an $\e{\infty}$-ring, let $(\mathrm{CAlg}_{A/})^{\omega, \leq 0}$ be the
(ordinary) category of $0$-cotruncated, compact $\e{\infty}$-$A$-algebras;
this includes any finite cover of $A$, for example, since finite covers of
$A$ are locally \'etale.
Then we have a fully faithful inclusion
of $\infty$-categories
\[ \mathrm{Gal}_G(A) \subset \mathrm{Fun}(BG, (\mathrm{CAlg}_{A/})^{\omega, \leq 0}). \]
Although $BG$ is not compact in the $\infty$-category of $\infty$-categories,
the truncation to $n$-categories for any $n$ is: $BG$ can be represented as a
simplicial set with finitely many simplices in each dimension.
Therefore, the right-hand-side has the property that it commutes with filtered
colimits in $A$ by \Cref{0truncatedcolim}.
Thus, for any filtered diagram $A\colon I \to \mathrm{CAlg}$, the functor
\[ \varinjlim_{i \in I}\mathrm{Gal}_G(A_i) \to \mathrm{Gal}_G( \varinjlim_{i
\in I} A_i), \]
is fully faithful.
Moreover, given a $G$-Galois extension $B$ of $A = \varinjlim_I A_i$, there
exists $i \in I$ and a compact, 0-cotruncated $A_i$-algebra $B_i$ with a $G$-action, such that
$A \to B$ is obtained by base change from $A_i \to B_i$.
It now suffices to show that $A_i \to B_i$ becomes $G$-Galois after some base
change $A_i \to A_j$.
For any $j \in I$ receiving a map from $i$, we let $B_j = A_j \otimes_{A_i}
B_i$.
We are given that $\varinjlim_{j \in I_{i/}} B_j$ is a faithful $G$-Galois extension of
$\varinjlim_{j \in I_{i/}} A_j$ and we want to claim that there exists $j$
such that $B_j$ is a faithful $G$-Galois extension of $A_j$.
Now, the condition for $A_j \to B_j$ to be faithfully $G$-Galois has two parts:
\begin{enumerate}
\item $B_j \otimes_{A_j} B_j \to \prod_G B_j$ should be an equivalence.
\item $A_j \to B_j$ should be descendable.
\end{enumerate}
The first condition is detected at a ``finite stage'' since both the source
and target are compact objects of $\mathrm{CAlg}_{A_j/}$.
Unfortunately, we do not know how to use this line of argument alone to argue that
the $A_j \to B_j$'s are faithful $G$-Galois for some $j$, although we suspect that it
is possible.
Instead, we use some obstruction theory. The map $A \to B$
exhibits $B$ as a perfect $A$-module. For any $\mathbf{E}_{1}$-ring $R$, let
$\mod^\omega(R)$ be the stable $\infty$-category of perfect $R$-modules. Then the
natural functor
\[ \varinjlim_I \mod^\omega( A_i) \to \mod^\omega(A) , \]
is an equivalence of $\infty$-categories.\footnote{One does not even need to worry
about idempotent completeness here because we are in a stable setting, and any
self-map $e\colon A \to A$ with $e^2 \simeq e$ can be extended to an idempotent.}
It follows that we can ``descend'' the perfect $A$-module $B$ to a perfect
$A_j$-module $B'_j$ for some $j$ (asymptotically unique), and we can descend the
multiplication map $B \otimes_A B \to B$ (resp. the unit map $A \to B$) to
$B'_j \otimes_{A_j} B'_j \to B'_j$ (resp. $A_j \to B'_j$). We can also assume
that homotopy associativity holds for $j$ ``large.''
The $G$-action on $B$ in the \emph{homotopy category} of perfect
$A$-modules descends to an action on $B'_j$ in the \emph{homotopy category} of
perfect $A_j$-modules, and the equivalence $B \otimes_A B \simeq \prod_G B$
descends to an equivalence $B'_j \otimes_{A_j} B'_j \simeq \prod_G B'_j$.
Finally, the fact that the thick subcategory that $B$ generates contains $A$
can also be tested at a finite stage.
The upshot is that, for $j$ large, we can ``descend'' the $G$-Galois extension
$A \to B$ to a perfect $A_j$-module $B'_j$ with the portion of the structure of a
$G$-Galois extension that one could see \emph{solely from the homotopy
category.} However, using obstruction theory one can promote this to a genuine
Galois extension. In \Cref{obstruct} below,
we show that $B'_j$ can be promoted to an $\mathbf{E}_{\infty}$-algebra (in $A_j$-modules)
for $j \gg 0$ with a $G$-action, which is a faithful $G$-Galois extension.
It follows that the $B'_j$ lift $B$ to $A_j$ for $j \gg 0$, and even with the
$G$-action (which is unique in a faithful Galois extension; see Theorem 11.1.1
of \cite{rognes}).
\end{proof}
\begin{theorem} \label{obstruct}
Let $A'$ be an $\mathbf{E}_{\infty}$-ring, and let $B'$ be a perfect $A'$-module such
that the thick subcategory generated by $B'$ contains $A'$. Suppose
given:
\begin{enumerate}
\item A homotopy commutative, associative and unital multiplication $B'\otimes_{A'} B' \to B'$.
\item A $G$-action on $B'$ in the homotopy category, commuting with the
multiplication and unit maps, such that the map $B'
\otimes_{A'} B' \to \prod_G B'$ is an equivalence of $A$-modules.
\end{enumerate}
Then $B'$ has a unique $\mathbf{E}_{\infty}$-multiplication extending the given
homotopy commutative one, and $A \to B$ is faithful $G$-Galois (in
particular, the $G$-action in the homotopy category extends to a strict one of $\mathbf{E}_{\infty}$-maps on $B$).
\end{theorem}
Here we use an argument, originally due to Hopkins in a different setting, that will be
elaborated upon further in joint work with Heuts; as such, we give a sketch of the
proof.
\begin{proof} We use the obstruction theory of \cite{robinsonobstruct} (see also \cite[Sec. 3]{angeltveit}) to produce a unique
$\mathbf{E}_{1}$-structure.
Since $B' \otimes_{A'} B' $ is a finite product of copies of $B'$, it follows
that $B'$ satisfies a perfect universal coefficient formula in the sense of
that paper.
The obstruction theory
developed there
states that the
obstructions to producing an $\mathbf{E}_{1}$-structure lie in $\mathrm{Ext}^{n,
3-n}_{\pi_*(B' \otimes_{A'} B')}( B'_*, B'_*)$ for $n\geq 4$, and the
obstructions to uniqueness in the groups
$\mathrm{Ext}^{n,
2-n}_{\pi_*(B' \otimes_{A'} B')}( B'_*, B'_*)$ for $n \geq 3$.
The hypotheses of the lemma imply that $B'_*$ is a projective $\pi_*(B'
\otimes_{A'} B')$-module, though, so that all the obstructions (both to
uniqueness and existence) vanish.
Our next goal is to promote this to an $\mathbf{E}_{\infty}$-multiplication extending the
given $\mathbf{E}_{1}$-structure.
We claim that the space of $\mathbf{E}_{1}$-maps between
any tensor power $B'^{\otimes m}$ and any other tensor power $B'^{\otimes n}$ of $B'$ is homotopy
discrete and equivalent to the collection of maps of $A$-\emph{ring spectra}: that
is, homotopy classes of maps $B'^{\otimes m} \to B'^{\otimes n}$ (in
$A$-modules) that commute
with the multiplication laws \emph{up to homotopy.}
This is a consequence of the analysis in \cite{rezkHM} (in particular,
Theorem 14.5 there), and the fact that the
$B'^{\otimes n}$-homology of $B'^{\otimes m}$ is \'etale, so that the
obstructions of \cite{rezkHM} all vanish.
It follows that if $\mathcal{C}$ is the smallest symmetric monoidal $\infty$-category
of $\mathrm{Alg}(\mod(A'))$ (i.e., $\mathbf{E}_{1}$-algebras in $\mod(A')$) containing $B'$, then
$\mathcal{C}$ is equivalent to an ordinary symmetric monoidal category, which
is equivalent to a full subcategory of the category of $A$-ring spectra. Since
$B'$ is a commutative algebra object in that latter category, it follows that
it is a commutative algebra object of $\mathrm{Alg}(\mod(A'))$, and
thus gives an $\mathbf{E}_{\infty}$-algebra.
The $G$-action, since it was by maps of $A$-ring spectra, also comes along.
\end{proof}
\subsection{The even periodic and regular case}
Our first calculation of a Galois group was in \Cref{connectivegal}, where
we
showed that the Galois group of a connective $\e{\infty}$-ring was entirely
algebraic.
In this section, we will show (\Cref{etalegalois}) that the analogous statement
holds for an even periodic $\e{\infty}$-ring with regular (noetherian) $\pi_0$.
As in the proof of \Cref{connectivegal}, the strategy is to reduce to
considering ring spectra with K\"unneth isomorphisms. Unfortunately, in the
nonconnective setting, the ``residue field'' ring spectra one wants can be constructed only as
$\e{1}$-algebras (rather than as $\e{\infty}$-algebras), so one has to work somewhat
harder.
\begin{definition}
An $\e{\infty}$-ring $A$
is \textbf{even periodic} if:
\begin{enumerate}
\item $\pi_i A = 0$ if $i$ is odd.
\item The multiplication
map $\pi_2 A \otimes_{\pi_0 A} \pi_{-2} A \to \pi_0 A$ is an isomorphism.
\end{enumerate}
In particular, $\pi_2 A$ is an invertible $\pi_0 A$-module; if it is free
of rank one, then $\pi_*(A) \simeq \pi_0(A) [t_{2}^{\pm 1}]$ where $|t_2| = 2$.
\end{definition}
Even periodic $\e{\infty}$-rings (such as complex $K$-theory $KU$) play a central role in chromatic homotopy
theory because of the connection, beginning with Quillen, with the theory of
\emph{formal groups.} We will also encounter even periodic $\e{\infty}$-rings
in studying stable module $\infty$-categories for finite groups below.
The $\infty$-categories of modules over them turn out to be fundamental
building blocks for many other stable homotopy theories, so an understanding of
their Galois theory will be critical for us.
We begin with the simplest case.
\begin{proposition}
\label{fieldreg}
Suppose $A$ is an even periodic $\e{\infty}$-ring with $\pi_0 A \simeq k[t^{\pm
1}]$ where $|t| = 2$ and $k$ a field. Then the Galois theory of $A$ is
algebraic: $\pi_{ 1} \mathrm{Mod}(A) \simeq \mathrm{Gal}(k^{\mathrm{sep}}/k)$.
\end{proposition}
\begin{proof}
We want to show that any finite cover of $A$ is \'etale at the level of
homotopy groups; flat would suffice.
Let $B$ be a $G$-Galois extension of $A$. Then $B \otimes_A B \simeq \prod_G
B$. Since $\pi_*(A)$ is a graded field, it follows that
\[ \pi_*(B) \otimes_{\pi_*(A)} \pi_*(B) \simeq \prod_G \pi_*(B). \]
Moreover, since $B$ is a perfect $A$-module, it follows that $\pi_*(B)$ is a
finite-dimensional $\pi_*(A)$-module.
Making a base-change $t \mapsto 1$, we can work in $\mathbb{Z}/2$-graded
$k$-vector spaces rather than graded $k[t^{\pm 1}]$-modules.
So we get a $\mathbb{Z}/2$-graded commutative (in the graded sense) $k$-algebra
$B'_* = B'_0 \oplus B'_1$ with the property that we have an equivalence of
$\mathbb{Z}/2$-graded $B'_*$-algebras
\begin{equation} \label{split} B'_* \otimes_k B'_* \simeq \prod_G B'_*.
\end{equation}
Observe that this tensor product is the \emph{graded} tensor product.
From this, we want to show that $B'_1 = 0$, which will automatically force
$B'_0$ to be \'etale over $k$. Suppose
first that the characteristic of $k$ is not 2. By \Cref{gradedloc} below, there exists a map of graded $k$-algebras $B_*' \to
\overline{k}$. We
can thus compose with the map $k \to B'_* \to \overline{k}$ and use
\eqref{split} to conclude that $B'_* \otimes_k \overline{k} \simeq \prod_G
\overline{k}$ as a graded $k$-algebra.
This in particular implies that $B'_1 = 0$ and that $B'_0$ is a finite separable
extension of $k$, which proves \Cref{fieldreg} away from the prime 2.
Finally, at the prime 2,
we need to show that \eqref{split} still implies that $B'_1 =0 $.
In this case, $B'_0 \oplus B'_1$ is a \emph{commutative} $k$-algebra and
\eqref{split} implies that it must be \'etale. After extending scalars to
$\overline{k}$, $B'_0 \oplus B'_1$ must, as a
commutative ring, be isomorphic to $\prod_G \overline{k}$. However, any
idempotents in $B'_0 \oplus B'_1$ are clearly concentrated in degree zero.
So, we can make the same conclusion at the prime $2$.
\end{proof}
\begin{lemma}
\label{gradedloc}
Let $k$ be an algebraically closed field with $2 \neq 0$, and $A'_*$ a nonzero
finite-dimensional $\mathbb{Z}/2$-graded
commutative $k$-algebra. Then there exists a map of graded $k$-algebras $A'_*\to k$.
\end{lemma}
\begin{proof}
Induction on $\dim A'_1$. If $A'_1 = 0$, we can use the ordinary theory of
artinian rings over algebraically closed fields. If there exists a nonzero $x \in A'_1$, we can form the two-sided ideal $(x)$: this is equivalently the left
or right ideal generated by $x$. In particular, anything in $(x)$ has square
zero. It follows that $1 \notin (x)$ and we get a map
of $k$-algebras
\[ A'_* \to A'_*/(x), \]
where $A'_*/(x)$ is a \emph{nontrivial} finite-dimensional $\mathbb{Z}/2$-graded commutative ring
of smaller dimension in degree one. We can thus continue the process.
\end{proof}
We can now prove our main result.
\begin{theorem} \label{etalegalois}
Let $A$ be an even periodic $\e{\infty}$-ring with $\pi_0 A$
regular noetherian. Then the Galois theory of $A$ is algebraic. \end{theorem}
Most of this result appears in \cite{BR2}, where the Galois group
of $E_n$ is identified at an odd prime (as the Galois group of its $\pi_0$).
Our methods contain the modifications needed to handle the prime $2$ as well.
\begin{remark}
This will also show that all Galois extensions of $A$ in the sense of
\cite{rognes} are faithful.
\end{remark}
\begin{proof} [Proof of \Cref{etalegalois}]
Fix a finite group $G$ and let $B$ be a $G$-Galois extension of $A$, so that
\[ A \simeq B^{h G}, \quad B \otimes_A B \simeq \prod_G B. \]
By \Cref{galdual}, $B$ is a perfect $A$-module; in particular, the homotopy
groups of $B$ are finitely generated $\pi_0 A$-modules.
Our goal is to show that $B$ is even periodic and that $\pi_0 B$ is \'etale
over $\pi_0 A$. To do this, we may reduce to the case of $\pi_0 A$
{regular} \emph{local}, by
checking at each localization.
We are now in the following situation. The $\e{\infty}$-ring $A$ is even
periodic, with $\pi_0 A$ local with its maximal ideal generated by a
regular sequence $x_1, \dots, x_n \in \pi_0 A$ for $n = \dim \pi_0 A$.
Let $k$ be the residue field of $\pi_0 A$.
In this case, then one can define a \emph{multiplicative homology theory}
$P_*$ on
the category of $A$-modules
via
\[ P_*(M) \stackrel{\mathrm{def}}{=} \pi_* ( M/(x_1, \dots, x_n) M) \simeq
\pi_* (M \otimes_A A/(x_1, \dots, x_n)), \]
where $A/(x_1, \dots, x_n) \simeq A/x_1 \otimes_A \dots \otimes_A A/x_n$.
More precisely, it is a consequence of the work of Angeltveit
\cite[Sec. 3]{angeltveit} that $A/(x_1, \dots, x_n)$ can
be made (noncanonically) an
$\e{1}$-algebra in $\mathrm{Mod}(A)$.
In particular, $A/(x_1, \dots, x_n)$ is, at the very least, a ring object in the
homotopy category of $A$-modules; this weaker assertion, which is all that we
need, is proved directly in \cite[Theorem 2.6]{EKMM}.
The fact that each $A/x_i$ acquires the structure of a ring object in the
homotopy category of $A$-modules already means that for any $A$-module $M$, the
homotopy groups of $M/x_i M\simeq M \otimes_A A /x_i$ are actually
$\pi_0(A)/(x_i)$-modules.
In any event, $M \mapsto P_*(M)$ is a multiplicative homology theory taking values in
$k[t^{\pm 1}]$-modules. It satisfies a K\"unneth isomorphism,
\[ P_*(M) \otimes_{k[t^{\pm 1}]} P(N) \simeq P_*(M \otimes_A N) , \]
by a standard argument: with $N$ fixed, both sides define homology theories on $A$-modules;
there is a natural map between the two; moreover, this map is an isomorphism for $M = A$.
This implies that the natural map is an isomorphism by a five-lemma argument.
Note that the $\e{1}$-ring $A/(x_1, \dots, x_n)$ is usually not homotopy
commutative if $ p = 2$.
For convenience, rather than working in the category of graded $k[t^{\pm
1}]$-modules, we will work in the (equivalent) category of $\mathbb{Z}/2$-graded $k$-vector
spaces, and denote the modified functor by $Q_*$ (instead of $P_*$).
Since $A \to B$ is $G$-Galois, it follows from $B \otimes_A B \simeq \prod_G
B$ that there is an isomorphism of $\mathbb{Z}/2$-graded $k[G]$-modules,
\[ Q_*(B) \otimes_k Q_*(B) \simeq \prod_{G} Q_*(B). \]
In particular, it follows that
\begin{equation} \label{dims} \dim Q_0 (B) + \dim Q_1(B) = |G|. \end{equation}
We now use a Bockstein spectral sequence argument to bound the rank of
$\pi_0 B$ and $\pi_1 B$.
\begin{lemma} \label{BSSlem}
Let $M$ be a perfect $A$-module. Suppose that $\dim_k Q_0(M) = a$. Then the
rank of $\pi_0
M$ as a $\pi_0 A$-module (that is, the dimension after tensoring with the
fraction field) is at most $a$.
\end{lemma}
\begin{proof}
Choose a system of parameters $x_1, \dots, x_n$ for the maximal ideal of $\pi_0
A$.
If $M$ is as in the statement of the lemma, then we are given that
\[ \dim \pi_0(M/(x_1, \dots, x_n) M) \leq a. \]
We consider the sequence of $A$-modules
\[ M_i = M/(x_1, \dots, x_i)M = M \otimes_A A/x_1 \otimes_A \dots \otimes_A
A/x_i; \]
here $\pi_0(M_i)$ is a finitely generated module over the regular local ring $\pi_0(A)/(x_1, \dots, x_i)$.
For instance, $\pi_0(M_n)$ is a module over the residue field $k$, and our
assumption is that its rank is at most $a$.
\newtheorem*{indstep}{Inductive step}
We make the following inductive step.
\begin{indstep}
If $\pi_0(M_{i+1})$ has rank $\leq a$ as a module over the regular local ring
$\pi_0(A)/(x_1, \dots, x_{i+1})$, then $\pi_0(M_i)$ has rank $\leq a$ as a
module over the regular local ring $\pi_0(A)/(x_1, \dots, x_i)$.
\end{indstep}
To see this, consider the cofiber sequence
\[ M_i \stackrel{x_i}{\to} M_i \to M_{i+1}, \]
and the induced injection in homotopy
groups
\[ 0 \to \pi_0(M_i)/x_{i}\pi_0 M_i \to \pi_0(M_{i+1}). \]
We now apply the following sublemma.
By descending induction on $i$, this will imply the desired claim.
\newcommand{\mathrm{rank}}{\mathrm{rank}}
\begin{sublemma}
Let $(R, \mathfrak{m})$ be a regular local ring, $x \in \mathfrak{m} \setminus
\mathfrak{m}^2$. Consider a finitely generated $R$-module $N$. Given an
injection
\[ 0 \to N/xN \to N', \]
where $N'$ is a finitely generated $R/(x)$-module, we have
\[ \mathrm{rank}_{R} N \leq \mathrm{rank}_{R/(x)} N'. \]
\end{sublemma}
\begin{proof}
When $R$ is a discrete valuation ring (so that $R/(x)$ is a field), this follows from the structure theory of
finitely generated modules over a PID.
To see this in general, we may localize at the prime ideal $(x) \subset R$
(and thus replace the pair $(R, R/(x))$ with $R_{(x)}, R_{(x)}/(x) R_{(x)}$),
which does not affect the rank
of either side, and which reduces us to the DVR case.
\end{proof}
With the sublemma, we can conclude that $\mathrm{rank}_{\pi_0(A)/(x_1, \dots, x_i)} \pi_0(M_i) \leq a$ for all $i$
by descending induction on $i$, which completes the proof of \Cref{BSSlem}.
\end{proof}
By \Cref{BSSlem}, it now follows that $\pi_0 B$, as a $\pi_0 A$-module, has
rank at most $a = \dim_k Q_0(B)$, where $a \leq |G|$. However, when we invert everything in $\pi_0 A$
(i.e., form the fraction field $k( \pi_0 A))$, then ordinary Galois theory goes into
effect (\Cref{fieldreg}) and $\pi_0 B \otimes_{\pi_0 A} k( \pi_0 A)$ is
a finite \'etale $\pi_0 A$-algebra with Galois group $G$.
In particular, it follows that $a = |G|$.
As a result, by \eqref{dims}, $Q_1(B) = 0$. It follows, again by the Bockstein spectral
sequence, in the form of \Cref{easyBSS} below, that $B$ is evenly graded and
$\pi_* B$ is free as an $A$-module.
In particular, $\pi_0(B \otimes_A B) \simeq \pi_0 B \otimes_{\pi_0 A} \pi_0 B$,
which means that we get an isomorphism
\[ \pi_0 B \otimes_{\pi_0 A} \pi_0 B \simeq \prod_G \pi_0 B, \]
so that $\pi_0 B$ is \'etale over $\pi_0 A$ (more precisely, $\mathrm{Spec} \pi_0 B
\to \mathrm{Spec} \pi_0 A$ is a $G$-torsor), as desired.
This completes the proof of \Cref{etalegalois}.
\end{proof}
\begin{lemma}[] \label{easyBSS}
Let $A$ be an even periodic $\e{\infty}$-ring such that $\pi_0 A$ is regular local
and $n$-dimensional,
with maximal ideal $\mathfrak{m} = (x_1, \dots, x_n)$. Let $M$ be a perfect
$A$-module such that the $A$-module $M/(x_1, \dots, x_n)M$ satisfies $\pi_1(
M/(x_1, \dots, x_n) M) = 0$. Then $\pi_1(M) = 0$ and $\pi_0(M)$ is a free
$\pi_0(A)$-module.
\end{lemma}
\begin{proof}
\Cref{easyBSS} follows from a form of the Bockstein spectral sequence: the
evenness implies that there is no room for differentials;
Proposition 2.5 of \cite{HoveyS} treats the case of $A = E_n$.
We can give a direct argument as follows.
Namely, we show that $\pi_1(M/(x_1, \dots, x_i) M) = 0$ for $i = 0,
1, \dots, n$, by descending induction on $i$. By assumption, it holds for $i
= n$. The inductive step is proved as in the proof of \Cref{BSSlem}, except
that Nakayama's lemma is used to replace the sublemma.
This shows that $\pi_1(M) = 0$.
Now, inducting in the other direction (i.e., in ascending order in $i$), we find that $x_1, \dots, x_n$ defines a
regular sequence on $\pi_0(M)$ and
the natural map
\[ \pi_0(M)/(x_1, \dots, x_i) \to \pi_0(M/(x_1, \dots, x_i)), \]
is an isomorphism. This implies that the depth of $\pi_0(M)$ as a
$\pi_0(A)$-module is equal to $n$, so that $\pi_0(M)$ is a free
$\pi_0(A)$-module.
\end{proof}
\section{Local systems, cochain algebras, and stacks}
The rest of this paper will be focused on the calculations of Galois groups in
certain examples of stable homotopy theories, primarily those arising from
chromatic homotopy theory and modular representation theory.
The basic ingredient, throughout, is to write a given stable homotopy theory as
an \emph{inverse limit} of simpler stable homotopy theories to which one can apply
known algebraic techniques such as \Cref{etalegalois} or \Cref{connectivegal}.
Then, one puts together the various Galois groupoids that one has via
techniques from descent theory.
In the present section, we will introduce these techniques in slightly more elementary
settings.
\subsection{Inverse limits and Galois theory}
Our approach can be thought of as an elaborate version of van Kampen's theorem.
To begin, let us recall the setup of this.
Let $X$ be a topological space, and
let $U, V \subset X$ be open subsets which cover $X$. In this case, the diagram
\[ \xymatrix{
U \cap V \ar[d] \ar[r] & U \ar[d] \\
V \ar[r] & X
},\]
is a homotopy pushout. In order to give a covering space $Y \to
X$, it suffices to give a
covering space $Y_U \to U$, a covering space $Y_V \to V$, and an isomorphism
$Y_U|_{U \cap V} \simeq Y_V|_{U \cap V}$ of covers of $U \cap V$. In other
words, the diagram of categories
\begin{equation} \label{vankampeneq}
\xymatrix{
\mathrm{Cov}_X \ar[d] \ar[r] & \mathrm{Cov}_U \ar[d] \\
\mathrm{Cov}_{V} \ar[r] & \mathrm{Cov}_{U \cap V}
},\end{equation}
is cartesian, where for a space $Z$, $\mathrm{Cov}_Z$ denotes the category of
topological covering spaces of $Z$. It follows that the dual diagram on fundamental \emph{groupoids}
\[ \xymatrix{
\pi_{\leq 1}(U \cap V) \ar[d] \ar[r] & \pi_{\leq 1}(V) \ar[d] \\
\pi_{\leq 1}(V) \ar[r] & \pi_{\leq 1}(X)
}\]
is, dually, \emph{cocartesian.}
In particular, van Kampen's theorem is a formal consequence of descent theory
for covers.
As a result, one can hope to find analogs of van Kampen's theorem in other
setting. For instance, if $X$ is a \emph{scheme} and $U, V \subset X$ are open subschemes,
then descent theory implies that the diagram
\eqref{vankampeneq} (where $\mathrm{Cov}$ now refers to \emph{finite} \'etale covers) is
cartesian, so the dual diagram on \'etale fundamental groupoids is cocartesian.
Our general approach comes essentially from the next result:
\begin{proposition}
Let $K$ be a simplicial set and let $p\colon K \to \mathrm{CAlg}( \mathrm{Pr}^L_{\mathrm{st}})$ be a functor to
the $\infty$-category $\mathrm{CAlg}( \mathrm{Pr}^L_{\mathrm{st}})$ of stable homotopy theories.
Then we have a natural equivalence in $\mathrm{GalCat}$,
\begin{equation} \label{clgw}
\clg^{\mathrm{w.cov}} \left( \varprojlim_K p \right) \simeq \varprojlim_{k \in K} \clg^{\mathrm{w.cov}}( p(k) )
. \end{equation}
\label{vkweak}
\end{proposition}
\newcommand{\mathrm{Tors}}{\mathrm{Tors}}
\begin{proof}
The statement that \eqref{clgw} is an equivalence equates to the statement that for
any finite group $G$, to give a $G$-torsor in the stable homotopy
theory $\varprojlim_K p$ is equivalent to
giving a compatible family of $G$-torsors in $p(k), k \in K$. (Recall, however, from
\Cref{limgalcat} that infinite limits in $\mathrm{GalCat}$ exist, but they do not
commute with the restriction $\mathrm{GalCat} \to \mathrm{Cat}_\infty$ in general.) We observe that
we have a natural functor from the left-hand-side of \eqref{clgw} to the
right-hand-side which is fully faithful (as both are subcategories of the
$\infty$-category of commutative algebra objects in $\varprojlim_K p$), so that
the functor
\[ \mathrm{Tors}_G\left( \clg^{\mathrm{w.cov}} \left( \varprojlim_K p \right)\right)
\to \varprojlim_{k \in K} \mathrm{Tors}_G(\clg^{\mathrm{w.cov}}( p(k) ))
\]
is fully faithful.
We need to show that if $A \in \mathrm{Fun}(BG, \clg^{\mathrm{w.cov}}(
\varprojlim_K p))$ has the property that its image in $\mathrm{Fun}(BG,
\clg^{\mathrm{w.cov}}(p(k)))$ for each $k \in K$ is a $G$-torsor, then it is a
$G$-torsor to begin with.
However, $A$ is dualizable, since it is dualizable locally (cf.
\cite[Prop. 4.6.1.11]{higheralg}), and it is faithful,
since it is faithful locally, i.e., at each $k \in K$. The map $A \otimes A \to \prod_G A$ is an
equivalence since it is an equivalence locally, and putting these together, $A$
is a $G$-torsor.
\end{proof}
In the case where we work with finite covers, rather than weak finite covers, additional finiteness hypotheses
are necessary.
\begin{proposition}
\label{vankampen}
Let $K$ be a simplicial set and let $p\colon K \to \mathrm{2}\text{-}\mathrm{Ring}$ be a functor.
Then we have a natural fully faithful inclusion
\begin{equation} \label{clgf} \clg^{\mathrm{cov}}( \varprojlim_K p(k)) \to \varprojlim_K
\clg^{\mathrm{cov}}( p(k)), \end{equation}
which is an equivalence if $K$ is finite.
\end{proposition}
\begin{proof}
Since both sides are subcategories of $\mathrm{CAlg}( \varprojlim_K p(k)) =
\varprojlim_K \mathrm{CAlg}(p(k))$, the fully faithful inclusion is evident. The
main content
of the result is that if $K$ is
finite, then the inclusion is an equivalence. In other words, we want to show
that
given a commutative algebra object in $\varprojlim_K p(k)$ which becomes a
finite cover upon restriction to each $p(k)$, then it is a finite cover in the
inverse limit.
Since both sides of \eqref{clgf} are Galois categories (thanks to
\Cref{finlimgal}), it suffices to show that $G$-torsors on either side are
equivalent. In other words, given a compatible diagram of $G$-torsors in the
$\clg^{\mathrm{cov}}(p(k))$, we want the induced diagram in $\mathrm{CAlg}(\varprojlim_K p(k))$ to
be a finite cover.
So let $A \in \mathrm{Fun}(BG, \mathrm{CAlg}( \varprojlim_K p))$ be such that its
evaluation at each vertex $k \in K$ defines a $G$-torsor in $\clg^{\mathrm{cov}}(
p(k))$. We need to show that $A \in \clg^{\mathrm{cov}}( \varprojlim_K p)$. For this, in view
of \Cref{Gtorsor}, it suffices to show that $A$ admits descent. But this
follows in view of \Cref{descfinloc} and the fact that the image of $A$ in
each $k \in K$ admits descent in the stable homotopy theory $p(k)$.
\end{proof}
Using the Galois correspondence, one finds:
\begin{corollary} \label{vk2}
In the situation of \Cref{vankampen} or \Cref{vkweak}, we have an equivalence
in $\mathrm{Pro}( \mathrm{Gpd}_{\mathrm{fin}})$:
\begin{equation}
\label{VK}
\varinjlim_K \pi^{\mathrm{weak}}_{\leq 1} p(k) \simeq \pi_{\leq
1}^{\mathrm{weak}}( \varprojlim_K p(k)), \quad
\varinjlim_K \pi_{\leq 1} p(k) \simeq \pi_{\leq 1}( \varprojlim_K p(k)).
\end{equation}
\end{corollary}
For example, let $U, V \subset X$ be open subsets of a scheme $X$. Then we have
an equivalence
\[ \mathrm{QCoh}(X) \simeq \mathrm{QCoh}(U) \times_{\mathrm{QCoh}(U \cap V)} \mathrm{QCoh}(V), \]
by descent theory. The resulting homotopy pushout diagram that one obtains on
fundamental groupoids (by \eqref{VK}) is the
van Kampen theorem for open immersions of schemes.
Using this, one can also obtain a van Kampen theorem for gluing \emph{closed}
immersions of schemes.
For simplicity, we state the result for commutative rings. Let $A', A, A''$ be
(discrete) commutative rings and consider \emph{surjections}
$A' \twoheadrightarrow A, A'' \twoheadrightarrow A$.
In this case, one has a pull-back square (as we recalled in \Cref{modclosed})
\[ \xymatrix{
\mathrm{Mod}^\omega(A' \times_A A'') \ar[d] \ar[r] & \mathrm{Mod}^\omega(A') \ar[d] \\
\mathrm{Mod}^\omega(A'') \ar[r] & \mathrm{Mod}^\omega(A)
}.\]
Note that the analog without the compactness, or more generally connectivity, hypothesis
would fail.
Using \eqref{VK}, and the observation that the Galois groupoid depends only on
the dualizable objects, we obtain the following well-known corollary:
\begin{corollary}
We have a pushout of profinite groupoids $$\pi_{\leq 1}^{\mathrm{et}}( \mathrm{Spec} (A' \times_A A'')) \simeq
\pi_{\leq 1}^{\mathrm{et}}(
\mathrm{Spec} A') \sqcup_{\pi_{\leq 1}^{\mathrm{et}}( \mathrm{Spec} A)}
\pi_{\leq 1}^{\mathrm{et}}( \mathrm{Spec}
A'').$$
\end{corollary}
This result is one expression of the intuition that $\mathrm{Spec} (A' \times_A A'')$
is obtained by ``gluing together'' the schemes $\mathrm{Spec} A', \mathrm{Spec} A''$ along the closed
subscheme $\mathrm{Spec} A$. This idea in derived algebraic geometry has been studied extensively in
\cite{DAGIX}.
These ideas are often useful even in cases when one can only \emph{approximately}
resolve a stable homotopy theory as an inverse limit of simpler ones; one can
then obtain \emph{upper bounds} for Galois groups.
For example, let $K$ be a simplicial set, and consider
a diagram $f\colon K \to \mathrm{CAlg}$. Let $A = \varprojlim_K f(k)$. In this case, one has
always has a functor
\[ \mathrm{Mod}(A)\to \varprojlim_K \mathrm{Mod}({f(k)}), \]
which is \emph{fully faithful} on the perfect $A$-modules since the right
adjoint preserves the unit. If $K$ is finite, it
is fully faithful on all of $\mathrm{Mod}(A)$.
It follows that, \emph{regardless} of any finiteness hypotheses on $K$, there are fully faithful inclusions
\begin{equation} \label{variousinc} \clg^{\mathrm{cov}}(\mathrm{Mod}(A)) \subset \clg^{\mathrm{cov}} (
\varprojlim_K \mathrm{Mod}({f(k)}))
\subset
\varprojlim_K \clg^{\mathrm{cov}}(
\mathrm{Mod}({f(k)}))
. \end{equation}
We will explore the interplay between these different Galois categories in the
next section.
They can be used to give {upper bounds} on the Galois group
of $A$ since fully faithful inclusions of connected Galois categories are
dual to \emph{surjections} of profinite groups.
\subsection{$\infty$-categories of local systems}
\label{subseclocsys}
In this subsection, we will introduce the first example of the general van
Kampen approach (\Cref{vankampen}), for the case of a \emph{constant} functor.
Let $X$ be a connected space, which we consider as an $\infty$-groupoid.
Let $(\mathcal{C}, \otimes, \mathbf{1})$ be a stable homotopy theory, which
we will assume connected for simplicity.
\begin{definition}
The functor category $\mathrm{Fun}(X, \mathcal{C})$
acquires the structure of a symmetric monoidal $\infty$-category via
the ``pointwise'' tensor product.
We will call this the $\infty$-category of \textbf{$\mathcal{C}$-valued local
systems} on $X$ and denote it by $\mathrm{Loc}_X(\mathcal{C})$.
\end{definition}
This is a special case of the van Kampen setup of the previous section, when we
are considering a functor from $X$ to $\mathrm{2}\text{-}\mathrm{Ring}$ or $\mathrm{CAlg}( \mathrm{Pr}^L_{\mathrm{st}})$ which is
constant with value $\mathcal{C}$.
This means that, with no conditions whatsoever, we have
\[ \pi_1^{\mathrm{weak}}( \mathrm{Loc}_X( \mathcal{C})) \simeq \widehat{\pi_1 X }
\times\pi_1^{\mathrm{weak}}(\mathcal{C}), \]
in view of \Cref{vkweak}, where $\widehat{\pi_1 X}$ denotes the profinite
completion of the fundamental group $\pi_1 X$. Explicitly,
given a functor $f\colon X \to \mathrm{FinSet}$,
we obtain (by mapping into $\mathbf{1}$) a local system in $\mathrm{CAlg}(\mathcal{C})$
parametrized by $X$. These are always weak finite covers in
$\mathrm{Loc}_X(\mathcal{C})$, and these come from finite covers of $X$ or local
systems of finite sets on $X$.
Given weak finite covers in $\mathcal{C}$ itself, we can take the constant
local systems at those objects to obtain weak finite covers in
$\mathrm{Loc}_X(\mathcal{C})$.
If, further, $X$ is a {finite} CW complex, it follows that
\[ \pi_1( \mathrm{Loc}_X( \mathcal{C})) \simeq \widehat{\pi_1 X }
\times\pi_1(\mathcal{C}) , \]
in view of \Cref{vankampen}.
We will use this to begin describing the Galois theory of a basic class of
nonconnective $\e{\infty}$-rings, the cochain algebras on connective ones.
In particular, let $\mathcal{C} = \mod(E)$ for an $\e{\infty}$-algebra $E$, so
that we can regard $\mathrm{Loc}_X( \mathrm{Mod}(E)) = \mathrm{Fun}(X, \mod(E))$ as parametrizing ``local
systems of $E$-modules on $X$.''
The unit object in $\mathrm{Loc}_X( \mathrm{Mod}(E))$ has endomorphism $\e{\infty}$-ring given
by the cochain algebra $C^*(X; E)$.
Therefore, we have an adjunction
of stable homotopy theories
\[ \mod( C^*(X; E)) \rightleftarrows \mathrm{Loc}_X( \mathrm{Mod}(E)), \]
between modules over the $E$-valued cochain algebra $C^*(X; E)$ and
$\mathrm{Loc}_X( \mathrm{Mod}(E))$, where the right adjoint $\Gamma$ takes the global sections
(i.e., inverse limit) over $X$.
The left adjoint is fully faithful when restricted to the perfect $C^*(X;
E)$-modules and in general if $\mathbf{1}$ is compact in $\mathrm{Loc}_X( \mathrm{Mod}(E))$.
Therefore, we get surjections of fundamental groups
\begin{equation} \label{somefundgps}
\widehat{\pi_1 X } \times \pi_1( \mathrm{Mod}(E))
\simeq \pi_1^{\mathrm{weak}}( \mathrm{Loc}_X( \mathrm{Mod}(E))) \twoheadrightarrow
\pi_1 (\mathrm{Loc}_X( \mathrm{Mod}(E))) \twoheadrightarrow
\pi_1( \mathrm{Mod}(C^*(X; E))).
\end{equation}
In this subsection and the next, we will describe the objects and maps in
\eqref{somefundgps} in some specific instances.
\begin{example}
If $X$ is simply connected, then this map is an isomorphism, given the natural
section $\mathrm{Mod}(E) \to \mathrm{Loc}_X(\mathrm{Mod}(E))$ which sends an $E$-module to the constant
local system with that value, so $E$ and $C^*(X; E)$ have the same
fundamental group.
\end{example}
Suppose $X$ has the homotopy type of a \emph{finite} CW complex, so
that the functor $\Gamma$ is obtained via a finite homotopy limit and in
particular commutes with all homotopy colimits.
In this case, as we mentioned earlier, the unit object in $\mathrm{Loc}_X( \mathrm{Mod}(E))$ is compact, so that the map
$\pi_1^{\mathrm{weak}}( \mathrm{Loc}_X( \mathrm{Mod}(E))) \to \pi_1( \mathrm{Loc}_X(\mathrm{Mod}(E)))$ is an isomorphism.
In this case, the entire problem
boils down to understanding the image of the fully faithful,
colimit-preserving functor $\mathrm{Mod}( C^*(X; E)) \to
\mathrm{Loc}_X( \mathrm{Mod}(E))$.
By definition, $\mathrm{Mod}( C^*(X; E))$ is generated by the unit object, so its image
in $\mathrm{Loc}_X( \mathrm{Mod}(E))$ consists of the full subcategory of $\mathrm{Loc}_X(
\mathrm{Mod}(E))$ generated by the unit
object, which is the \emph{trivial} constant local system. In particular, we
should think of $\mathrm{Mod}( C^*(X; E)) \subset \mathrm{Loc}_X( \mathrm{Mod}(E))$ as the
``ind-unipotent'' local systems of $E$-modules parametrized by $X$.
We can see some of that algebraically.
\begin{definition}
Let $A$ be a module over a commutative ring $R$ and let $G$ be a group acting
on $A$ by $R$-endomorphisms. We say
that the action is \textbf{unipotent} if there exists a finite filtration
of $R$-modules
\[ 0 \subset A_1 \subset A_2 \subset \dots \subset A_{n-1} \subset A_n = A, \]
which is preserved by the action of $G$, such that the $G$-action on each
$A_i/A_{i-1}$ is trivial. We say that the $G$-action is \textbf{ind-unipotent} if
$A$ is a filtered union of $G$-stable submodules $A_\alpha \subset A$ such
that the action of $G$ on each $A_\alpha$ is unipotent.
\end{definition}
\begin{proposition}
\label{unipotentthing}
Let $X$ be a connected space. Consider an object $M$ of $\mathrm{Loc}_X(\mathrm{Mod}(E))$ and let
$M_x$ be the underlying $E$-module for some $x \in X$.
Suppose $M$ belongs to the localizing subcategory of $\mathrm{Loc}_X(\mathrm{Mod}(E))$ generated
by the unit.
Then, the action of $\pi_1(X, x)$ on each
$\pi_0E$-module $\pi_k (M_x)$ is
ind-unipotent.
Conversely, suppose $E$ is connective. Given $M \in \mathrm{Loc}_X( \mathrm{Mod}(E))$
such that the monodromy action of $\pi_1(X, x)$ on each
$\pi_k (M_x)$ is ind-unipotent,
then if $M$ is additionally $n$-coconnective
for some $n$ and if $X$ is a finite CW complex, we have $M \in \mathrm{Mod}( C^*(X; E))
\subset \mathrm{Loc}_X( \mathrm{Mod}(E))$.
\end{proposition}
\begin{proof}
Clearly the unit object of $\mathrm{Loc}_X( \mathrm{Mod}(E))$ has unipotent action of
$\pi_1(X, x)$ on its homotopy groups: the monodromy
action by $ \pi_1(X, x)$ is trivial.
The collection of objects of $\mathrm{Loc}_X(\mathrm{Mod}(E))$ with ind-unipotent action of
$\pi_1(X, x)$ is seen to be a localizing subcategory using long exact sequences.
The first assertion follows.
For the final assertion, since $X$ is a finite CW complex, the functor
$\mathrm{Mod}( C^*(X; E)) \to \mathrm{Loc}_X(\mathrm{Mod}(E))$ is fully faithful and commutes with
colimits.
We can write $M$ as a colimit of the local systems
of $E$-modules
\[ 0 \simeq \tau_{\geq n} M \to \tau_{\geq n-1} M \to \tau_{\geq n-2} M
\to \dots , \]
where each term in the local system has only finitely many homotopy groups. It suffices
to show that each $\tau_{\geq k} M$ belongs to $\mathrm{Mod}( C^*(X; E)) \subset \mathrm{Loc}_X(
\mathrm{Mod}(E))$. Working inductively, one reduces to the case where $M$ itself has a
single nonvanishing homotopy group (say, a $\pi_0$) with ind-unipotent action
of $\pi_1(X, x)$. Since the subcategory of $\mathrm{Loc}_X(\mathrm{Mod}(E))$ consisting of local
systems $M$ with $\pi_*(M_x) = 0$ for $\ast \neq 0$ is an ordinary category,
equivalent to the category of local systems of $\pi_0 E$-modules on $X$, our
task is one of algebra. One reduces (from the algebraic definition of
ind-unipotence) to showing that if $M_0$ is a $\pi_0 E$-module, then the
induced object in $\mathrm{Loc}_X( \mathrm{Mod}(E))$ with trivial $\pi_1(X, x)$-action belongs
to $\mathrm{Mod}(C^*(X; E))$. However, this object comes from the $C^*(X; E)$-module
$C^*(X; \tau_{\leq 0} E) \otimes_{\pi_0 E} M_0$.
\end{proof}
\begin{remark}
\label{rems1}
Suppose $X$ is \emph{one-dimensional}, so that $X$ is a wedge of
finitely many circles. Then, for any $E$, any $M \in \mathrm{Loc}_X(\mathrm{Mod}(E))$ such that
the action of $\pi_1(X, x)$ is ind-unipotent on $\pi_*(M_x)$
belongs to the image of $\mathrm{Mod}( C^*(X; E)) \to \mathrm{Loc}_X( \mathrm{Mod}(E))$. In other words,
one needs no further hypotheses on $E$ or $M_x$.
To see this,
we need to show (by \Cref{luriess}) that the inverse limit functor
\[ \Gamma = \varprojlim_X\colon \mathrm{Loc}_X( \mathrm{Mod}(E)) \to \mathrm{Mod}( C^*(X; E)), \]
is \emph{conservative} when restricted to those local systems with the above
ind-unipotence property on homotopy groups.
Recall that one has a spectral sequence
\[ E_2^{s,t} = H^s( X; \pi_{t}M_x) \implies \pi_{t-s} \Gamma(X, M), \]
for computing
the homotopy groups of the inverse limit. The $s = 0$ line of the $E_2$-page is
\emph{never} zero if the action is ind-unipotent unless $M = 0$: there are
always fixed points for the action of $\pi_1(X, x)$ on $\pi_*(M_x)$.
If $X$ is one-dimensional, the spectral sequence degenerates at $E_2$ for
dimensional reasons; this forces the inverse limit $\varprojlim_X M$ to be
nonzero unless $M = 0$.
\end{remark}
As we saw earlier in this subsection, in order to construct finite covers of the unit object in
$\mathrm{Loc}_X( \mathrm{Mod}(E))$, we can consider a local system of finite sets
$\left\{Y_x\right\}_{x \in X}$ on $X$ (i.e., a finite cover of $X$), and
consider the local system $\{C^*(Y_x; E)\}_{x \in X}$ of $\e{\infty}$-algebras
under $E$.
The induced object in $\mathrm{Loc}_X( \mathrm{Mod}(E))$ will generally not be unipotent in this
sense. In fact, unless there is considerable torsion, this will almost never be
the case.
For example, suppose $G$ is a finite group, and let $R$ be a commutative ring.
Consider the $G$-action on $\prod_G R$. The group action is ind-unipotent if
$G$ is a $p$-group (for some prime number $p$) where $p$ is nilpotent in $R$.
\begin{proof}
Suppose $q \mid |G|$ and $q$ is not nilpotent in $R$, but the $G$-action on
$\prod_G R$ is ind-unipotent. It follows that we can invert $q$ and, after some
base extension, assume that $R$ is a \emph{field} with $q \neq 0$. We can
even assume $\zeta_q \in R$. We need to
show that the standard representation is not ind-unipotent when $q \mid |G|$;
this follows from restricting $G$ to $\mathbb{Z}/q \subset G$, and observing that
various nontrivial one-dimensional characters occur and these must map trivally
into any unipotent representation.
Conversely, if $G$ is a $p$-group and $p$ is nilpotent in $R$, then by
filtering $R$, we can assume $p = 0 $ in $R$. Now in fact \emph{any}
$R[G]$-module is ind-unipotent, because the augmentation ideal of $R[G]$ is
nilpotent.
\end{proof}
\begin{corollary}
\label{awayfromp}
Suppose $p$ is not nilpotent in the $\e{\infty}$-ring $R$. Then the
surjection $\widehat{\pi_1 X } \times \pi_1 \mathrm{Mod}(E) \twoheadrightarrow \pi_1
\mathrm{Mod}(C^*(X; E)$ factors through $\widehat{\pi_1 X}_{p^{-1}}$ where
$\widehat{\pi_1 X}_{p^{-1}}$ denotes the profinite completion away from $p$.
\end{corollary}
\begin{corollary}
If $R$ is a $\e{\infty}$-ring such that $\mathbb{Z} \subset \pi_0 R$, then
the map $\pi_1 \mathrm{Mod}(R) \to \pi_1 \mathrm{Mod}( C^*(X; R))$ is an isomorphism of profinite
groups.
\end{corollary}
\begin{remark}
In $K(n)$-local stable homotopy theory, the
comparison question between modules over the cochain $\e{\infty}$-ring and
local systems has been studied in \cite[sec. 5.4]{ambidexterity}.
\end{remark}
Putting these various ideas together, it is not too hard to prove the following
result, whose essential ideas are contained in \cite[Proposition
5.6.3]{rognes}.
Here $\widehat{\pi_1 X}_p$ denotes the pro-$p$-completion of $\pi_1 X$.
\begin{theorem}
\label{padicgalois}
Let $X$ be a finite CW complex. Then if $R$ is an $\e{\infty}$-ring with $p$
nilpotent and such that $\pi_i R = 0$ for $i \gg 0$ (e.g., a field of
characteristic $p$), then the natural map
\begin{equation} \label{pmap}
\widehat{\pi_1 X}_p \times \pi_1 \mathrm{Mod}(R) \to \pi_1 \mathrm{Mod}( C^*(X; R))
\end{equation}
is an isomorphism.
\end{theorem}
\begin{proof}
By \Cref{awayfromp}, the natural map $\widehat{\pi_1 X} \times \pi_1 \mathrm{Mod}(R)
\twoheadrightarrow \pi_1 \mathrm{Mod}( C^*(X; R))$ does in fact factor through
the quotient of the source where $\widehat{\pi_1 X }$ is replaced by its
pro-$p$-completion. It suffices to show that the induced map
\eqref{pmap} is an isomorphism. Equivalently, we need to show that if $Y \to X$
is a finite $G$-torsor for $G$ a $p$-group, then $C^*(X; R) \to C^*(Y; R)$ is a
faithful $G$-Galois extension.
Equivalently, we need to show that if $\left\{Y_x\right\}_{x \in X}$ is the
local system of finite sets defined by the finite cover $Y \to X$, then the
local system of $R$-modules $\left\{C^*(Y_x; R)\right\}_{x \in X}$
(which gives a $G$-Galois cover of the unit in $\mathrm{Loc}_X( \mathrm{Mod}(R))$)
actually belongs to
the image of $\mathrm{Mod}( C^*(X; R))$. However, this is a consequence of
\Cref{unipotentthing} because the monodromy action is by elements of the
$p$-group $G$. Any $G$-module over a ring with $p$ nilpotent is ind-unipotent.
\end{proof}
\begin{remark}
Let $Y \to X$ be a map of spaces, and let $R$ be as above. Then there are two natural local systems of
$R$-module spectra on $X$ that one can construct:
\begin{enumerate}
\item The object of $\mathrm{Loc}_X(\mod(R)))$ obtained from the $C^*(X;
R)$-module $C^*(Y; R)$, i.e., the local system $C^*(Y; R) \otimes_{C^*(X; R)}
C^*(\ast; R)$ which is a local system as $\ast$ ranges over $X$.
\item Consider the fibration $Y \to X$ as a local system of spaces $\{Y_x\}
$ on $X$, $x \in X$, and apply $C^*(\cdot; R)$ everywhere.
\end{enumerate}
In general, these local systems are not the same: they are the same only if the
$R$-valued
\emph{Eilenberg-Moore spectral sequence} for the square
\[ \xymatrix{
Y_x \ar[d] \ar[r] & Y \ar[d] \\
\left\{x\right\} \ar[r] & X
},\]
converges, for every choice of basepoint $x \in X$.
This question can be quite subtle, in general. \Cref{padicgalois} is
essentially equivalent to the convergence of the $R$-valued Eilenberg-Moore
spectral sequence when $Y \to X$ is a $G$-torsor for $G$ a $p$-group. This is
the approach taken by Rognes in \cite{rognes}.
\end{remark}
Finally, we close with an example suggesting further questions.
\begin{example}
The topological part of the Galois group of $C^*(S^1; \mathbb{F}_p)$ is
precisely $\widehat{\mathbb{Z}}_p$. The Galois covers come from the maps
\[ C^*(S^1; \mathbb{F}_p) \to C^*(S^1; \mathbb{F}_p), \]
dual to the degree $p^n$ maps $S^1 \to S^1$.
This would not work over the sphere $S^0$ replacing $\mathbb{F}_p$, in view
of \Cref{awayfromp}. However, this \emph{does} work in $p$-adically completed
homotopy theory.
Let $\sp_p$ be the $\infty$-category of $p$-complete (i.e., $S^0/p$-local) spectra, and let
$\widehat{S}_p$ be the $p$-adic sphere, which is the unit of $\sp_p$. The map
$C^*(S^1; \widehat{S}_p) \to C^*(S^1; \widehat{S}_p)$ which is dual to the
degree $p$ map $S^1 \to S^1$ is a
$\mathbb{Z}/p$-weak Galois extension in $\sp_p$.
In particular, it will follow that the weak Galois group of $\sp_p$ is
the product of $\widehat{\mathbb{Z}_p}$ with that of $\sp_p$ itself.
To see this,
note that we have a fully faithful embedding
\[ L_{S^0/p} \mathrm{Mod}( C^*(S^1; \widehat{S}_p)) \simeq \mathrm{Mod}_{\sp_p}( C^*(S^1;
\widehat{S}_p)) \subset \mathrm{Loc}_{S^1}( \sp_p). \]
In $\mathrm{Loc}_{S^1}( \sp_p)$, we need to show that the local system of $p$-complete
spectra obtained from the cover $S^1 \stackrel{p}{\to} S^1$ actually belongs to the
subcategory of $\mathrm{Loc}_{S^1}( \sp_p)$ generated under colimits by the unit
(equivalently, by the constant local systems).
In order to prove this claim, it suffices to prove the analog after quotienting
by $p^n$ for each $p$, since for any $p$-complete spectrum $X$, we have
\[ X \simeq \Sigma^{-1} L_{S^0/p} ( \varinjlim_n (X \otimes S^0/p^n)), \]
as the colimit $\varinjlim_n S^0/p^n$ (where the successive maps are
multiplication by $p$)
has $p$-adic completion given by the suspension of the $p$-adic sphere.
But on the other hand, we can apply \Cref{rems1} to the cofiber of $p^n$ on our
local system, since an order $p$ automorphism on a $p$-torsion abelian group
is always ind-unipotent.
By contrast, the analogous assertion would fail if we worked in the setting of
\emph{all} $C^*(S^1; \widehat{S}_p)$-modules (not $p$-complete ones): the
(weakly) Galois covers constructed are only Galois after $p$-completion. This
follows because $C^*(S^1; \widehat{S}_p)$ has coconnective rationalization, and
all the Galois covers of it are \'etale (as we will show in
\Cref{coconnectivecov}).
\end{example}
\subsection{Stacks and finite groups}
To start with, let $k$ be a separably closed field of characteristic $p$ and let $G$ be a finite group.
Consider the stable homotopy theory $\mathrm{Mod}_G(k)$ of $k$-module spectra equipped
with an action of $G$, or equivalently the $\infty$-category $\mathrm{Loc}_{BG}(
\mathrm{Mod}(k))$ of local systems of $k$-module spectra on $BG$. We will explore the Galois theory of $\mathrm{Mod}_G(k)$ and the
various inclusions \eqref{variousinc}.
\begin{theorem}
\label{Grepgal}
Let $k$ be separably closed of characteristic $p$.
$\pi_1^{\mathrm{weak}}( \mathrm{Mod}_G(k)) \simeq G$ but $\pi_1(\mathrm{Mod}_G(k))$ is the quotient of $G$ by the
normal subgroup generated by the order $p$ elements.
\end{theorem}
\begin{proof}
The assertion of $\pi_1^{\mathrm{weak}}( \mathrm{Mod}_G(k))$ is immediate: the weak ``Galois closure''
(i.e., maximal connected object in the Galois category) of the unit
in $\mathrm{Mod}_G(k)$ is $\prod_G k$, thanks to \Cref{vkweak}. The more difficult part of the result concerns
the (non-weak) Galois group.
Any finite cover $A \in \mathrm{CAlg}( \mathrm{Mod}_G(k))$ must be given by an action of $G$ on an underlying
$\e{\infty}$-$k$-algebra which must be $\prod_S k$ for $S$ a finite set; $S$
gets a natural $G$-action, which determines everything.
In particular, we get that $A$ must be a product of copies of $\prod_{G/H} k $.
We need to determine which of these are actually finite covers. We can always
reduce to the Galois case, so given a surjection $G \twoheadrightarrow G'$, we
need a criterion for when $\prod_{G'} k \in \mathrm{CAlg}( \mathrm{Mod}_G(k))$ is a finite cover.
Fix an order $p$ element $g \in G$. We claim that if $\prod_{G'} k \in
\mathrm{CAlg}(\mathrm{Mod}_G(k))$ is a finite cover, then $g$ must map to the identity in $G'$. In fact,
otherwise, we could restrict to $\mathbb{Z}/p \subset G$ to find (after
inverting an idempotent of the restriction) that $\prod_{\mathbb{Z}/p} k$ would be a finite cover
in $\mathrm{Mod}_{\mathbb{Z}/p}(k)$. This is impossible since
$( \prod_{\mathbb{Z}/p} k)^{h \mathbb{Z}/p} \simeq k$ while $k^{h
\mathbb{Z}/p}$ has infinitely many homotopy groups; thus the unit cannot be in
the thick $\otimes$-ideal generated by
$\prod_{\mathbb{Z}/p} k)$. It follows from this that if $\prod_{G'} k$ is a
finite cover in $\mathrm{Mod}_G(k)$, then every order $p$ element must map to the
identity in
$G'$.
Conversely, suppose $G \twoheadrightarrow G'$ is a surjection annihilating
every order $p$ element. We claim that $\prod_{G'} k$ is a finite cover in
$\mathrm{Mod}_G(k)$. Since it is a $G'$-Galois extension of the unit, it suffices to
show that it is descendable by \Cref{Gtorsor}. For this, by the
Quillen stratification theory (in particular, \Cref{BC}), one can check this
after restricting to an elementary abelian $p$-subgroup. But after such a
restriction, our commutative algebra object becomes a finite product of copies
of the unit.
\end{proof}
\begin{corollary}
\label{galhG}
Let $k$ be a separably closed field of characteristic $p>0$. The Galois group $C^*(BG; k) \simeq
k^{hG}$ is given by the quotient of the pro-$p$-completion of $G$ by the order
$p$ elements in $G$.
\end{corollary}
By the pro-$p$-completion of $G$, we mean the maximal quotient of $G$ which is
a $p$-group. In other words, we take the smallest normal subgroup $N \subset G$
such that $|G|/|N|$ is a power of $p$, and then take the normal subgroup $N'$ generated
by $N$ and the order $p$ elements in $G$. The Galois group of $C^*(BG; k)$ is
the quotient $G/N'$.
\begin{proof}
Observe that the $\infty$-category of perfect $C^*(BG; k)$-modules is a full
subcategory of the $\infty$-category $\mathrm{Loc}_{BG}(\mathrm{Mod}(k)) \simeq \mathrm{Mod}_G(k)$ of
$k$-module spectra equipped with a $G$-action. We just showed in \Cref{Grepgal}
that the Galois group of the latter was the quotient of $G$ by the normal
subgroup generated by the order $p$ elements. In other words, the
descendable connected Galois
extensions of the unit in $\mathrm{Mod}_G(k)$ were the products $\prod_{G'} k$ where $G
\twoheadrightarrow G'$ is a surjection of groups annihilating the order $p$
elements.
It remains to determine which of these Galois covers actually belong to the
thick subcategory generated by the unit $\mathbf{1} \in \mathrm{Mod}_G(k)$. As we have
seen, that implies that the monodromy action of $\pi_1(BG) \simeq G$ on
homotopy groups is
ind-unipotent; this can only happen (for a permutation module) if $G'$ is a
$p$-group. If $G'$ is a $p$-group, though, then the unipotence
assumption holds and $\prod_{G'} k$ does belong
to the thick subcategory generated by the unit, so these do come from $\mathrm{Mod}(
C^*(BG; k))$.
\end{proof}
\begin{remark}
Even if we were interested only in
$\e{\infty}$-rings and their modules, for which the Galois group and weak
Galois group coincide, the proof of \Cref{galhG} makes clear the importance of
the distinction (and the theory of descent via thick subcategories) in general
stable homotopy theories. We needed thick subcategories and Quillen stratification
theory to run the argument.
\end{remark}
\begin{example}
\label{weakinv}
We can thus obtain a weak \emph{invariance result} for Galois groups (which we
will use later). Let $R$ be an $\e{\infty}$-ring under $\mathbb{F}_p$, given
trivial $\mathbb{Z}/p$-action. Then the
Galois theories of $R$ and $R^{h \mathbb{Z}/p}$ are the same, i.e.,
$R \to R^{h \mathbb{Z}/p}$ induces an equivalence on Galois groupoids.
In fact, we know from $\mathrm{Mod}^\omega( R^{h \mathbb{Z}/p}) \subset \mathrm{Fun}(B
\mathbb{Z}/p, \mathrm{Mod}^\omega(R))$ that Galois extensions of $R^{h\mathbb{Z}/p}$
come either from those of $R$ or from the $\mathbb{Z}/p$-action.
However, $\prod_{\mathbb{Z}/p} R$ is not a $\mathbb{Z}/p$-torsor because the
thick $\otimes$-ideal it generates
in $\mathrm{Fun}( B \mathbb{Z}/p, \mathrm{Mod}^\omega(R))$
cannot contain the unit: in fact, the
Tate construction on $R$ with $\mathbb{Z}/p$ acting trivially is nonzero, while
the Tate construction on anything in the thick $\otimes$-ideal generated by
$\prod_{\mathbb{Z}/p} R$ is trivial.
\end{example}
Consider now, instead of a finite group, an algebraic stack $\mathfrak{X}$.
As discussed in \Cref{qcohintro}, one has a natural stable homotopy theory $\mathrm{QCoh}(\mathfrak{X})$ of
quasi-coherent complexes on $\mathfrak{X}$, obtained via
\[ \mathrm{QCoh}( \mathfrak{X}) = \varprojlim_{\mathrm{Spec} A\to \mathfrak{X}} D( \mathrm{Mod}(A)), \]
where we take the inverse limit over all maps $\mathrm{Spec} A\to X$; we could
restrict to smooth maps. It follows from \Cref{connectivegal} that a
\emph{weak finite cover} in $\mathrm{QCoh}( \mathfrak{X})$ is the compatible
assignment of a finite \'etale $A$-algebra for each map $\mathrm{Spec} A \to
\mathfrak{X}$. In other words, the weak Galois group of $\mathrm{QCoh}(\mathfrak{X})$ is the
\'etale fundamental group of the stack $\mathfrak{X}$.
If the unit object in $\mathrm{QCoh}(\mathfrak{X})$ is
compact, the weak Galois group and the Galois group of $\mathrm{QCoh}(
\mathfrak{X})$ are the same. One can make this conclusion
if $\mathfrak{X}$ is \emph{tame}, which roughly means that (if $\mathfrak{X}$
is Deligne-Mumford) the orders of the stabilizers are invertible (cf.
\cite[Theorems B and C]{HallRydh}). If this
fails, then the weak Galois group and the Galois group need not be the same,
and one gets a \emph{canonical quotient} of the \'etale fundamental group of an
algebraic stack, the Galois group of $\mathrm{QCoh}(\mathfrak{X})$.
\begin{example}
Let $G$ be a finite group, and let $\mathfrak{X} = BG$ over a separably closed field of characteristic
$p$. Then $\mathrm{QCoh}( \mathfrak{X})$ is precisely the $\infty$-category $\mathrm{Mod}_G(k)$
considered in the previous section. The fundamental group of $\mathfrak{X}$ is
$G$, and the main result of the previous subsection (\Cref{Grepgal}) implies that
the difference between the Galois group of $\mathrm{QCoh}( \mathfrak{X})$ and the \'etale fundamental group of
$\mathfrak{X}$ is precisely the order $p$ elements in the latter.
\end{example}
Thus, we know that for any map of stacks $B \mathbb{Z}/p \to \mathfrak{X}$ where $p$ is not
invertible on $\mathfrak{X}$, the $\mathbb{Z}/p$
must vanish in the fundamental group of $\mathrm{QCoh}( \mathfrak{X} )$ (but not necessarily
in the fundamental group of $\mathfrak{X}$). When $\mathfrak{X} = BG$ for some
finite group, this is the \emph{only} source of the difference between two
groups. We do not know what the difference looks like in general.
Next, as an application of these ideas, we include an example that shows that
the Galois group is a sensitive invariant of
an $\e{\infty}$-ring: that is, it can vary as the $\e{\infty}$-structure varies
within a fixed $\e{1}$-structure.
\begin{example}
Let $k$ be a separably closed field of characteristic $p > 0$.
Let $\alpha_{p^2}$ be the usual rank $p^2$ group scheme over $k$ and let
$(\alpha_{p^2})^{\vee}$ be its Cartier dual, which is another infinitesimal
commutative
group scheme.
Let $\mathbb{Z}/p^2$ be the usual constant group scheme.
Consider the
associated classifying stacks $B \mathbb{Z}/p^2$ and $B (
\alpha_{p^2})^{\vee}$, and the associated cochain $\e{\infty}$-rings
$C^*(B \mathbb{Z}/p^2; k)$ and $C^*( B (\alpha_{p^2})^{\vee}; k)$ defined as
endomorphisms of the unit of quasi-coherent sheaves.
Since $\alpha_{p^2}^{\vee}$ is infinitesimal, it follows that the fundamental
group of the stack $B ( \alpha_{p^2})^{\vee}$ is trivial and
in particular that $\pi_1 \mathrm{Mod}( C^*( B ( \alpha_{p^2})^{\vee}; k))$ is trivial.
In other words, we are using the geometry of the stack to \emph{bound above}
the possible Galois group for the $\e{\infty}$-ring of cochains with values in
the structure sheaf.
However, by \Cref{galhG}, we have $\pi_1 \mathrm{Mod}(
C^*(B\mathbb{Z}/p^2; k)) \simeq \mathbb{Z}/p$.
Finally, we note that there is a canonical equivalence of $\e{1}$-rings between
the two cochain algebras. In fact, the $k$-linear \emph{abelian} category of
(discrete) quasi-coherent sheaves on $B
\mathbb{Z}/p^2$ can be identified with the category of modules over the group
ring $k[\mathbb{Z}/p^2]$, which is noncanonically isomorphic to the algebra
$k[x]/(x^{p^2})$. The $k$-linear \emph{abelian} category of discrete
quasi-coherent sheaves on $B (
\alpha_{p^2})^{\vee}$ is identified with the category of modules over the ring
of functions on $\alpha_{p^2}$, which is $\mathbb{F}_p[x]/x^{p^2}$. In
particular, we get a $k$-linear \emph{equivalence} between either the
abelian or derived categories of sheaves in
either case. Since the cochain $\e{\infty}$-rings we considered are (as
$\e{1}$-algebras) the endomorphism rings of the object $k$ (which is the same
representation either way), we find that they
are equivalent as $\e{1}$-algebras.
\end{example}
\section{Invariance properties}
Let $R$ be a (discrete) commutative ring and let $I \subset R$ be a nilpotent
ideal. Then it is a classical result in commutative algebra, the
``topological invariance of the \'etale site,'' \cite[Theorem 8.3, Exp.
I]{sga1}, that the
\'etale site of $\mathrm{Spec} R$ and the closed subscheme $\mathrm{Spec} R/I$ are equivalent.
In particular, given an \'etale $R/I$-algebra $\overline{R}'$, it can be lifted
\emph{uniquely} to an \'etale $R$-algebra $R'$ such that $R'
\otimes_R R/I \simeq \overline{R}'$.
In this section, we will consider analogs
of this result for $\e{\infty}$-rings.
For example, we will prove:
\begin{theorem} \label{p=0}
Let $R$ be an $\e{\infty}$-algebra under $\mathbb{Z}$ with
$p$ nilpotent in $\pi_0 R$. Then the map
\[ R \to R \otimes_{\mathbb{Z}} \mathbb{Z}/p, \]
induces an isomorphism on fundamental groups.
\end{theorem}
Results such as \Cref{p=0} will be
extremely useful for us. For example, it will be integral to our computation
of
the Galois groups of stable module $\infty$-categories over finite groups.
\Cref{p=0}, which is immediate in the case of $R$ \emph{connective} (thanks
to \Cref{connectivegal} together with the classical topological invariance
result), seems to
be very non-formal in the general case.
Throughout this section, we assume that our stable homotopy theories are
\emph{connected.}
\subsection{Surjectivity properties}
We begin with some generalities from \cite{sga1}.
We have the following easy lemma.
\begin{lemma}
\label{surj}
Let $G \to H$ be a morphism of profinite groups. Then the following are
equivalent:
\begin{enumerate}
\item $G \to H$ is surjective.
\item For every finite (continuous) $H$-set $S$, $S$ is connected if and only
if the $G$-set obtained from $S$ by restriction is connected.
\end{enumerate}
\end{lemma}
Let $(\mathcal{C}, \otimes, \mathbf{1})$ be a (connected) stable homotopy
theory. Given a commutative algebra object $A \in \mathcal{C}$, we
have functors $\clg^{\mathrm{cov}}(\mathcal{C}) \to \clg^{\mathrm{cov}}( \mathrm{Mod}_{\mathcal{C}}(A))
,\clg^{\mathrm{w.cov}}(\mathcal{C}) \to \clg^{\mathrm{w.cov}}( \mathrm{Mod}_{\mathcal{C}}(A))
$ given by
tensoring with $A$. Using the Galois correspondence, this comes from the map of
profinite groups $\pi_1( \mathrm{Mod}_{\mathcal{C}}(A)) \to \pi_1( \mathcal{C})$ by
restricting continuous representations in finite sets.
The following is a consequence of \Cref{surj}.
\begin{proposition} \label{surjthing}
Let $A \in \mathrm{CAlg}(\mathcal{C})$ be a commutative algebra object with the
following property: given any $A' \in \mathrm{CAlg}(\mathcal{C} )$ which is a weak
finite cover,
the map
\begin{equation} \label{idemmap} \mathrm{Idem}(A') \to \mathrm{Idem}(A \otimes A')
\end{equation}
is an isomorphism. Then the induced maps
\[ \pi_1(\mathrm{Mod}_{\mathcal{C}}(A)) \to \pi_1( \mathcal{C}) ,
\quad \pi_1^{\mathrm{weak}}( \mathrm{Mod}_{\mathcal{C}}(A)) \to \pi_1^{\mathrm{weak}}(\mathcal{C}),
\]
are surjections of profinite groups.
\end{proposition}
Thus, it will be helpful to have some criteria for when
maps of the form \eqref{idemmap} are isomorphisms.
\begin{definition}
Given $A \in \mathrm{CAlg}(\mathcal{C})$, we will say that $A$ is \textbf{universally
connected} if for every $A' \in \mathrm{CAlg}(\mathcal{C})$, the map $\mathrm{Idem}(A') \to \mathrm{Idem}(A' \otimes A)$ in
\eqref{idemmap} is an isomorphism.
\end{definition}
It follows by \Cref{surjthing} that if $A$ is universally connected, then
$\pi_1^{\mathrm{weak}} (\mathrm{Mod}_{\mathcal{C}}(A)) \to \pi_1^{\mathrm{weak}}( {\mathcal{C}})$ and
$\pi_1( \mathrm{Mod}_{\mathcal{C}}(A)) \to \pi_1 ({\mathcal{C}})$ are surjections;
moreover, this holds after any base change in $\mathrm{CAlg}(\mathcal{C})$. That is, if
$A' \in \mathrm{CAlg}(\mathcal{C})$, then
the map $\pi_1 ( \mathrm{Mod}_{\mathcal{C}}(A \otimes A')) \to \pi_1(
\mathrm{Mod}_{\mathcal{C}}(A'))$ is a surjection, and similarly for the weak Galois
group.
Note first that if $A$ \emph{admits descent}, then \eqref{idemmap} is always an
injection, since for any $A'$, we can recover $A'$ as the totalization of the
cobar construction on $A$ tensored with $A'$ and since
$\mathrm{Idem}$ commutes with limits (\Cref{idemlimit}). In fact, it thus follows that if $A$ admits
descent, then
$\mathrm{Idem}(A')$ is the equalizer of the two maps $\mathrm{Idem}(A \otimes A')
\rightrightarrows \mathrm{Idem}(A \otimes A
\otimes A')$.
More generally, one can obtain a weaker conclusion under weaker hypotheses:
\begin{proposition}
\label{faithinj}
If $A \in \mathrm{CAlg}(\mathcal{C})$ is faithful (i.e., tensoring with $A$ is a
conservative functor $\mathcal{C} \to \mathcal{C}$), then the map \eqref{idemmap} is
always an injection, for any $A' \in \mathrm{CAlg}(\mathcal{C})$.
\end{proposition}
\begin{proof}
It suffices to show that if $e \in \mathrm{Idem}(A')$ is an idempotent which maps to
zero in $\mathrm{Idem}(A \otimes A')$, then $e$ was zero to begin with. The hypothesis
is that $A'[e^{-1}]$ becomes contractible after tensoring with $A$, and since
$A$ is faithful, it was contractible to begin with; that is, $e$ is zero.
\end{proof}
We thus obtain the following criterion for universal connectedness.
\begin{proposition}
\label{invprop}
Let $(\mathcal{C}, \otimes, \mathbf{1})$ be a connected stable homotopy theory. Suppose
$A \in \mathrm{CAlg}(\mathcal{C})$ is an object with the properties:
\begin{enumerate}
\item $A$ is descendable.
\item The multiplication map $A \otimes A \to A$ is faithful.
\end{enumerate}
Then $A$ is universally connected.
\end{proposition}
\begin{proof}
We will show that if $B \in \mathrm{CAlg}(\mathcal{C})$ is {arbitrary},
then the map $\mathrm{Idem}(B) \to \mathrm{Idem}(A \otimes B)$ is an \emph{isomorphism}.
Since $A$ is descendable, we know that there is an equalizer diagram
\[ \mathrm{Idem}(B) \to \mathrm{Idem}(A \otimes B) \rightrightarrows \mathrm{Idem}(A \otimes A
\otimes B). \]
To prove the proposition, it suffices to show that the two maps $\mathrm{Idem}(A \otimes B)
\rightrightarrows \mathrm{Idem}(A \otimes A \otimes B)$ are equal.
However, these
maps become equal after composing with the map $\mathrm{Idem}(A \otimes A \otimes
B) \to \mathrm{Idem}(A \otimes B)$ induced by the multiplication $A \otimes A \to
A$.
Since $A \otimes A \to A$ is faithful, the map
$\mathrm{Idem}(A \otimes A \otimes
B) \to \mathrm{Idem}(A \otimes B)$ is injective by \Cref{faithinj}, which thus proves the result.
\end{proof}
\Cref{invprop} is thus almost a tautology, although the basic idea will be quite useful for us.
Unfortunately, the hypotheses are rather restrictive. If $A$ is a local
artinian ring and $k$ the residue field, then the map $A \to k$ admits descent.
However, the multiplication map $k \otimes_A k \to k$ need not be faithful:
$k \otimes_A k$ has always infinitely many homotopy
groups (unless $A = k$ itself). Nonetheless, we can prove:
\begin{proposition} \label{surjart} Let $k$ be a field.
Let $A$ be a connective $\e{\infty}$-ring with a map $A \to k$
inducing a surjection on $\pi_0$. Suppose $A \to k$ admits descent. Then
$A \to k$ is universally connected.
\end{proposition}
\begin{proof}
Once again, we show that for any $A' \in \mathrm{CAlg}_{A/}$, the map $A'
\to A' \otimes_A k$ induces an isomorphism on idempotents.
Since $A \to k$ is descendable, it suffices to show that the two maps
\[ \mathrm{Idem}(A' \otimes_A k) \rightrightarrows \mathrm{Idem}(A' \otimes_A k \otimes_A k) \]
are the same.
For this, we know that the two maps become the same after composition with the
multiplication map $ A ' \otimes _A (k \otimes_A k) \to A' \otimes_A k$. To
show that the two maps are the same, it will suffice to show that they are
\emph{isomorphisms.} In other words, since we have a commutative diagram
\begin{equation} \label{idemdiag} \mathrm{Idem}( A ' \otimes_A k) \rightrightarrows \mathrm{Idem}(A' \otimes_A k \otimes_A
k) \to \mathrm{Idem}(A' \otimes_A k) , \end{equation}
where the composite arrow is the identity, it suffices to show that
\emph{either one} of the two maps $\mathrm{Idem}(A' \otimes_A k) \rightrightarrows
\mathrm{Idem}(A' \otimes_A k \otimes_A k)$ is an isomorphism.
More generally, we claim that for any $k$-algebra $R$, the map
\[ R \to R \otimes_k (k \otimes_A k), \]
induced by the map of $k$-algebras $k \to k \otimes_A k$, induces
an \emph{isomorphism}
on idempotents. (In \eqref{idemdiag}, this is the map that we get from free,
without using the fact that $A' \otimes_A k$ was the base-change of an
$A$-algebra.)
Since we have a K\"unneth isomorphism, this follows from the following
purely algebraic lemma.
\begin{lemma}
Let $R_*$ be a graded-commutative $k$-algebra and let $R'_*$ be a
graded-commutative \emph{connected} $k$-algebra: $R'_0 \simeq k$ and $R'_i = 0$
for $i < 0$. Then the natural map from idempotents in $R_*$ to idempotents in the graded
tensor product $R_*
\otimes_k R'_*$ is an isomorphism.
\end{lemma}
\begin{proof}
We have a map
\[ \mathrm{Idem}(R_*) \to \mathrm{Idem}(R_* \otimes_k R'_*), \]
which is injective, since the map $k \to R'_*$ admits a section in the category
of graded-commutative $k$-algebras. But the ``reduction'' map $\mathrm{Idem}(R_* \otimes_k R'_*) \to
\mathrm{Idem}(R_*)$ is also injective. In fact, since idempotents form a Boolean
algebra, it suffices to show that an idempotent
in $R_* \otimes_k R'_*$ that maps to zero in $R_*$ must have been zero to begin
with. However, such an idempotent would belong to the ideal $R_* \otimes_k R'_{>0}$,
which easily forces it to be zero.
\end{proof}
\end{proof}
\begin{example}
\Cref{surjart} applies in the setting of an artinian ring mapping to its residue
field. However, we also know that the map $A \to A/\mathfrak{m}$ for $A$
artinian and $\mathfrak{m}$ a maximal ideal can be obtained as a finite
composition of square-zero extensions, so we could also appeal to
\Cref{squarezerogeneral} below.
\end{example}
\subsection{Square-zero extensions}
Given the classical topological invariance of the \'etale site, the
following is not so surprising.
\begin{proposition}
\label{trivsqzero}
If $A$ is an $\e{\infty}$-ring and $M$ an $A$-module, then the natural map $A
\to A \oplus M$ (where $A \oplus M$ denotes the trivial ``square zero''
extension of $A$ by $M$), induces an isomorphism on fundamental groups.
\end{proposition}
This will follow from the following more general statement.
\begin{proposition}
Let $R$ be an $\e{\infty}$-ring with no nontrivial idempotents. Let $X$ be a
two-fold loop object in the $\infty$-category $\mathrm{CAlg}_{R//R}$ of $\e{\infty}$-$R$-algebras
over $R$. Then the map $R \to X$ induces an isomorphism on fundamental groups.
\end{proposition}
Note that a one-fold delooping is insufficient, because of the example of cochains on
$S^1$ (cf. \Cref{padicgalois}).
\begin{proof}
In view of \Cref{idemlimit}, we see that $X$ has no nontrivial idempotents.
Next, observe that we have maps $R \to X \to R$ by assumption, so that, at the
level of fundamental groups, we get a section of the map $\pi_1( \mathrm{Mod}(X)) \to
\pi_1( \mathrm{Mod}(R))$. In particular, the map $\pi_1( \mathrm{Mod}(X)) \to \pi_1( \mathrm{Mod}(R))$ is
surjective. We thus need to show that the map $\pi_1( \mathrm{Mod}(R)) \to \pi_1( \mathrm{Mod}(X))$
(coming from $X \to R$) is also surjective, which we can do via
\Cref{surjthing}.
To see that, suppose $X \simeq \Omega^2 Y$ where $Y$ is an object in
$\mathrm{CAlg}_{R//R}$. We want to show that the fundamental group of $\mathrm{Mod}(X)$ is surjected
onto by that of $\mathrm{Mod}(R)$. Consider the pull-back diagram
of $\e{\infty}$-algebras,
\[ \xymatrix{
\Omega^2 Y \ar[d] \ar[r] & R \ar[d] \\
R \ar[r] & \Omega Y
}.\]
Using \Cref{idemlimit} again,
we find that $\Omega Y$ has no nontrivial idempotents. Therefore,
we have maps
\[ \pi_1(\mathrm{Mod}(R)) \to \pi_1( \mathrm{Mod}(R) \times_{\mathrm{Mod}({\Omega Y})}
\mathrm{Mod}(R)) )
\twoheadrightarrow \pi_1( \mathrm{Mod}({\Omega^2 Y})) . \]
The second map is a surjection since it comes from a fully faithful inclusion
of stable homotopy theories
$\mathrm{Mod}( \Omega^2 Y) \subset \mathrm{Mod}(R) \times_{\mathrm{Mod}( \Omega Y)} \mathrm{Mod}(R)$. Since $
\Omega Y$ has no nontrivial idempotents,
$\pi_1 \mathrm{Mod}( \Omega Y)$ receives a map from $\pi_1 \mathrm{Mod}(R)$ and we have
$\pi_1( \mathrm{Mod}(R) \times_{\mathrm{Mod}({\Omega Y})}
\mathrm{Mod}(R)) ) \simeq \pi_1( \mathrm{Mod}(R)) \sqcup_{\pi_1 ( \mathrm{Mod}( \Omega Y))} \pi_1
(\mathrm{Mod}(R))$. This implies that the first map is a surjection too, as desired.
\end{proof}
We can also consider the behavior of the Galois group under (not
necessarily trivial) square-zero extensions.
Recall (see \cite[sec. 7.4.1]{higheralg}) that these are obtained as follows. Given an
$\e{\infty}$-ring $A$ and an $A$-module $M$, for every map $\phi\colon A \to A \oplus M$
in $\mathrm{CAlg}_{/A}$, we can form the pull-back
\[ \xymatrix{
A' \ar[d] \ar[r] & A \ar[d]^{0} \\
A \ar[r]^{\phi} & A \oplus M
},\]
where
$0\colon A \to A \oplus M$ is the standard map (informally, $a \mapsto (a, 0)$).
The resulting map $A' \to A$ is referred to as a \textbf{square-zero
extension} of $A$, by $\Omega M$.
\begin{corollary}
\label{sqzerosurj}
\label{squarezerogeneral}
Notation as above, the map $\pi_{1} \mathrm{Mod}( A') \to \pi_{ 1} \mathrm{Mod}(A)$ is
a surjection.
In fact, $A' \to A$ is universally connected.
\end{corollary}
\begin{proof}
It suffices to show that $A' \to A$ is universally connected.
This follows from the fact that $\mathrm{Idem}$ commutes with inverse limits, since one
checks that the two maps $A \rightrightarrows A \oplus M$ are universally
connected.
\end{proof}
The Galois group is not invariant under arbitrary square-zero extensions.
Let $A = \mathbb{C}[x^{\pm 1}]$ where $|x| = 0$ be the free
$\e{\infty}$-algebra under $\mathbb{C}$ on an invertible degree zero generator (so that $A$ is discrete).
Consider the $\mathbb{C}$-derivation $A \to A$ sending a Laurent polynomial $f(x) $ to its
derivative.
Then, when we form the pull-back
\[ \xymatrix{
A' \ar[d] \ar[r] & A \ar[d]^0 \\
A \ar[r]^{f \mapsto (f, f')} & A \oplus A
},\]
the pull-back is given by an $\e{\infty}$-algebra $A'$ with $\pi_0 A' \simeq
\mathbb{C}, \pi_{-1} A' \simeq \mathbb{C}$, and $\pi_i A' = 0$ otherwise. The
Galois theory of this $\e{\infty}$-ring is algebraic
because this $\e{\infty}$-ring is necessarily the free $\e{\infty}$-ring on a
degree $-1$ generator, or equivalently the trivial square-zero
extension $\mathbb{C} \oplus \Omega \mathbb{C}$. So its Galois group is
trivial, by \Cref{trivsqzero}.
However, the map $\mathbb{C} \oplus \Omega \mathbb{C} \to
\mathbb{C}[x^{\pm 1}]$ does not induce an isomorphism on Galois groups: that
of the former is trivial, while that of the latter is $\widehat{\mathbb{Z}}$.
\subsection{Stronger invariance results}
We will now prove the main invariance results of the present section.
\begin{theorem}
\label{invresult}
Let $A$ be a regular local ring with residue field $k$ and maximal ideal
$\mathfrak{m} \subset A$. Let $R$ be an
$\e{\infty}$-ring under $A$ such that $\mathfrak{m}$ is nilpotent in $\pi_0 R$.
Then the natural map
\[ R \to R \otimes_A k, \]
induces an isomorphism on fundamental groups.
\end{theorem}
\begin{proof}
We start by showing that $\pi_1(\mathrm{Mod}(R \otimes_A k)) \to \pi_1(\mathrm{Mod}(R))$ is always a
surjection; in other words, we must show that for any $\e{\infty}$-algebra $R'$
under $R$, the natural map
\begin{equation} \mathrm{Idem}(R') \to \mathrm{Idem}( R' \otimes_R (R \otimes_A k))
\simeq \mathrm{Idem}(R' \otimes_A k) \label{idema}\end{equation}
is an isomorphism.
Since $k$ is a perfect $A$-module, it follows that $R \otimes_A k$ is a perfect
$R$-module. Moreover, $R \otimes_A k$ is faithful as an $R$-module because
tensoring over $A$ with $k$ is faithful on the subcategory of $\mathrm{Mod}(A)$
consisting of $A$-modules whose homotopy groups are $\mathfrak{m}$-power
torsion. It follows that $R \to R \otimes_A k$ is descendable in view of
\Cref{cptdescent}.
Therefore, the map \eqref{idema} is an injection. Since the map
\[ k \otimes_A k \to k, \]
is descendable, as $k \otimes_A k$ is connective with bounded homotopy groups
and $\pi_0$ given by $k$, it follows from \Cref{invprop} that (by tensoring
this with $R$) that
$\pi_1(\mathrm{Mod}(R \otimes_A k)) \to \pi_1(\mathrm{Mod}(R))$ is a surjection.
Consider the cobar construction
\begin{equation} \label{RAcb} R \to R \otimes_A k \rightrightarrows R \otimes_A k \otimes_A k
\triplearrows \dots, \end{equation}
where all $\e{\infty}$-rings in question have no nontrivial idempotents.
We will use this and descent theory to complete the proof.
Note that we can make
the two maps
$\pi_{\leq 1}( \mathrm{Mod}(R \otimes_A k \otimes_A k)) \rightrightarrows
\pi_{\leq 1}( \mathrm{Mod}(R \otimes_A k))$ into pointed maps by choosing a basepoint of
$\pi_{\leq 1}\mathrm{Mod}(R
\otimes_A k)$ and using the multiplication map $R \otimes_A (k \otimes_A k) \to
R \otimes_A k$.
We conclude that (by descent theory and \eqref{RAcb}) that $\pi_1(\mathrm{Mod}(R))$ is the coequalizer of the two maps
\[ \pi_1 ( \mathrm{Mod}({ R \otimes_A k \otimes_A k})) \rightrightarrows \pi_1( \mathrm{Mod}({R
\otimes_A k})), \]
choosing basepoints as above.
We claim here that the multiplication map
$R \otimes_A (k \otimes_A k) \to R \otimes_A k$
induces a \emph{surjection} on fundamental groups.
Given this, we can construct a diagram
\[ \pi_1( \mathrm{Mod}(R \otimes_A k)) \twoheadrightarrow \pi_1( \mathrm{Mod}( R \otimes_A k
\otimes_A k)) \rightrightarrows \pi_1( \mathrm{Mod}(R \otimes_A k), \]
where the two composites are equal.
This completes the proof that $\pi_1 (\mathrm{Mod}(R)) \simeq \pi_1( \mathrm{Mod}(R \otimes_A
k))$, subject to the proof of surjectivity.
To prove surjectivity, we observe that $R \otimes_A k \otimes_A k \to R \otimes_A k$
induces a surjection on fundamental groups, in view of \Cref{surjart}, since $k
\otimes_A k \to k$ satisfies the conditions of that result; since $A$ is
regular, $k \otimes_A k$ is connective and has only finitely many nonzero
homotopy groups, so $k \otimes_A k \to k$ admits descent.
\end{proof}
It seems likely that \Cref{invresult} can be strengthened considerably,
although we have not succeeded in doing so.
For example, one would like to believe that if $R$ is a discrete commutative
ring and $I \subset R$ is an ideal of square zero, then given an
$\e{\infty}$-$R$-algebra $R'$, the map $R' \to R' \otimes_R R/I$ would induce
an isomorphism on fundamental groups. We do \emph{not} know whether this is
true in general. By \Cref{sqzerosurj}, it does induce a surjection at least.
The worry is that one does not have good control on the homotopy groups of a
relative tensor product of $\e{\infty}$-ring spectra; there is a spectral
sequence, but the filtration is in the opposite direction than what one wants.
However, in the case when the $\e{\infty}$-rings satisfy mild connectivity
hypotheses, one can prove the following much stronger result.
\begin{theorem} \label{slightlyconn}
Suppose $R$ is a connective $\e{\infty}$-ring with finitely many homotopy
groups and $I \subset \pi_0 R$ a nilpotent ideal. Let $R'$ be an $\e{\infty}$-$R$-algebra which is $(-n)$-connective for $n
\gg 0$. Then the map $R' \to R' \otimes_R \pi_0(R)/I$ induces an isomorphism on
fundamental groups.
\end{theorem}
For example, one could take $I = 0$, and the statement is already nontrivial.
We need first two lemmas:
\begin{lemma}
\label{adamssurj}
Let $A$ be a connective $\e{\infty}$-ring and let $A'$ be an
$\e{\infty}$-$A$-algebra which is $(-n)$-connective for $n \gg 0$. Then the
natural map
\begin{equation} \label{idemaa} \mathrm{Idem}(A') \to \mathrm{Idem}(A' \otimes_A \pi_0 A)
\end{equation}
is an isomorphism. In particular, it follows that $\pi_1 \mathrm{Mod}({A' \otimes_A
\pi_0 A }) \to \pi_1 \mathrm{Mod}({A'})$ is a surjection.
\end{lemma}
\begin{proof}
In fact, by a connectivity argument (taking an inverse limit over Postnikov
systems), the Adams spectral sequence based on the map $A \to \pi_0 A$ converges
for any $A$-module which is $(-n)$-connective for $n \gg 0$.
In other words, we have that
\[ A' = \mathrm{Tot}\left( A' \otimes_A \pi_0 A \rightrightarrows A' \otimes_A
\pi_0 A \otimes_A \pi_0 A \triplearrows \dots \right) ,\]
so that, since $\mathrm{Idem}$ commutes with limits, we find that $\mathrm{Idem}(A')$ is the
equalizer of the two maps $\mathrm{Idem}(A' \otimes_A \pi_0 A) \rightrightarrows \mathrm{Idem}(
A' \otimes_A \pi_0 A \otimes_A \pi_0 A)$. In particular,
\eqref{idemaa} is always injective. Moreover, by the same reasoning,
the multiplication map $\pi_0 A \otimes_A \pi_0 A \to \pi_0 A$ (which is also a map
from a connective $\e{\infty}$-ring to its zeroth Postnikov section) induces an
injection
\[ \mathrm{Idem}(A' \otimes_A \pi_0 A \otimes_A \pi_0 A ) \hookrightarrow \mathrm{Idem}( A' \otimes_A
\pi_0 A), \]
which equalizes the two maps
$\mathrm{Idem}(A' \otimes_A \pi_0 A) \rightrightarrows \mathrm{Idem}(
A' \otimes_A \pi_0 A \otimes_A \pi_0 A)$. It follows that the two maps were
equal to begin with, which proves that \eqref{idemaa} is an isomorphism.
\end{proof}
\begin{lemma} \label{idemnilp}
Let $A$ be a discrete $\e{\infty}$-ring and $J \subset A$ a square-zero ideal.
Then, given any $\e{\infty}$-$A$-algebra $A'$, the natural map $A' \to A'
\otimes_A A/J$ induces an isomorphism on idempotents.
\end{lemma}
\begin{proof}
This is a consequence of \Cref{sqzerosurj}.
\end{proof}
\begin{proof}[Proof of \Cref{slightlyconn}]
Let $R_0$ be the $\e{\infty}$-$R$-algebra given by $\pi_0(R)$ and consider
$R_0/I$ as well. Then we have maps $R \to R_0 \to R_0/I$ and we want to show
that, after base-changing to $R'$, the Galois groups are invariant.
We will do this in a couple of stages following the
proof of \Cref{invresult}.
First, suppose $I = 0$.
Using descent along $R \to R_0$, one concludes that
$\pi_1(\mathrm{Mod}({R'}))$ is the coequalizer of the two maps $\pi_1(\mathrm{Mod}({ R'
\otimes_R R_0
\otimes_R R_0})) \rightrightarrows \pi_1(\mathrm{Mod}({ R' \otimes_R R_0}))$.
We wish to claim that the two maps are equal.
Now the multiplication map
$R_0 \otimes_R R_0 \to R_0$ satisfies the
conditions of \Cref{adamssurj}, so one
concludes that the map $\pi_1( \mathrm{Mod}({R' \otimes_R R_0})) \to \pi_1( \mathrm{Mod}({R'
\otimes_R R_0 \otimes_R R_0}))
$ is a surjection, which coequalizes the
two maps considered above.
Therefore, the two maps are equal.
Next, we need to allow $I \neq 0$. By composition $R \to \tau_{\leq 0} R \to
R_0/I$, we may assume that $R$ itself is discrete. We may also assume that $I$
is square-zero. In this case, the map $R \to
R_0/I$ satisfies descent and is universally connected by \Cref{idemnilp}.
Therefore, we can apply the same argument as above, to write $\pi_1( \mathrm{Mod}({R'}))$
as the coequalizer of the two maps $\pi_1( \mathrm{Mod}({R' \otimes_{R_0} R_0/I
\otimes_{R_0} R_0/I })) \rightrightarrows \pi_1( \mathrm{Mod}({R' \otimes_{R_0} R_0/I}))$.
Moreover, these two maps are the same using
the surjection $\pi_1( \mathrm{Mod}({R' \otimes_{R_0} R_0/I} ) )\twoheadrightarrow
\pi_1( \mathrm{Mod}({R' \otimes_{R_0} R_0/I
\otimes_{R_0} R_0/I }))$ given to us by \Cref{adamssurj}
as above.
\end{proof}
\subsection{Coconnective rational $\e{\infty}$-algebras}
Let $k$ be a field of characteristic zero, and let $A$ be an
$\e{\infty}$-$k$-algebra such that:
\begin{enumerate}
\item $\pi_i A = 0$ for $i > 0$.
\item The map $k \to \pi_0 A$ is an isomorphism.
\end{enumerate}
Following \cite{DAGVIII}, we will call such $\e{\infty}$-$k$-algebras
\textbf{coconnective;} these are the $\e{\infty}$-rings which enter, for
instance, in rational homotopy theory. In the following, we will prove:
\begin{theorem} \label{coconnectivecov}
If $A$ is a coconnective $\e{\infty}$-$k$-algebra, then every finite cover of
$A$ is \'etale. In particular,
\[ \pi_{ 1} \mathrm{Mod}(A) \simeq \mathrm{Gal}(\overline{k}/k). \]
\end{theorem}
\begin{proof}
We will prove \Cref{coconnectivecov}
using tools from \cite{DAGVIII}.
Namely, it is a consequence of \cite[Proposition 4.3.13]{DAGVIII} that every
coconnective $\e{\infty}$-$k$-algebra $A$ can be obtained
as a totalization of a cosimplicial $\e{\infty}$-$k$-algebra $A^\bullet$
where $A^i$, for each $i \geq 0$, is in the form $k \oplus V[-1]$ where $V$ is
a vector space over $k$, and this is considered as a trivial ``square zero'' extension.
In rational homotopy theory, this assertion is dual to the statement that a
connected space can be built as a geometric realization of copies of
wedges of $S^1$.
Now we know from \Cref{trivsqzero} that the Galois groupoid is invariant under
trivial square-zero extensions,
so it follows that $\pi_{ 1} \mathrm{Mod}(A^i) \simeq
\mathrm{Gal}(\overline{k}/k)$, with the finite covers arising only from
the \'etale extensions (or equivalently, finite \'etale extensions of $k$
itself).
It follows easily from this that the finite covers in the $\infty$-category
$\mathrm{Tot} \mod( A^\bullet)$ are in natural equivalence with the finite
\'etale extensions of $k$, and
this completes the proof, since the $\infty$-category of perfect $A$-modules
embeds fully faithfully into this totalization.
\end{proof}
Note that the strategy of this proof is to give an \emph{upper bound} for the
Galois theory of the $\e{\infty}$-ring $A$ by writing it as an inverse limit of
square-zero $\e{\infty}$-rings. One might, conversely, hope to use Galois
groups to prove that $\e{\infty}$-rings \emph{cannot} be built as
inverse limits of certain simpler ones.
For example, in characteristic $p$, the example of cochain algebras shows that
the analog of \Cref{coconnectivecov} is false; in particular, one cannot write
a given coconnective $\e{\infty}$-ring in characteristic $p$ as a totalization
of square-zero extensions.
\section{Stable module $\infty$-categories}
Let $G$ be a finite group and let $k$ be a perfect field of characteristic $p>0$, where
$p$ divides the order of $G$.
The theory of $G$-representations in $k$-vector spaces is significantly more
complicated than it would be in characteristic zero because the group ring
$k[G]$ is not semisimple: for example, the group $G$ has $k$-valued cohomology.
If one wishes to focus primarily on, for example, the cohomological information
specific to characteristic $p$, then projective $k[G]$-modules are
essentially irrelevant
and, factoring them out, one has the theory of \emph{stable module
categories} reviewed earlier in \Cref{stmodcat}.
One obtains a compactly generated, symmetric monoidal stable $\infty$-category
$\mathrm{St}_G(k)$ obtained as the $\mathrm{Ind}$-completion of the Verdier quotient of $\mathrm{Fun}(BG,
\mathrm{Mod}^\omega(k))$ by the thick $\otimes$-ideal of perfect $k[G]$-module spectra.
Our goal in this section is to describe the Galois group of a stable module
$\infty$-category for a finite group.
Since any element in the stable module $\infty$-category can be viewed as an ordinary
linear
representation of $G$ (for compact objects, finite-dimensional representations)
modulo a certain equivalence relation, these results ultimately come down to
concrete statements about the tensor structure on linear representations of $G$
modulo projectives.
Our basic result (\Cref{galelem}) is that the Galois theory of a stable module
category for an \emph{elementary abelian} $p$-group is entirely algebraic. We
will use this, together with the Quillen stratification theory, to obtain a
formula for the Galois group of a general stable module $\infty$-category, and calculate
this in special cases.
\subsection{The case of $\mathbb{Z}/p$}
Our first goal is to determine the Galois group of $\mathrm{St}_V(k)$ when $V$ is
\emph{elementary abelian}, i.e. of the form $(\mathbb{Z}/p)^n$.
In this case, recall (\Cref{keller}) that $\mathrm{St}_V(k)$ is symmetric monoidally equivalent to the $\infty$-category of
modules over the Tate construction $k^{tV}$.
We will start by considering the case $V = \mathbb{Z}/p$.
\begin{proposition}
\label{galoistaterankone}
Let $k$ be a field of characteristic $p > 0$.
The Galois theory of the Tate construction $k^{t \mathbb{Z}/p}$ is algebraic.
\end{proposition}
\begin{proof}
Without loss of generality, we can assume $k$ perfect.
In the case $p = 2$, $k^{t \mathbb{Z}/2}$ has homotopy groups given by
\[ k^{t \mathbb{Z}/2} \simeq k[t^{\pm 1}], \]
where $|t| = -1$. A (simpler) version of \Cref{fieldreg} shows that any Galois extension
of $k^{t \mathbb{Z}/2}$ is \'etale, since $\pi_0$ satisfies a perfect K\"unneth
isomorphism for $k^{t \mathbb{Z}/2}$-modules and every module over $k^{t
\mathbb{Z}/2}$ is algebraically flat.
It follows that if $k^{t \mathbb{Z}/2} \to R$ is $G$-Galois, for $G$ a finite
group, then $\pi_0 R$ is a finite $G$-Galois extension of $k$.
The case of an odd prime is slightly more subtle.
In this case, we have
\[ k^{t \mathbb{Z}/p} \simeq k[t^{\pm 1}] \otimes_k E(u), \quad |t| = - 2, |u| =
-1, \]
so that we get a tensor product of a Laurent series ring and an exterior
algebra.
Since the homotopy ring is no longer regular, we will have to show that any $G$-Galois
extension of $k^{t \mathbb{Z}/p}$ is flat at the level of homotopy groups.
We can do this by comparing with the Tate construction $W(k)^{t \mathbb{Z}/p}$,
where $W(k)$ is the ring of Witt vectors on $k$ and $\mathbb{Z}/p$ acts
trivially on $W(k)$. The $\e{\infty}$-ring $W(k)^{t \mathbb{Z}/p}$ has homotopy
groups given by
\[ \pi_* W(k)^{t \mathbb{Z}/p} \simeq k[t^{\pm 1}], \quad |t| = 2, \]
and the $\e{\infty}$-ring that we are interested in is given by
\[ k^{t \mathbb{Z}/p} \simeq W(k)^{t \mathbb{Z}/p} \otimes_{W(k)} k. \]
Now \Cref{fieldreg} tells us that the Galois theory of $W(k)^{t \mathbb{Z}/p}$
is algebraic, and the invariance result \Cref{invresult} enables us to conclude
the same for $k^{t \mathbb{Z}/p}$.
\end{proof}
\subsection{Tate spectra for elementary abelian subgroups}
Let $k$ be a field of characteristic $p$. We know that $k^{t \mathbb{Z}/p}$ has
homotopy groups given by a tensor product of an exterior and Laurent
series algebra
on generators
in degrees $-1, -2$, respectively. For an elementary abelian $p$-group of
higher rank, the picture is somewhat more complicated: the homotopy ring
behaves irregularly (with entirely square-zero material in positive
homotopy groups), but the Tate construction is still built up from a diagram
of $\e{\infty}$-rings whose homotopy rings come from tensor products of
polynomial (or Laurent series) rings and exterior algebras. This diagram
roughly lives over $\mathbb{P}_k^{n-1}$ where $n$ is the rank of the given
elementary abelian $p$-group, and the stable module $\infty$-category
$\mathrm{St}_{(\mathbb{Z}/p)^n}(k)$ can be described as quasi-coherent sheaves on a
derived version of projective space (\Cref{affinestmod}).
In this subsection, we will review this picture, which will be useful when we
describe the Galois groups in the next section.
We consider the case of $p > 2$, and leave the minor modifications for $p = 2$ to the
reader.
Fix an elementary abelian $p$-group $V = (\mathbb{Z}/p)^n$, and let $V_k = V
\otimes_{\mathbb{F}_p} k$. Consider first the
homotopy fixed points $k^{hV}$, whose homotopy ring is given by
\[ \pi_*(k^{hV}) \simeq E( V_k^{\vee}) \otimes \mathrm{Sym}^*(V_k^{\vee}), \]
where the exterior copy of $V_k^{\vee}$ is concentrated in degree $-1$, and the
polynomial copy of $V_k^{\vee}$ is concentrated in degree $-2$. For each nonzero homogeneous
polynomial $f \in \mathrm{Sym}^*(V_k^{\vee})$, we can form the localization
$k^{hV}[f^{-1}]$, whose degree zero part \emph{modulo nilpotents} is given by
the localization
$\mathrm{Sym}^*(V_k^{\vee})_{(f)}$ (i.e., the degree zero part of the
localization $\mathrm{Sym}^*(V_k^{\vee})[f^{-1}]$). There is also a small nilpotent
part that comes from the evenly graded portion of the exterior algebra.
In particular, we find, using natural maps between localizations:
\begin{enumerate}
\item For every Zariski open \emph{affine} subset $U \subset \mathbb{P}(
V_k^{\vee})$, we obtain
a (canonically associated) $\e{\infty}$-ring $\mathcal{O}^{\mathrm{top}}(U)$ by localizing $k^{h V}$ at an
appropriate homogeneous form.
Precisely, $U$ is given as the complement to the zero locus of a homogeneous
form $f \in \mathrm{Sym}^*(V_k^{\vee})$, and we invert $f$ in $k^{hV}$: $\mathcal{O}^{\mathrm{top}}(U) =
k^{hV}[f^{-1}]$.
\item For every inclusion $U \subset U'$ of Zariski open affines, we obtain a map
of $\e{\infty}$-algebras (under $k^{hV}$) $\mathcal{O}^{\mathrm{top}}(U') \to \mathcal{O}^{\mathrm{top}}(U)$.
These maps are canonical; $\mathcal{O}^{\mathrm{top}}(U'), \mathcal{O}^{\mathrm{top}}(U)$ are localizations of
$k^{hV}$ and $\mathcal{O}^{\mathrm{top}}(U)$ has more elements inverted.
\item For each $U \subset \mathbb{P}(V_k^{\vee})$, the $\e{\infty}$-ring
$\mathcal{O}^{\mathrm{top}}(U)$ has a unit in degree two. The
ring
$\pi_0(\mathcal{O}^{\mathrm{top}}(U))$ is canonically an algebra over the (algebraic) ring of
functions $\mathcal{O}_{\mathrm{alg}}(U)$ on $U \subset
\mathbb{P}(V_k^{\vee})$, and is a tensor product of
$\mathcal{O}_{\mathrm{alg}}(U)$ with the even components of an exterior algebra over $k$.
\item We have
natural isomorphisms of sheaves of graded $\mathcal{O}_{\mathrm{alg}}$-modules
\[
\pi_*( \mathcal{O}^{\mathrm{top}}) \simeq E(V_k^{\vee}) \otimes_{\mathcal{O}_{\mathrm{alg}}} \bigoplus_{r \in \mathbb{Z}}
\mathcal{O}(r)
, \]
where $\mathcal{O}(1)$ is the usual hyperplane bundle on
$\mathbb{P}(V_k^{\vee})$ and $\mathcal{O}(r) \simeq \mathcal{O}(1)^{\otimes
r}$ is concentrated in degree $-2r$. The generators of the exterior algebra
$E(V_k^{\vee})$ are in degree $-1$.
\end{enumerate}
It follows that the homotopy groups $\pi_*(\mathcal{O}^{\mathrm{top}}(U))$ for $ U \subset
\mathbb{P}(V_k^{\vee})$ fit together into \emph{quasi-coherent sheaves} on the
site of affine Zariski opens $U \subset \mathbb{P}(V_k^{\vee})$ and
inclusions between them. In
particular, we can view the association $U \mapsto \mathcal{O}^{\mathrm{top}}(U)$ as defining
a \emph{sheaf} of $\e{\infty}$-ring spectra (under $k$, or even under $k^{hV}$)
over the Zariski site of $\mathbb{P}(V_k^{\vee})$, whose sections over an affine
open $U \subset \mathbb{P}(V_k^{\vee})$ are given by $\mathcal{O}^{\mathrm{top}}(U)$.
We will now describe our basic comparison result.
Since $\mathcal{O}^{\mathrm{top}}$ is a sheaf of $\e{\infty}$-algebras under $k^{hV}$, we obtain a
symmetric monoidal, colimit-preserving
functor
\[ \mathrm{Mod}( k^{hV}) \to \mathrm{QCoh}( \mathcal{O}^{\mathrm{top}}), \]
into the $\infty$-category $\mathrm{QCoh}(\mathcal{O}^{\mathrm{top}})$ of \emph{quasi-coherent
$\mathcal{O}^{\mathrm{top}}$-modules}, defined as the homotopy limit $$\mathrm{QCoh}( \mathcal{O}^{\mathrm{top}}) = \varprojlim_{U \subset
\mathbb{P}(V_k^{\vee})} \mathrm{Mod}( \mathcal{O}^{\mathrm{top}}(U)),$$
where the homotopy limit is taken over all open affine subsets of
$\mathbb{P}(V_k^{\vee})$.
Restricting to $\mathrm{Mod}^\omega(k^{hV}) \simeq \mathrm{Fun}(BV, \mathrm{Mod}^\omega(k))$, we
obtain a symmetric monoidal exact functor
\[ \mathrm{Fun}(BV, \mathrm{Mod}^\omega(k)) \to \mathrm{QCoh}( \mathcal{O}^{\mathrm{top}}).\]
We observe that the standard representation of $V$, as an object of the former,
is sent to zero in $\mathrm{QCoh}( \mathcal{O}^{\mathrm{top}})$. In fact, the standard representation of $V$
corresponds to a $k^{hV}$-module with only one nonvanishing homotopy group, and
it therefore vanishes under the types of \emph{periodic} localization that one takes
in order to form $\mathcal{O}^{\mathrm{top}}( U)$ for $U \subset \mathbb{P}(V_k^{\vee})$ an open
affine.
Using the universal property of the stable module $\infty$-category, we obtain
a factorization
\[ \mathrm{Fun}(BV, \mathrm{Mod}^\omega(k)) \to \mathrm{St}_V(k) \to \mathrm{QCoh}(\mathcal{O}^{\mathrm{top}}), \]
where the functor $\mathrm{St}_V(k) \to \mathrm{QCoh}(\mathcal{O}^{\mathrm{top}})$ is symmetric monoidal and
colimit-preserving.
\begin{theorem}
\label{affinestmod}
The functor $\mathrm{Mod}(k^{tV}) \simeq \mathrm{St}_V(k) \to \mathrm{QCoh}(\mathcal{O}^{\mathrm{top}})$ is an equivalence of symmetric
monoidal $\infty$-categories.
\end{theorem}
\begin{proof}
We start by observing that, by construction of the Verdier quotient
(\Cref{vq}), the stable module $\infty$-category $\mathrm{St}_V(k)$
is obtained as a \emph{localization} of $\mathrm{Mod}(k^{hV}) \simeq \mathrm{Ind}(
\mathrm{Fun}(BV, \mathrm{Mod}^\omega(k)))$, and in particular $k^{tV}$ is a localization
of the $\e{\infty}$-ring $k^{hV}$.
By construction, $k^{tV}$ is the
localization of $k^{hV}$ at the map of $k^{hV}$-modules $M \to 0$, where $M$ is
the $k^{hV}$-module corresponding to the standard representation of $V$.
So, in particular, the localization functor
\[ \mathrm{Mod}(k^{hV}) \to \mathrm{Mod}(k^{tV}), \]
given by tensoring up, has a fully faithful right adjoint which embeds
$\mathrm{Mod}(k^{tV})$ as the subcategory of all $k^{hV}$-modules $N$ such that
$\hom_{\mathrm{Mod}(k^{hV})}(M, N)$ is contractible.
If we write $e_1, \dots, e_n \in \pi_{-2}( k^{hV})$ for polynomial generators
of $k^{hV}$, then $k^{hV}/(e_1, \dots, e_n) \in \mathrm{Mod}^\omega(k^{hV})$ generates the same
thick subcategory as $M$, as we observed in the discussion immediately
preceding \Cref{quasi}.
So, the $k^{tV}$-modules are precisely the $k^{hV}$-modules $N$ such that
\[ N/(e_1, \dots, e_n) N \simeq 0 \in \mathrm{Mod}(k^{hV}), \]
using self-duality of
$k^{hV}/(e_1, \dots, e_n)$.
Now, we have a morphism of $\e{\infty}$-rings
\begin{equation} \label{projspace} k^{hV} \to \Gamma( \mathbb{P}(V_k^{\vee}), \mathcal{O}^{\mathrm{top}}), \end{equation}
and our first task is to show that this morphism induces an equivalence
$k^{tV} \to \Gamma( \mathbb{P}(V_k^{\vee}), \mathcal{O}^{\mathrm{top}})$. Observe first that, after
inverting any of $e_1, \dots, e_n \in \pi_{-2}(k^{hV})$,
\eqref{projspace} becomes an equivalence since we already know what
$\mathcal{O}^{\mathrm{top}}$ looks like on the basic open affines; we also know that taking global
sections over $\mathbb{P}(V_k^{\vee})$ is a finite homotopy limit and thus
commutes with arbitrary homotopy colimits.
However, we also know that
\( k^{hV}/(e_1, \dots, e_n) \) maps to the zero $\mathcal{O}^{\mathrm{top}}$-module since, on
every basic open affine of $\mathbb{P}(V_k^{\vee})$, one of the $\left\{e_i\right\}$ is always invertible.
Thus we get a map $k^{tV} \to \Gamma( \mathbb{P}(V_k^{\vee}), \mathcal{O}^{\mathrm{top}})$ of
$k^{hV}$-modules with the
dual properties:
\begin{enumerate}
\item Both modules smash to zero with $k^{hV}/(e_1, \dots, e_n)$.
\item The map induces an equivalence after inverting each $e_i$, $1 \leq i \leq
n$.
\end{enumerate}
By a formal argument,
it now follows that $k^{tV} \to\Gamma( \mathbb{P}(V_k^{\vee}), \mathcal{O}^{\mathrm{top}})$ is an
equivalence to begin with. In fact, we show that, for each $i$, the map
\begin{equation} \label{indstepp}k^{tV}/(e_1, \dots, e_i) \to\Gamma( \mathbb{P}(V_k^{\vee}), \mathcal{O}^{\mathrm{top}}) /(e_1,
\dots, e_i)\end{equation}
is an equivalence by \emph{descending} induction on $i$. For $i = n$, both
sides are contractible. If we are given that
\eqref{indstepp} is an equivalence, then the map
$k^{tV}/(e_1, \dots, e_{i-1}) \to\Gamma( \mathbb{P}(V_k^{\vee}), \mathcal{O}^{\mathrm{top}}) /(e_1,
\dots, e_{i-1})$
has the property that it becomes an equivalence after either inverting $e_i$
(by the second property above) or by smashing with $k^{hV}/(e_i)$ (by the
inductive hypothesis); it thus has to be an equivalence in turn. This completes
the inductive step and the proof that $k^{tV} \simeq \Gamma(
\mathbb{P}(V_k^{\vee}), \mathcal{O}^{\mathrm{top}})$.
All in all, we have shown that the functor
\[ \mathrm{Mod}(k^{tV}) \simeq \mathrm{St}_V(k) \to \mathrm{QCoh}(\mathcal{O}^{\mathrm{top}}) \]
is \emph{fully faithful.}
To complete the proof of
\Cref{affinestmod}, we need to show that the global sections functor is
conservative on $\mathrm{QCoh} (\mathcal{O}^{\mathrm{top}})$. However, if $\mathcal{F} \in \mathrm{QCoh}( \mathcal{O}^{\mathrm{top}})$
has the property that $\Gamma(\mathbb{P}(V_k^{\vee}), \mathcal{F})$ is
contractible, then the same holds for $\mathcal{F}[e_i^{-1}]$. By analyzing the
descent spectral sequence, it follows that the global sections of
$\mathcal{F}[e_i^{-1}]$ are precisely the sections of $\mathcal{F}$ over the
$i$th
basic open affine chart of $\mathbb{P}(V_k^{\vee})$.
Thus, if $\Gamma( \mathbb{P}(V_k^{\vee}), \mathcal{F})$ is contractible, then
$\mathcal{F}$ has contractible sections over each of the basic open affines,
and is thus contractible to begin with. (This argument is essentially the
ampleness of $\mathcal{O}(1)$.)
\end{proof}
\subsection{$G$-Galois extensions for topological groups}
Our next goal is to calculate the Galois group for $k^{t V}$ for any elementary
abelian $p$-group $V$. In the case of rank one, we had a trick for
approaching the Galois group. Although $k^{tV}$ was not even
periodic, there was a good integral model (namely,
$W(k)^{t V}$) which was related to $k^{tV}$ by reducing mod $p$, so that we
could
use an invariance property to reduce to the (much easier) $\e{\infty}$-ring
$W(k)^{t V}$.
When the rank of $V$ is greater than one, both these tricks break down. There
is no longer a comparable integral model of an $\e{\infty}$-ring such as
$k^{h \mathbb{Z}/p} \otimes k^{t \mathbb{Z}/p}$, as far as we know. Our strategy is based instead on a comparison with the Tate spectra for \emph{tori},
which are much more accessible. To interpolate between the Tate spectra for
tori and the Tate spectra for elementary abelian $p$-groups, we will need a bit
of the theory of Galois extensions for topological groups, which was considered
in \cite{rognes}. We will describe the associated theory of descent in this
section. We refer to \cite{toruspic} for further applications of these ideas
to the Picard group and the classification of localizing subcategories of the
stable module category (recovering older results), as well as a discussion of
how this formulation of $G$-Galois extensions relates to that of Rognes
\cite{rognes} (who uses a definition similar to \Cref{defgalr}).
\begin{definition}
\label{topgalois}
Fix a topological group $G$ which has the homotopy type of a finite CW complex
(e.g., a compact Lie group).
Let $R$ be an $\e{\infty}$-ring and let $R'$ be an $\e{\infty}$-$R$-algebra
with an action of $G$ (in the $\infty$-category of
$\e{\infty}$-$R$-algebras).
We will say that $R'$ is a faithful
\textbf{$G$-Galois extension} of $R$ if there exists a descendable $\e{\infty}$-$R$-algebra $R''$
such that we have an equivalence
of $\e{\infty}$-$R''$-algebras
\[ R' \otimes_R R'' \simeq C^*(G; R''), \]
which is compatible with the $G$-action.
\end{definition}
Note that the cochain $\e{\infty}$-ring $C^*(G; R'')$ is the ``coinduced'' $G$-action on an $R''$-module.
It follows in particular that the natural map $R \to R'^{h G}$ is an
equivalence, and is so universally; for any $\widetilde{R} \in \mathrm{CAlg}_{R/}$, the
natural map
$\widetilde{R} \to (R' \otimes_{R} \widetilde{R})^{h G}$ is an equivalence.
Moreover, $R'$ is perfect as an $R$-module, since this can be checked locally
(after base-change to $R''$) and $G$ has the homotopy type of a finite CW
complex. It follows from general properties of descendable morphisms that
faithful $G$-Galois extensions are preserved under base-change.
We will need the following version of classical Galois
descent, which has been independently considered in various forms by
several authors, for instance
\cite{hess, GL, meier, banerjee}.
\begin{theorem}
\label{galdescthm}
Let $G$ be a topological group of the homotopy type of a finite CW complex, and
let $R \to R'$ be a faithful $G$-Galois extension of $\e{\infty}$-rings.
The natural functor
\begin{equation} \label{descf} \mathrm{Mod}(R) \to \mathrm{Mod}(R')^{h G}, \end{equation}
is an equivalence of $\infty$-categories.
\end{theorem}
The ``natural functor'' comes from the expression $R \simeq R'^{hG}$; the
$G$-action on $R'$ induces one on the symmetric monoidal $\infty$-category
$\mathrm{Mod}(R')$. In particular, we get a \emph{fully faithful} embedding $\mathrm{Mod}^\omega(R) \to
\mathrm{Mod}(R')^{hG}$ for free.
\begin{proof}
Suppose first that $R' \simeq C^*(G; R)$ with the $G$-action coming from
the translation action of $G$ on itself. Then, we have a fully faithful,
colimit-preserving embedding
\[ \mathrm{Mod}( R') \subset \mathrm{Loc}_G( \mathrm{Mod}(R)), \]
as we saw in \Cref{subseclocsys}. The $G$-action here on $\mathrm{Loc}_G(\mathrm{Mod}(R))$ comes
from the translation action again. Taking homotopy fixed points, we get
\begin{equation} \label{locsys1} \mathrm{Mod}(R')^{hG} \subset \mathrm{Loc}_{G_{hG}}( \mathrm{Mod}(R))
\simeq \mathrm{Loc}_{\ast}( \mathrm{Mod}(R)) \simeq \mathrm{Mod}(R), \end{equation}
because the construction $X \mapsto \mathrm{Loc}_X( \mathrm{Mod}(R))$ sends homotopy colimits in
$X$ to homotopy limits of stable $\infty$-categories. The natural functor
$\mathrm{Mod}(R) \to \mathrm{Mod}(R')^{hG}$ now composes all the way over in
\eqref{locsys1} to the identity, so that it must have been an equivalence to
begin with since all the maps in \eqref{locsys1} are fully faithful.
Now suppose $R \to R'$ is a general $G$-Galois extension, so that there
exists a descendable $\e{\infty}$-$R$-algebra $T$ such that $R \to R'$
becomes a trivial Galois extension after base-change along $R \to T$.
The functor \eqref{descf} is a functor of $R$-linear $\infty$-categories so,
to show that it is an equivalence, it suffices to show that \eqref{descf}
induces an equivalence after applying the construction $\otimes_{\mathrm{Mod}(R)}
\mathrm{Mod}(T)$: that is, after considering $T$-module objects in each
$\infty$-category (cf. \Cref{2descformal}). In other words, to show that \eqref{descf} is an
equivalence, it suffices to tensor up and show that
\[ \mathrm{Mod}(T) \to \left( \mathrm{Mod}(R')\right)^{hG} \otimes_{\mathrm{Mod}(R)} \mathrm{Mod}(T)
\simeq \left( \mathrm{Mod}(R') \otimes_{\mathrm{Mod}(R)} \mathrm{Mod}(T)\right)^{hG} \simeq \mathrm{Mod}( C^*(G;
T))^{hG}
,\]
is an equivalence of $\infty$-categories, which we just proved.
\end{proof}
It follows in particular that whenever we have a $G$-Galois extension in the above
sense, for $G$ a \emph{topological} group then we can relate the fundamental
groups of $R $ and $R'$.
In fact, we have, in view of \Cref{galdescthm},
\[ \clg^{\mathrm{cov}}(R) \simeq \clg^{\mathrm{cov}}(R')^{hG}. \]
Using the Galois correspondence, it follows that there is a $G$-action on the
object $\pi_{\leq 1}\mathrm{Mod}(R') \in \mathrm{Pro}( \mathrm{Gpd}_{\mathrm{fin}})$, and the homotopy \emph{quotient}
in $\mathrm{Pro}( \mathrm{Gpd}_{\mathrm{fin}})$ by this $G$-action
is precisely the fundamental groupoid of $\mathrm{Mod}(R)$, i.e.,
\[ \pi_{\leq 1} \mathrm{Mod}(R) \simeq \left( \pi_{\leq 1 } \mathrm{Mod}(R')\right)_{hG} \in
\mathrm{Pro}( \mathrm{Gpd}_{\mathrm{fin}}). \]
We now describe homotopy orbits in $\mathrm{Pro}( \mathrm{Gpd}_{\mathrm{fin}})$ in the case that will be of
interest.
Let $X \in \mathrm{Pro}( \mathrm{Gpd}_{\mathrm{fin}})$ be a \emph{connected} profinite groupoid and consider an
action of a \emph{connected} topological group $G$ on
$X$.
\begin{proposition}
To give an action of $G$ on $X \in \mathrm{Pro}( \mathrm{Gpd}_{\mathrm{fin}})^{\geq 0}$ is equivalent to giving a
homomorphism of groups $\pi_1(G) \to \pi_1(X)$ whose image is contained in the
center of $\pi_1(X)$. In other words, the 2-category $\mathrm{Fun}(BG,
\mathrm{Pro}(\mathrm{Gpd}_{\mathrm{fin}})^{\geq 0})$ can be described as follows:
\begin{enumerate}
\item Objects are profinite groups $F$ together with maps $\phi\colon \pi_1(G) \to F$
whose image is contained in the center of $F$.
\item 1-morphisms between pairs $(F, \phi)$ and $(F', \phi')$ are continuous
homomorphisms $\psi\colon F \to F'$ such that the diagram
\[ \xymatrix{
\pi_1(G) \ar[d]^{\phi} \ar[rd]^{ \phi'} \\
F \ar[r]^{\psi} & F'
},\]
commutes.
\item 2-morphisms are given by conjugacies between homomorphisms.
\end{enumerate}
In particular, the forgetful functor $\mathrm{Fun}( BG, \mathrm{Pro}( \mathrm{Gpd}_{\mathrm{fin}})^{\geq 0}) \to \mathrm{Pro}(
\mathrm{Gpd}_{\mathrm{fin}})^{\geq 0}$ induces fully faithful maps on the hom-spaces.
\end{proposition}
\begin{proof}
In order to give an action of $X \in \mathrm{Pro}( \mathrm{Gpd}_{\mathrm{fin}})^{\geq 0}$, we need to
construct a map of $\e{1}$-spaces $G \to \mathrm{Aut}_{\mathrm{Pro}( \mathrm{Gpd}_{\mathrm{fin}})^{\geq
0}}(X)$, where
$\mathrm{Aut}_{\mathrm{Pro}( \mathrm{Gpd}_{\mathrm{fin}})^{\geq
0}}(X)$ is the automorphism $\e{1}$-algebra of $X$. Since, however, $G$ is
connected, it is equivalent to specifying a map of $\e{1}$-algebras (or loop
spaces) into
$\tau_{\geq 1}\mathrm{Aut}_{\mathrm{Pro}( \mathrm{Gpd}_{\mathrm{fin}})^{\geq
0}}(X)$. However, we know from \Cref{mappingspaces} that
$\tau_{\geq 1}\mathrm{Aut}_{\mathrm{Pro}( \mathrm{Gpd}_{\mathrm{fin}})^{\geq
0}}(X)$ is precisely a $K(Z(\pi_1(X)), 1)$, so the space of $\e{1}$-maps as
above is simply the \emph{set} of homomorphisms $\pi_1(G) \to Z( \pi_1(X))$.
Finally, we need to understand the mapping spaces in $\mathrm{Fun}( BG, \mathrm{Pro}(
\mathrm{Gpd}_{\mathrm{fin}})^{\geq 0})$. Consider two connected profinite groupoids $X, Y$ with
$G$-actions. The space of maps $X \to Y$ in $\mathrm{Fun}(BG, \mathrm{Pro}( \mathrm{Gpd}_{\mathrm{fin}}))$ is
equivalent to the homotopy fixed points $\hom_{\mathrm{Pro}( \mathrm{Gpd}_{\mathrm{fin}})}( X, Y)^{hG}$,
where $\hom_{\mathrm{Pro}( \mathrm{Gpd}_{\mathrm{fin}})}(X, Y)$ is a groupoid as discussed earlier.
In
general, given any groupoid $\mathscr{G}$ with an action of $G$, the functor
$\mathscr{G}^{hG} \to \mathscr{G}$ is fully faithful.
The action of $G$ means that every element in $\pi_1(G)$ determines a natural
transformation from the identity to itself on $\mathscr{G}$, and the homotopy
fixed points pick out the full subcategory of $\mathscr{G}$ spanned by elements
on which that natural transformation is the identity (for any $\gamma \in
\pi_1(G)$).
In the case of $\hom_{\mathrm{Pro}( \mathrm{Gpd}_{\mathrm{fin}})}(X, Y)$, the objects are
continuous homomorphisms $\psi\colon \pi_1 X \to \pi_1 Y$, and the morphisms between
objects are conjugacies. For $\gamma \in \pi_1(G)$, we obtain elements
$\gamma_x \in \pi_1(X)$ and $\gamma_y \in \pi_1(Y)$ (in view of the $G$-action
on $X, Y$), and the action of $\gamma$ on $\hom_{\mathrm{Pro}(\mathrm{Gpd}_{\mathrm{fin}})}(X, Y)$ at the
homomorphism $\psi$ is given by the element $\psi(\gamma_x)
\psi(\gamma_y)^{-1}$, which determines a self-conjugacy from $\psi$ to itself.
To say that this self-conjugacy is the identity for any $\gamma$, i.e., that
the map is $G$-equivariant (which here is a \emph{condition} instead of extra data), is precisely
the second description of the 1-morphisms.
\end{proof}
\begin{remark}
The above argument would have worked in any $(2, 1)$-category where we could
write down the $\pi_1$ of the automorphism $\e{1}$-algebra easily.
\end{remark}
In particular, if $G$ acts trivially on $Y \in \mathrm{Pro}( \mathrm{Gpd}_{\mathrm{fin}})^{\geq 0}$,
then to give a map $X \to Y$ is equivalent to giving a map in $\mathrm{Pro}( \mathrm{Gpd}_{\mathrm{fin}})$
which annihilates the image of $\pi_1(G) \to \pi_1(X)$.
It follows that the \emph{homotopy quotients} $X_{hG}$ in $\mathrm{Pro}( \mathrm{Gpd}_{\mathrm{fin}})$ can be
described by
taking the quotient of $\pi_1 X$ by the closure of the image of $\pi_1(G)$:
this is the universal profinite groupoid with a trivial $G$-action to which
$X$ maps.
Putting all of this together, we find:
\begin{corollary}
\label{basicexact}
Let $G$ be a connected topological group of the homotopy type of a finite CW
complex, and let $R \to R'$ be a faithful $G$-Galois extension. Then we have an exact sequence of profinite groups
\begin{equation} \label{topgalexact} \widehat{\pi_1 G} \to \pi_1 \mathrm{Mod}(R') \to \pi_1 \mathrm{Mod}(R) \to 1. \end{equation}
\end{corollary}
\begin{remark}
Throughout this section, we shall be somewhat cavalier about the
use of basepoints, since we will be working with connected profinite groupoids.
\end{remark}
\subsection{The general elementary abelian case}
Let $V$ be an elementary abelian $p$-group and let $k$ be a field of
characteristic $p$.
In this section, we will prove our main result that the Galois theory of
$k^{tV}$ is algebraic. In order to do this, we will use the presentation in
\Cref{affinestmod} of $\mathrm{Mod}(k^{tV})$ via quasi-coherent sheaves on a ``derived'' version of
$\mathbb{P}(V_k^{\vee})$.
Any $G$-Galois extension of $k^{tV}$ clearly gives a $G$-Galois extension of
$\mathcal{O}^{\mathrm{top}}(U)$ for any $U \subset \mathbb{P}(V_k^{\vee})$ by base-change. Conversely,
the affineness result \Cref{affinestmod} implies that to give a
$G$-Galois extension of $k^{tV}$ is equivalent to giving $G$-Galois extensions
of $\mathcal{O}^{\mathrm{top}}(U)$ for $U \subset \mathbb{P}(V_k^{\vee})$ affine together with the
requisite compatibilities. This would be doable if $\mathcal{O}^{\mathrm{top}}(U)$ was even
periodic with regular $\pi_0$, although the exterior generators present an
obstacle. Nonetheless, by a careful comparison with the analog for
\emph{tori}, we will prove:
\begin{theorem}
\label{galelem}
Let $V$ be an elementary abelian $p$-group.
If $k$ is a field of characteristic $p$, all finite
coverings of $k^{t V}$ are \'etale, so $\pi_1 ( \mathrm{Mod}(k^{tV})) \simeq
\mathrm{Gal}(k^{\mathrm{sep}}/k)$.
\end{theorem}
\begin{proof}
Since projective space is (geometrically) simply connected, it suffices to show that the Galois theory of
\[ k^{t \mathbb{Z}/p} \otimes_k k^{h (\mathbb{Z}/p)^{n}} \simeq k^{t
\mathbb{Z}/p} \otimes_k C^*(B (\mathbb{Z}/p)^n; k), \]
for $n > 0$, is algebraic, and thus given by the (algebraic) \'etale
fundamental group of the
corresponding affine open cell in $\mathbb{P}(V_k^{\vee})$.
These $\e{\infty}$-rings are the $\mathcal{O}^{\mathrm{top}}(U)$ for $U \subset
\mathbb{P}(V_k^{\vee})$ the basic open affines of projective space.
It will follow
that a faithful Galois extension of $k^{tV}$ is locally algebraically \'etale over
$\mathbb{P}(V_k^{\vee})$.
For this, we will use the fibration sequence
\[ S^1 \to B \mathbb{Z}/p \to B S^1, \]
induced by the inclusion $\mathbb{Z}/p \subset S^1$ with quotient $S^1$. This is a principal
$S^1$-bundle and we find in particular an $S^1$-action on $C^*(B \mathbb{Z}/p;
k)$ such that
\begin{equation} C^*(B S^1; k) \simeq C^*(B \mathbb{Z}/p; k)^{h S^1}
\end{equation}
In fact, the map $C^*(BS^1; k) \to C^*(B \mathbb{Z}/p; k)$ is a faithful $S^1$-Galois
extension (in the sense of \Cref{topgalois}): by the Eilenberg-Moore spectral sequence, and the fiber square
\[ \xymatrix{
B \mathbb{Z}/p \times S^1 \ar[d] \ar[r] & B \mathbb{Z}/p \ar[d] \\
B \mathbb{Z}/p \ar[r] & B S^1
},\]
expressing the earlier claim that $B \mathbb{Z}/p \to BS^1$ is an $S^1$-torsor,
it follows that
$$C^*(B \mathbb{Z}/p;k ) \otimes_{C^*(B S^1; k)} C^*(B(\mathbb{Z}/p);k )
\simeq C^*(S^1; k) \otimes_k C^*(B\mathbb{Z}/p; k),
$$
with the ``coinduced'' $S^1$-action on the right.
Moreover, $C^*(BS^1;k ) \to C^*(B\mathbb{Z}/p; k)$ is descendable: in fact, a look
at homotopy groups shows that the latter is a wedge of the former and its shift.
Let $\mathbb{T}^n \simeq (S^1)^n$ be the $n$-torus, which contains
$(\mathbb{Z}/p)^n$ as a subgroup.
Similarly, we find that there is a $\mathbb{T}^n$-action on
$C^*(B(\mathbb{Z}/p)^n; k)$ in the $\infty$-category of $C^*( B \mathbb{T}^n;
k)$-algebras which exhibits
$C^*(B(\mathbb{Z}/p)^n; k)$ as a faithful $\mathbb{T}^n$-Galois extension of
$C^*(B(\mathbb{Z}/p)^n; k)$.
We can now apply a bit of descent theory.
Fix any $C^*( B \mathbb{T}^n; k)$-algebra $R$, and
let $R' \simeq R \otimes_{C^*(B\mathbb{T}^n; k)} C^*(B (\mathbb{Z}/p)^n; k)$.
Since $R'$ is a faithful $\mathbb{T}^n$-Galois extension of $R$, we have a
(natural) exact
sequence
given by \Cref{basicexact}:
\begin{equation} \label{hugeexact} \widehat{\mathbb{Z}}^n \to \pi_1( \mathrm{Mod}( R'))
\to \pi_1 (\mathrm{Mod}(R)) \to 1. \end{equation}
Finally, we may attack the problem of determining the Galois theory of $k^{t
\mathbb{Z}/p} \otimes_k k^{h(\mathbb{Z}/p)^n}
$ where $n > 0$.
We have
\[ \pi_* C^*( B (\mathbb{Z}/p)^{n+1}; k) \simeq
k[e_0, e_1, \dots, e_n] \otimes E(\epsilon_0, \dots, \epsilon_n), \quad |e_i |
= -2, \ |\epsilon_i|
= -1.
\]
Our goal is to determine the Galois theory of the localization $k^{t
\mathbb{Z}/p} \otimes_k k^{h (\mathbb{Z}/p)^n} \simeq C^*(
B(\mathbb{Z}/p)^{n+1}; k)[e_0^{-1}]$.
Now, we also have
$$\pi_* C^*( B\mathbb{T}^{n+1}; k) \simeq k[e_0, \dots, e_n], \quad |e_i| =
-2,$$
and the map $C^*(B \mathbb{T}^{n+1}; k) \to C^*( B( \mathbb{Z}/p)^{n+1}; k)$
sends the $\left\{e_i\right\}$ to the $\left\{e_i\right\}$. This map is a
faithful $\mathbb{T}^{n+1} $-Galois extension.
As we did for $C^*(B (\mathbb{Z}/p)^{n+1}; k)$, consider the localization
$C^*(B \mathbb{T}^{n+1}; k) [e_0^{-1}]$, whose homotopy groups are given by
\begin{equation} \pi_* C^*(B \mathbb{T}^{n+1}; k)[e_{0}^{-1}] \simeq k[e_0^{\pm 1},
f_1, \dots,
f_n], \quad |f_i| = 0, \end{equation}
where for $i \geq 1$, $f_i = e_i/e_0$. In particular, the
Galois theory of
$C^*(B \mathbb{T}^{n+1}; k)[e_{0}^{-1}]$ is algebraic thanks to \Cref{etalegalois}, and by
\eqref{hugeexact}, we have an exact sequence
\begin{equation}
\widehat{\mathbb{Z}}^{n+1} \to \pi_1 \mathrm{Mod}( C^*(B ( \mathbb{Z}/p)^{n+1};
k)[e_0^{-1}]) \to \pi_1 \mathrm{Mod}( C^*(B \mathbb{T}^{n+1};
k)[e_0^{-1}]) \to 1
\end{equation}
Our argument will be that the first map is necessarily \emph{zero}, which will
show that the Galois theory of
$C^*(
B(\mathbb{Z}/p)^{n+1}; k)[e_0^{-1}]$ is algebraic as desired.
In order to do this, we will use a naturality argument.
We can form the completion
$$A = \widehat{ C^*(B \mathbb{T}^{n+1}; k) [e_0^{- 1}] }_{(f_1, \dots, f_n)},$$
at the ideal $(f_1, \dots, f_n)$,
whose homotopy groups now become the tensor product of
the Laurent series ring $k[e_0^{\pm 1}]$ together with a \emph{power series}
ring $k[[f_1, \dots, f_n]]$.
We will prove:
\begin{lemma} \label{analglem}
The Galois theory of $A' \stackrel{\mathrm{def}}{=}A \otimes_{C^*(B
\mathbb{T}^{n+1}; k)} C^*(
B(\mathbb{Z}/p)^{n+1}; k)$ is entirely algebraic (and, in particular, that of $A$).
\end{lemma}
\begin{proof}
The $\e{\infty}$-ring $A' = A \otimes_{C^*(B \mathbb{T}^{n+1}; k)} C^*(
B(\mathbb{Z}/p)^{n+1}; k)$, which by definition is the $\e{\infty}$-ring obtained
from $C^*( B ( \mathbb{Z}/p)^{n+1}; k)$ obtained by inverting the generator $e_0$
and completing with respect to the ideal $(f_1, \dots, f_n)$, admits another
description: it is the homotopy fixed points $(k^{t \mathbb{Z}/p})^{h (\mathbb{Z}/p)^{n}}$ where
$(\mathbb{Z}/p)^{n}$ acts trivially.\footnote{In general, the formation of
homotopy fixed points do not commute with localization from $k^{h
\mathbb{Z}/p}$ to $k^{t \mathbb{Z}/p}$: the failure is precisely measured by
the need to take the completion.}
Since we
have computed the Galois theory of $k ^{t \mathbb{Z}/p}$ and found it to be
algebraic in
\Cref{galoistaterankone}, this, together with \Cref{weakinv}, implies the claim.
\end{proof}
Finally, consider the diagram
obtained from the faithful $\mathbb{T}^{n+1}$-Galois
extensions
$
C^*( B\mathbb{T}^{n+1}; k)[e_0^{-1}]
\to
C^*( B(\mathbb{Z}/p)^{n+1}; k)[e_0^{-1}]$ and $A \to A'$,
\[ \xymatrix{
\widehat{\mathbb{Z}}^{n+1} \ar[d] \ar[r] & \ar[d] \pi_1( \mathrm{Mod}( A'))\ar[r] & \ar[d] \pi_1 (\mathrm{Mod}( A)) \ar[r] & 1 \\
\widehat{\mathbb{Z}}^{n+1} \ar[r] & \pi_1 \mathrm{Mod}( C^*(B
(\mathbb{Z}/p)^{n+1}; k)[e_0^{-1}]) \ar[r] & \pi_1\mathrm{Mod}( C^*(B
\mathbb{T}^{n+1};
k)[e_0^{-1}]) \ar[r] & 1 }. \]
In the top row, in view of \Cref{analglem}, the map out of
$\widehat{\mathbb{Z}}^{n+1}$
must be zero. It follows that the same must hold in the bottom row. In other
words,
the Galois theory of $C^*(B (\mathbb{Z}/p)^{n+1}; k)[e_0^{-1}]$ is equivalent to
the (algebraic) Galois theory of $C^*( B \mathbb{T}^{n+1}; k)[e_0^{-1}]$.
As we saw at the beginning, this is precisely the step we needed to see that
the Galois theory of the Tate construction $k^{tV}$ is ``locally'' algebraic
over $\mathbb{P}(V_k^{\vee})$, and this completes the proof of \Cref{galelem}.
\end{proof}
\begin{remark}
This argument leaves open a natural question: is the Galois theory of a
general localization $C^*(B ( \mathbb{Z}/p)^{n+1}; k)[f^{-1}]$ algebraic?
\end{remark}
\subsection{General finite groups}
Let $G$ be any finite group. In this section, we will put together the
various pieces (in particular, \Cref{galelem} and Quillen stratification
theory)
to give a description of the Galois group of the
stable module $\infty$-category $\mathrm{St}_G(k)$ over a field $k$ of characteristic $p
> 0$.
For each subgroup $H \subset G$, recall the commutative algebra object
$A_H = \prod_{G/H} k \in \mathrm{CAlg}(\mathrm{Mod}_G(k))$. $A_H$ has the property that
\( \mathrm{Mod}_{\mathrm{Mod}_G(k)}(A_H) \simeq \mathrm{Mod}_H(k), \)
and the adjunction $\mathrm{Mod}_G(k) \rightleftarrows \mathrm{Mod}_{\mathrm{Mod}_G(k)}(A_H)$ whose left
adjoint tensors with $A_H$ can be identified with \emph{restriction} to the
subgroup $H$. We will need an analog of this at the level of stable module
categories. We refer to \cite[sec. 5.3]{MNNequiv} for a discussion of these types
of equivalences and for a proof of a general result including this in the
$\infty$-categorical setting.
\begin{proposition}[Balmer \cite{balmerstack}]
\label{moduleres}
Let $\mathscr{A}_H \in \mathrm{CAlg}( \mathrm{St}_G(k))$ be the image of $A_H$ in the stable
module $\infty$-category. Then we can identify $\mathrm{Mod}_{\mathscr{A}_H}( \mathrm{St}_G(k)) \simeq
\mathrm{St}_H(k)$ and we can identify the adjunction $\mathrm{St}_G(k) \rightleftarrows
\mathrm{Mod}_{\mathscr{A}_H}( \mathrm{St}_G(k))$ with the restriction-coinduction adjunction
$\mathrm{St}_G(k) \rightleftarrows \mathrm{St}_H(k)$.
\end{proposition}
\newcommand{\md^{\omega}}{\mathrm{Mod}^{\omega}}
\newcommand{\mathrm{Res}}{\mathrm{Res}}
\Cref{moduleres} suggests that we can perform a type of descent in stable
module $\infty$-categories by restricting
to appropriate subgroups. In particular, we can hope to reduce the calculation
of certain invariants in $\mathrm{St}_G(k)$ to those of $\mathrm{St}_H(k)$ where $H \subset
G$ are certain subgroups, by performing descent along commutative algebra
objects of the form $\mathscr{A}_H$. We shall carry this out for the Galois
group.
Let $G$ be any finite group, and let $\mathcal{A}$ be a collection of subgroups
of $G$ such that any elementary abelian $p$-subgroup of $G$ is contained in a
conjugate of an element of $\mathcal{A}$.
For each $H \in \mathcal{A}$, we consider the
object $\prod_{G/H} k \in \mathrm{CAlg}(\mathrm{Mod}_G(k))$.
\begin{proposition}
The commutative algebra object $A = \prod_{H \in \mathcal{A}} \left(\prod_{G/H}
k\right) \in \mathrm{CAlg}( \mathrm{Mod}_G(k))$ admits descent.
\end{proposition}
\begin{proof}
In order to
prove this, by \Cref{BC}, it suffices to prove that the above commutative algebra
admits descent after restriction from $G$ to each elementary abelian
$p$-subgroup. However, when we restrict from $G$ to each elementary abelian
$p$-subgroup, the above commutative algebra object contains a copy of the unit
object as a direct factor (as commutative algebras), so that it
clearly admits descent.
\end{proof}
\newcommand{\s}[1]{\mathscr{#1}}
In particular, it follows that the image $\mathscr{A} \in \mathrm{CAlg}(\mathrm{St}_G(k))$ of the above commutative algebra
object $A = \prod_{H \in \mathcal{A}} \left(\prod_{G/H} k\right) \in \mathrm{Mod}_G(k)$
in the stable module $\infty$-category also
admits descent.
It follows that we have an equivalence
of symmetric monoidal $\infty$-categories
\begin{equation} \label{descdecompstm} \mathrm{St}_G(k) \simeq
\mathrm{Tot}\left(
\mathrm{Mod}_{\mathrm{St}_G(k)}(\mathscr{A}) \rightrightarrows \mathrm{Mod}_{\mathrm{St}_G(k)}(\mathscr{A}
\otimes \mathscr{A}) \triplearrows \dots \right)
.\end{equation}
There is a classical cofinality argument that enables us to rewrite this
inverse limit in a different fashion.
Recall:
\begin{definition}
The \textbf{orbit category} $\mathcal{O}(G)$ is the category of all finite
$G$-sets of the form $G/H$ for $H \subset G$ a subgroup.
\end{definition}
We have a functor
\[ \mathcal{O}(G) \to \mathrm{CAlg}( \mathrm{Pr}^L_{\mathrm{st}}), \quad G/H \mapsto \mathrm{St}_H(k) = \mathrm{Mod}_{\mathrm{St}_G(k)}\left(
\prod_{G/H} k\right). \]
Note that given any finite $G$-set $S$, we can form a commutative algebra
object in $\mathrm{St}_G(k)$ given by $\prod_S k = k^S$. This construction takes
coproducts of $G$-sets to products.
\newcommand{\mathcal{F}}{\mathcal{F}}
Suppose $\mathcal{A}$ is a collection of subgroups of $G$ which is closed under
finite intersections and conjugation by elements of $G$.
We will use the following notation:
\newcommand{\mathcal{O}_{\mathcal{A}}(G)}{\mathcal{O}_{\mathcal{A}}(G)}
\newcommand{\mathcal{O}'_{\mathcal{A}}(G)}{\mathcal{O}'_{\mathcal{A}}(G)}
\begin{definition}
We let $\mathcal{O}_{\mathcal{A}}(G)\subset \mathcal{O}(G)$ be the full
subcategory spanned by the $G$-sets $G/H$ for $H \in \mathcal{A}$.
We let $\mathcal{O}'_{\mathcal{A}}(G) \subset \mathcal{O}_{\mathcal{A}}(G)$ be the full subcategory including only the
$\left\{G/H\right\}$ for $H \in \mathcal{A}$ and $H \neq 1$.
\end{definition}
Using standard cofinality arguments (cf. \cite[sec. 6.5]{MNNequiv}), we
obtain from the descent statement \eqref{descdecompstm}:
\begin{corollary}
Let $\mathcal{A}$ be a collection of subgroups of $G$.
Suppose that $\mathcal{A}$ is closed under conjugation and finite intersections.
Suppose every elementary abelian $p$-subgroup of $G$ is contained in a subgroup
belonging to $\mathcal{A}$. Then we have a decomposition
\begin{equation}
\label{stmdec}
\mathrm{St}_G(k) \simeq \varprojlim_{G/H \in \mathcal{O}_{\mathcal{A}}(G)^{op}}
\mathrm{St}_H(k).
\end{equation}
\end{corollary}
These types of descent statements at the level of homotopy
categories have been developed in \cite{balmerstack}.
We also have an analogous (but easier) decomposition
$$
\mathrm{Mod}_G(k) \simeq \varprojlim_{G/H \in \mathcal{O}_{\mathcal{A}}(G)^{op}}
\mathrm{Mod}_H(k).
$$
Using \Cref{galelem}, we get:
\begin{theorem}
\label{galgpstmodcat}
Let $\mathcal{A}$ be the collection of elementary abelian $p$-subgroups of $G$.
If $k$ is a separably closed field of characteristic $p$, then the Galois group of $\mathrm{St}_G(k)$ is the profinite completion of
the fundamental group of
the nerve of the category $\mathcal{O}'_{\mathcal{A}}(G)$.
\end{theorem}
\begin{proof}
The decomposition \eqref{stmdec} implies that there is a decomposition
\[ \pi_{\leq 1} (\mathrm{St}_G(k) ) = \varinjlim_{G/H \in \mathcal{O}_{\mathcal{A}}(G)} \pi_{\leq 1} (
\mathrm{St}_H(k)). \]
Now by \Cref{galelem}, when $H $ is nontrivial we have $\pi_{\leq 1} (
\mathrm{St}_H(k)) = \ast$. When $H = 1$, then $\mathrm{St}_H(k) = 0$ so that the Galois
groupoid is empty. It follows that the functor $\mathcal{O}_{\mathcal{A}}(G) \to \mathrm{Pro}( \mathrm{Gpd}_{\mathrm{fin}})$,
$G/H \mapsto \pi_{\leq 1} (
\mathrm{St}_H(k))$ is the left Kan extension of the constant functor $\ast$ on $\mathcal{O}'_{\mathcal{A}}(G)
\subset \mathcal{O}_{\mathcal{A}}(G)$. This implies the result.
\end{proof}
Unfortunately, we do not know in general a more explicit description of the
Galois group. We will give a couple of simple examples below.
\begin{theorem}
\begin{enumerate}
\item
Let $G$ be a finite group whose center contains an order $p$ element (e.g., a
$p$-group). Then the Galois group of $\mathrm{St}_G(k)$ is the
quotient of $G$ by the normal subgroup generated by the order $p$ elements: the
functor
\( \mathrm{Mod}_G(k) \to \mathrm{St}_G(k), \)
induces an isomorphism on fundamental groups.
\item Suppose $G$ is a finite group such that the intersection of any three
$p$-Sylow subgroups of $G$ is nontrivial. Then
$\mathrm{Mod}_G(k) \to \mathrm{St}_G(k)$ induces an isomorphism on fundamental groups.
\end{enumerate}
\end{theorem}
\begin{proof}
Consider the first case.
Choose an order $p$
subgroup $C$ contained in the center of $G$, and consider the collection
$\mathcal{A}$ of all nontrivial elementary abelian $p$-subgroups of $G$ which contain $C$.
Note that $\mathcal{A}$ does not contain the trivial subgroup.
Then
we get decompositions
$\mathrm{St}_G(k) \simeq \varprojlim_{G/H \in \mathcal{O}_{\mathcal{A}}(G)^{op}}
\mathrm{St}_H(k)$ and similarly for $\mathrm{Mod}_G(k)$.
In both cases, the Galois groupoid of each term in the inverse limit is
is a point. It follows that
\[ \pi_1( \mathrm{St}_G(k)) \simeq \pi_1 ( \mathrm{Mod}_G(k)) \simeq \pi_1 N( \mathcal{O}_{\mathcal{A}}(G)), \]
and since we have already computed the Galois group of $\mathrm{Mod}_G(k)$ (\Cref{Grepgal}),
we are done.
For the second case, let $G$ be a finite group such that the intersection of
any three $p$-Sylows in $G$ is nontrivial. Here we will argue slightly
differently. We fix a $p$-Sylow $P \subset
G$ and consider the commutative algebra
object $B = \prod_{G/P} k \in \mathrm{CAlg}( \mathrm{Mod}_G(k))$ and its image $\mathscr{B} \in
\mathrm{CAlg}( \mathrm{St}_G(k))$.
We observe that $B, B \otimes B, B \otimes B \otimes B$ have the same
fundamental groupoids as $\mathscr{B}, \mathscr{B} \otimes \mathscr{B},
\mathscr{B }\otimes \mathscr{B} \otimes \mathscr{B}$, respectively: in fact,
this follows from the previous item (that the Galois groups for $\mathrm{Mod}_H(k)$ and
$\mathrm{St}_H(k)$ where $H$ is a \emph{nontrivial} $p$-group are isomorphic), since
the hypotheses imply that the
$G$-set $G/P \times G/P \times G/P$ has no free component to it.
Therefore, by
descent theory, the Galois groups of $\mathrm{Mod}_G(k)$ and $\mathrm{St}_G(k)$ must be
isomorphic; note that the Galois group only depends on the 3-truncation of the descent
diagram.
\end{proof}
On the other hand, there are cases in which there are finite covers in the
stable module $\infty$-category that do not come from the representation category.
\begin{corollary}
Let $k$ be a separably closed field of characteristic $p$.
Let $G$ be a finite group such that the maximal elementary abelian $p$-subgroup
of $G$ has rank one (i.e., there is no embedding $\mathbb{Z}/p \times
\mathbb{Z}/p \subset G$) and any two such are conjugate. In this case, the Galois group of $\mathrm{St}_G(k)$ is the
Weyl group of a subgroup $\mathbb{Z}/p \subset G$.
\end{corollary}
\begin{proof}
This is an immediate consequence of \Cref{galgpstmodcat}.
\end{proof}
For example, we find that the Galois group of the stable module
$\infty$-category of $\Sigma_p$ is precisely a $( \mathbb{Z}/p)^{\times}$,
which is the Weyl group of $\mathbb{Z}/p \subset \Sigma_p$.
We can see this very explicitly. The Tate construction $k^{t \Sigma_p}$ has
homotopy groups given by
\[ \pi_* ( k^{t \Sigma_p}) \simeq E(\alpha_{2p-1}) \otimes P(\beta_{2p-2}^{\pm
1}), \]
whereas we have $k^{t \mathbb{Z}/p} \simeq E(\alpha_{-1}) \otimes P( \beta_2^{\pm
1})$. The extension $k^{t \Sigma_p} \to k^{t \mathbb{Z}/p}$ is Galois, and is
obtained roughly by adjoining a $(p-1)$st root of the invertible element
$\beta_{2p-2}$.
\section{Chromatic homotopy theory}
In this section, we begin exploring the Galois group in chromatic stable
homotopy theory; this was the original motivating example for this project.
In particular, we consider Galois groups over certain $E_n$-local
$\e{\infty}$-rings such as $\mathrm{TMF}$ and $L_n S^0$, and over the $\infty$-category
$L_{K(n)} \sp$ of $K(n)$-local spectra.
\subsection{Affineness and $\mathrm{TMF}$}
\label{sec:dstack}
Consider the $\e{\infty}$-ring $\mathrm{TMF}$ of (periodic) topological modular forms.
We refer to \cite{TMF} for a detailed treatment.
Our goal in this section is to describe its Galois theory.
The homotopy groups of $\mathrm{TMF}$ are very far from regular; there is considerable
torsion and nilpotence in $\pi_*(\mathrm{TMF})$ at the primes $2$ and $3$, coming from
the stable stems. This presents a significant difficulty in the computation of arithmetic invariants of $\mathrm{TMF}$
and $\mathrm{Mod}( \mathrm{TMF})$.
Nonetheless, $\mathrm{TMF}$ itself is built up as an inverse limit of much simpler
(at least, simpler at the level of homotopy groups) $\e{\infty}$-ring spectra. Recall the construction of
Goerss-Hopkins-Miller-Lurie, which builds $\mathrm{TMF}$ as the global sections of a
sheaf of $\e{\infty}$-ring spectra on the \'etale site of the moduli stack of
elliptic curves $M_{{ell}}$.
Given a commutative ring $R$, and an elliptic curve $C \to \mathrm{Spec} R$ such that
the classifying map $\mathrm{Spec} R \to M_{{ell}}$ is \'etale, the construction assigns an
$\e{\infty}$-ring $\mathcal{O}^{\mathrm{top}}( \mathrm{Spec} R)$ with the basic properties:
\begin{enumerate}
\item $\mathcal{O}^{\mathrm{top}}( \mathrm{Spec} R)$ is even periodic.
\item We have a canonical identification $\pi_0 \mathcal{O}^{\mathrm{top}}( \mathrm{Spec} R) \simeq R $ and
a canonical identification of the formal group of $\mathcal{O}^{\mathrm{top}}( \mathrm{Spec} R)$ and the
formal completion $\widehat{C}$.
\end{enumerate}
The construction makes the assignment $(\mathrm{Spec} R \to M_{{ell}}) \mapsto \mathcal{O}^{\mathrm{top}}( \mathrm{Spec} R)$
into a \emph{functor} from the affine \'etale site of $M_{{ell}}$ to the
$\infty$-category of $\e{\infty}$-rings,
and one defines
\begin{equation} \label{invlimTMF}\mathrm{TMF} = \Gamma( M_{{ell}}, \mathcal{O}^{\mathrm{top}}) \stackrel{\mathrm{def}}{=} \varprojlim_{\mathrm{Spec}
R \to M_{{ell}}} \mathcal{O}^{\mathrm{top}}( \mathrm{Spec} R).\end{equation}
The moduli stack of elliptic curves is \emph{regular}: any \'etale map $\mathrm{Spec} R \to M_{{ell}}$
has the property that $R$ is a regular, two-dimensional domain.
The Galois theory of each $\mathcal{O}^{\mathrm{top}}( \mathrm{Spec} R)$ is thus purely algebraic in view of
\Cref{etalegalois}.
It follows that from the
expression \eqref{invlimTMF} that we have a fully faithful embedding
\begin{equation} \label{easyqc}\mathrm{Mod}^{\omega}( \mathrm{TMF}) \subset \varprojlim_{\mathrm{Spec} R \to M_{{ell}}} \mathrm{Mod}^{\omega}( \mathcal{O}^{\mathrm{top}}(
\mathrm{Spec} R)), \end{equation}
which proves that an \emph{upper bound} for the Galois group of $\mathrm{TMF}$ is
given by the Galois group of the moduli stack of elliptic curves.
It is a folklore result that the moduli stack of elliptic curves, over
$\mathbb{Z}$, is simply connected; see for instance \cite{conrad}. Therefore, one has:
\begin{theorem} \label{TMFsep}
$\mathrm{TMF}$ is separably closed, i.e., has trivial Galois group.
\end{theorem}
Using more sophisticated arguments, one can
calculate the Galois groups not only of $\mathrm{TMF}$, but also of various
localizations (where the algebraic stack is no longer simply connected). This
proceeds by a strengthening of \eqref{easyqc}.
\begin{definition}
The $\infty$-category $\mathrm{QCoh}( \mathcal{O}^{\mathrm{top}})$ of \textbf{quasi-coherent
$\mathcal{O}^{\mathrm{top}}$-modules} is the inverse limit $\varprojlim_{\mathrm{Spec} R \to M_{{ell}}} \mathrm{Mod}(
\mathcal{O}^{\mathrm{top}}( \mathrm{Spec} R))$.
\end{definition}
As usual, we have an adjunction
\[ \mathrm{Mod}( \mathrm{TMF}) \rightleftarrows \mathrm{QCoh}( \mathcal{O}^{\mathrm{top}}), \]
since $\mathrm{TMF}$ is the $\e{\infty}$-ring of endomorphisms of the unit in $\mathrm{QCoh}(
\mathcal{O}^{\mathrm{top}})$. At least away from the prime 2 (this restriction is removed in
\cite{MM}), it is a result of Meier, proved in \cite{meier}, that the adjunction
is an equivalence: $\mathrm{TMF}$-modules are equivalent to quasi-coherent
$\mathcal{O}^{\mathrm{top}}$-modules. In particular, the unit object in $\mathrm{QCoh}( \mathcal{O}^{\mathrm{top}})$ is compact,
which would not have been obvious a priori.
It follows that we can make a stronger version of the argument in
\Cref{TMFsep}. We will do this below in more generality.
In \cite{MM}, L. Meier and the author
formulated a more general context for ``affineness'' results such as this.
We review the results. Let $M_{FG}$ be the moduli stack of formal groups. Let $X$ be a Deligne-Mumford stack and let $X \to
M_{FG}$ be a flat map. It follows that for every \'etale map $\mathrm{Spec} R \to X$,
the composite $\mathrm{Spec} R \to X \to M_{FG}$ is flat and there is a canonically
associated even periodic, \emph{Landweber-exact} multiplicative homology theory associated to
it. An \emph{even periodic refinement} of this data is a lift of the diagram of
homology theories to $\e{\infty}$-rings. In other words, it is a sheaf $\mathcal{O}^{\mathrm{top}}$
of even periodic $\e{\infty}$-rings on the affine \'etale site of $X$ with
formal groups given by the map $X \to M_{FG}$. This enables in particular the
construction of an $\e{\infty}$-ring $\Gamma(X, \mathcal{O}^{\mathrm{top}})$ of \emph{global
sections}, obtained as a homotopy limit in a similar manner as
\eqref{invlimTMF}, and a stable homotopy theory $\mathrm{QCoh}( \mathcal{O}^{\mathrm{top}})$ of
quasi-coherent modules.
Now, one has:
\begin{theorem}[{\cite[Theorem 4.1]{MM}}] \label{MMres}
Suppose $X \to M_{FG}$ is a flat, quasi-affine map and let the sheaf $\mathcal{O}^{\mathrm{top}}$
of $\e{\infty}$-rings on the \'etale site of $X$ define an even periodic
refinement of $X$. Then the natural adjunction
\[ \mathrm{Mod}( \Gamma( X, \mathcal{O}^{\mathrm{top}})) \rightleftarrows \mathrm{QCoh} ( \mathcal{O}^{\mathrm{top}}), \]
is an equivalence of $\infty$-categories.
\end{theorem}
In particular, in \cite[Theorem 5.6]{MM}, L. Meier and the author showed that, given $X \to
M_{FG}$ \emph{quasi-affine}, then one source of Galois extensions of $\Gamma(
X, \mathcal{O}^{\mathrm{top}})$ was the Galois theory of the \emph{algebraic} stack.
If $X$ is regular, we can give the following refinement.
\begin{theorem}
\label{galstack}
Let $X$ be a regular Deligne-Mumford stack.
Let $X \to M_{FG}$ be a flat, quasi-affine map and fix an even periodic sheaf
$\mathcal{O}^{\mathrm{top}}$ as above. Then we have a canonical identification
\[ \pi_1 ( \mathrm{Mod}( \Gamma(X, \mathcal{O}^{\mathrm{top}}))) \simeq \pi_1^{\mathrm{et}} X. \]
\end{theorem}
\begin{proof}
This is now a quick corollary of the machinery developed so far. By
\Cref{MMres}, we can identify modules over $\Gamma(X, \mathcal{O}^{\mathrm{top}})$ with
quasi-coherent sheaves of $\mathcal{O}^{\mathrm{top}}$-modules. In particular, we can equivalently
compute the Galois group, which is necessarily the same as the \emph{weak}
Galois group, of $\mathrm{QCoh}(\mathcal{O}^{\mathrm{top}})$. Using
\[ \mathrm{QCoh}(\mathcal{O}^{\mathrm{top}}) = \varprojlim_{\mathrm{Spec} R \to X} \mathrm{Mod}( \mathcal{O}^{\mathrm{top}}( \mathrm{Spec} R)), \]
where the inverse limit ranges over all \'etale maps $\mathrm{Spec} R \to X$,
we find that the weak Galois groupoid of $\mathrm{QCoh}( \mathcal{O}^{\mathrm{top}})$ is the colimit of the weak Galois
groupoids of the various $\mathcal{O}^{\mathrm{top}}( \mathrm{Spec} R)$. Since we know that these are
algebraic (\Cref{etalegalois}), we conclude that we arrive precisely at the
colimit of Galois groupoids that computes the Galois groupoid of $X$.
\end{proof}
In addition to the case of $\mathrm{TMF}$, we find:
\begin{corollary}
\begin{enumerate}
\item
The Galois group of $\mathrm{Tmf}_{(p)}$ (for any prime $p$) is equal to the \'etale
fundamental group of $\mathbb{Z}_{(p)}$.
\item
The Galois group of $KO$ is $\mathbb{Z}/2$: the map $KO \to KU$ exhibits $KU$
as the Galois closure of $KO$.
\end{enumerate}
\end{corollary}
Here $\mathrm{Tmf}$ is the non-connective, non-periodic flavor of topological modular
forms associated to the compactified moduli stack of elliptic curves.
\begin{proof}
The first claim follows because the compactified moduli stack of elliptic
curves is geometrically simply connected; this follows via the
expression as a weighted projective stack $\mathbb{P}(4, 6)$ when $6$ is
inverted. The second
assertion follows from \Cref{etalegalois}, which shows that $KU$ is simply
connected, since $\mathrm{Spec} \mathbb{Z}$ is.
\end{proof}
\subsection{$K(n)$-local homotopy theory}
Let $K(n)$ be a Morava $K$-theory at height $n$. The $\infty$-category
$L_{K(n)} \sp$ of $K(n)$-local spectra, which plays a central role in modern
chromatic homotopy theory, has been studied extensively in the
monograph \cite{HoveyS}.
$L_{K(n)} \sp$ is a basic example of a stable homotopy theory where the unit object
is \emph{not} compact, although $L_{K(n)} \sp$ is compactly generated (by the
localization of a finite type $n$ complex, for instance). We describe the
Galois theory of $L_{K(n)} \sp$ here,
following ideas of \cite{DH, BR2, rognes}, and many other authors.
According to the ``chromatic'' picture, phenomena in stable homotopy theory are
approximated by the geometry of the moduli stack $M_{FG}$ of formal groups.
When localized at a prime $p$, there is a basic open substack $M_{FG}^{ \leq
n}$ of $M_{FG}$
parametrizing formal groups whose \emph{height} (after specialization to any
field of characteristic $p$) is $\leq n$. There is a closed substack $M_{FG}^{n} \subset
M_{FG}^{\leq n}$ parametrizing formal groups of height \emph{exactly} $n$ over
$\mathbb{F}_p$-algebras. The operation of $K(n)$-localization corresponds
roughly to formally completing along this closed substack (after first
restricting to the open substack $M_{FG}^{\leq n}$, which is
$E_n$-localization). In particular, the Galois theory of $L_{K(n)} \sp$ should
be related to that of this closed substack.
It turns out that $M_{FG}^{n}$ has an extremely special geometry.
The substack $M_{FG}^{n}$ is essentially the ``classifying stack'' of a
large profinite group (with a slight Galois twist) known as the \emph{Morava
stabilizer group.}
\renewcommand{\mathscr{G}}{\mathbb{G}}
\newcommand{\mathbb{G}^{\mathrm{ext}}}{\mathbb{G}^{\mathrm{ext}}}
\begin{definition}
Let $k = \overline{\mathbb{F}_p}$ and consider a height $n$ formal group
$\mathfrak{X}$ over $k$. We define the \textbf{$n$th Morava stabilizer group}
$\mathscr{G}_n$ to be the automorphism group of $\mathfrak{X}$ (in the category of
formal groups).
\end{definition}
Any two height $n$ formal groups over $k$ are isomorphic, so it does not matter
which one we use.
\begin{definition}
We define the \textbf{$n$th extended Morava stabilizer group} $\mathbb{G}^{\mathrm{ext}}_n$
to be the group of pairs $(\sigma, \phi)$ where $\sigma \in \mathrm{Aut}(
\overline{\mathbb{F}_p}/\mathbb{F}_p)$ and $\phi\colon \mathfrak{X} \to \sigma^*
\mathfrak{X}$ is an isomorphism of formal groups.
\end{definition}
In fact, $\mathfrak{X}$ can be defined over the prime field $\mathbb{F}_p$
itself, so that $\sigma^* \mathfrak{X}$ is canonically identified with
$\mathfrak{X}$,
and in this case, every automorphism of $\mathfrak{X}$ is defined over
$\mathbb{F}_{p^n}$. This gives $\mathscr{G}_n$ a natural profinite structure (by looking
explicitly at coefficients of power series), and $\mathbb{G}^{\mathrm{ext}}_n \simeq \mathscr{G}_n \rtimes
\mathrm{Gal}(\overline{\mathbb{F}_p}/\mathbb{F}_p)$.
The picture is that the stack $M_{FG}^{n}$ is the classifying stack of the
group \emph{scheme} of automorphisms of a height $n$ formal group over
$\mathbb{F}_p$. This itself is a pro-\'etale
group scheme which becomes constant after extension of scalars to
$\mathbb{F}_{p^n}$. This picture is justified by the result that any two $n$
formal group are \'etale locally isomorphic, and the scheme of automorphisms
is in fact as claimed.
This picture has been reproduced closely in chromatic homotopy theory.
Some of the most important objects in $L_{K(n)}\sp$ are the \emph{Morava
$E$-theories} $E_n$.
Let $\kappa$ be a perfect field of characteristic $p$ and let $\mathfrak{X}$ be
a formal group of height $n$ over $\kappa$, defining a map $\mathrm{Spec} \kappa \to
M_{FG}^{n}$. The ``formal completion'' of $M_{FG}$ along this map can be
described by \emph{Lubin-Tate theory}; in other words, the universal
deformation $\mathfrak{X}_{\mathrm{univ}}$ of the formal group $\mathfrak{X}$ lives over the ring
$W(\kappa)[[v_1, \dots, v_{n-1}]]$ for $W(\kappa)$ the ring of Witt vectors on
$\kappa$.
The association $(\kappa, \mathfrak{X}) \mapsto (W(\kappa)[[v_1, \dots, v_{n-1}]],
\mathfrak{X}_{\mathrm{univ}})$
defines a functor from pairs $(\kappa, \mathfrak{X})$
to pairs of complete local rings and formal groups over them.
The result of Goerss-Hopkins-Miller \cite{goersshopkins, rezkHM} is that the above functor can be lifted to topology.
Each pair
$(W(\kappa)[[v_1, \dots, v_{n-1}]],
\mathfrak{X}_{\mathrm{univ}})$ can be realized by a homotopy commutative ring
spectrum $E_n = E_n( \kappa; \mathfrak{X})$ in view of the Landweber exact
functor theorem. However, in fact one can construct a functor (essentially
uniquely)
\[ (\kappa, \mathfrak{X}) \mapsto E_n(\kappa; \mathfrak{X}) \]
to the $\infty$-category of $\e{\infty}$-rings,
lifting this diagram of formal groups: for each $(\kappa, \mathfrak{X})$,
$E_n(\kappa; \mathfrak{X})$ is even periodic with formal group identified with
the universal deformation $\mathfrak{X}_{\mathrm{univ}}$ over $W(\kappa)[[v_1,
\dots, v_{n-1}]]$.
We formally now state a definition that we have used before.
\begin{definition}
Any $E_n(\kappa; \mathfrak{X})$ will be referred to as a \textbf{Morava
$E$-theory} and will be sometimes simply written as $E_n$.
\end{definition}
Since $M_{FG}^{n}$ is the classifying stack of a pro-\'etale
group scheme, we should expect, if we take $\kappa = \overline{\mathbb{F}_p}$,
an appropriate action of the extended Morava stabilizer group on $E_n(\kappa;
\mathfrak{X})$. An action of the group $\mathbb{G}^{\mathrm{ext}}_n$ is given to us
on $E_n(\kappa; \mathfrak{X})$ by the Goerss-Hopkins-Miller theorem.
However, we should expect a ``continuous'' action of $\mathbb{G}^{\mathrm{ext}}_n$ on $E_n( \kappa;
\mathfrak{X})$ on $\mathrm{Mod}( E_n(\kappa; \mathfrak{X}))$
whose homotopy fixed points are $L_{K(n)} \sp$.
Although this does not seem to have been fully made precise,
given an open subgroup $U \subset \mathbb{G}^{\mathrm{ext}}_n$, Devinatz-Hopkins \cite{DH} construct
homotopy fixed points $E_n(\kappa; \mathfrak{X})^{hU}$ which have the desired
properties (for example, if $U \subset \mathbb{G}^{\mathrm{ext}}_n$, one obtains $L_{K(n)} S^0$).
It was observed in \cite{rognes} that for $U \subset \mathbb{G}^{\mathrm{ext}}_n$ open normal, the maps
\[ L_{K(n)} S^0 \to E_n(\kappa; \mathfrak{X})^{hU} \]
are $\mathbb{G}^{\mathrm{ext}}_n/U$-Galois in $L_{K(n)} \sp$; they become \'etale after base-change
to $E_n(\kappa; \mathfrak{X})$.
The main result
of this section is that this gives precisely the Galois group of $K(n)$-local
homotopy theory.
\begin{theorem} \label{knlocalgal}
The Galois group of $L_{K(n)} \sp$ (which is also the weak Galois group) is the extended Morava stabilizer group
$\mathbb{G}^{\mathrm{ext}}_n$.
\end{theorem}
Away from the prime $2$, this result is essentially due to
Baker-Richter \cite{BR2}.
We will give a direct proof using descent theory.
Let $E_n$ be a Morava $E$-theory.
Using descent for linear $\infty$-categories along $L_n S^0 \to
E_n$ (\Cref{proconstdescentC} and \Cref{HR}), we find:
\begin{proposition}
$E_n \in \mathrm{CAlg}( L_{K(n)} \sp)$ satisfies descent.
In particular, we have an equivalence
\[ L_{K(n)} \sp \simeq \mathrm{Tot}\left( L_{K(n)} \mathrm{Mod}(E_n) \rightrightarrows
L_{K(n)} \mathrm{Mod}(L_{K(n)}(E_n \otimes E_n)) \triplearrows \dots \right). \]
\end{proposition}
\begin{proof}
This follows directly from the fact that since the cobar construction $L_n S^0
\to E_n$ defines a constant pro-object in $\sp$ (with limit $L_nS^0$), it defines a constant
pro-object (with limit $L_{K(n)}S^0$) in $L_{K(n)}\sp$ after $K(n)$-localizing everywhere.
\end{proof}
Therefore, we need
to understand the Galois groups of stable homotopy theories such as
$L_{K(n)}\mathrm{Mod}(E_n)$. We did most of the work in \Cref{etalegalois}, although the
extra localization adds a small twist that we should check first.
Let $A$ be an even periodic $\e{\infty}$-ring with $\pi_0 A$ a complete
regular local ring with maximal ideal $\mathfrak{m} = (x_1, \dots, x_n)$,
where $x_1 ,\dots, x_n$ is a system of parameters for $\mathfrak{m}$. Let
$\kappa(A) = A/(x_1,\dots, x_n)$ be
the topological ``residue field'' of $A$, as considered earlier.
\begin{proposition}
\label{etalegall}
Given a $\kappa(A)$-local $A$-module $M$, the following are equivalent:
\begin{enumerate}
\item $M$ is dualizable in $L_{\kappa(A)} \mathrm{Mod}(A)$.
\item $M$ is a perfect $A$-module.
\end{enumerate}
\end{proposition}
\begin{proof}
Only the claim that the first assertion implies the second needs to be shown.
If $M$ is dualizable in $L_{\kappa(A)} \mathrm{Mod}(A)$, then it follows that, since
the \emph{homology theory} $\kappa(A)_*$ is a monoidal functor,
$\kappa(A)_*(M)$ must be dualizable in the category of graded
$\kappa(A)_*$-modules. In particular, $\kappa(A)_0(M)$ and $\kappa(A)_1(M)$ are
finite-dimensional vector spaces. From this, it follows that $\pi_*(M)$ itself
must be a finitely generated $\pi_*(A)$-module, since $\pi_*(M)$ is
(algebraically) complete.
For example, given any $i$, we show that
the $\pi_0(A)$-module
\( \pi_0 (M/(x_1, \dots, x_i) M) \) is finitely generated by descending
induction on $i$; when $i = 0$ it is the assertion we want. When $i = n$, the
finite generation follows from our earlier remarks. If we know finite
generation at $i$, then we use the cofiber sequence
\[ M/(x_1, \dots, x_{i-1}) \stackrel{x_i}{\to} M/(x_1, \dots, x_{i-1}) \to
M/(x_1, \dots, x_i), \]
to find that
\[ \pi_0(M/(x_1, \dots, x_{i-1})) \otimes_{\pi_0(A)} \pi_0(A)/(x_i) \subset
\pi_0( M/(x_1, \dots, x_i)), \]
is therefore finitely generated. However, by the $x_i$-adic completeness of
$\pi_0 (M/(x_1, \dots, x_{i-1}))$, this implies that $\pi_0(M/(x_1, \dots,
x_{i-1}))$ is finitely generated.
Finally, since $\pi_*(A)$ has finite global dimension, this is
enough to imply that $M$ is perfect as an $A$-module.
\end{proof}
\begin{proof}[Proof of \Cref{knlocalgal}]
We thus get an equivalence
\[ \clg^{\mathrm{w.cov}}( L_{K(n)} \sp)
\simeq \mathrm{Tot}\left( \clg^{\mathrm{w.cov}}( L_{K(n)} \mathrm{Mod}(E_n)) \rightrightarrows \clg^{\mathrm{w.cov}}(
L_{K(n)} \mathrm{Mod}(E_n \otimes E_n)) \triplearrows \dots \right).
\]
However, we have shown, as a consequence of \Cref{etalegall} and \Cref{etalegalois}, that
$\clg^{\mathrm{w.cov}}( L_{K(n)} \mathrm{Mod}(E_n))$ is actually equivalent to the full subcategory spanned
by the \emph{finite \'etale} commutative algebra objects. Since finite \'etale
algebra objects are preserved under base change, we can replace the above
totalization via
\[ \clg^{\mathrm{w.cov}}( L_{K(n)} \sp)
\simeq \mathrm{Tot}\left( \clg^{\mathrm{w.cov}}_{\mathrm{alg}}( L_{K(n)} \mathrm{Mod}(E_n))
\rightrightarrows \clg^{\mathrm{w.cov}}_{\mathrm{alg}}(
L_{K(n)} \mathrm{Mod}(E_n \otimes E_n)) \triplearrows \dots \right),
\]
where the subscript $\mathrm{alg}$ means that we are only looking at the
classical finite covers, i.e., the category is equivalent to the category of
finite \'etale covers of $ \pi_0$.
In other words, we obtain a cosimplicial commutative ring, and we need to take
the geometric realization of the \'etale fundamental groupoids to obtain the
fundamental group of $L_{K(n)} \sp$.
Observe that each commutative ring $\pi_0 L_{K(n)}(E_n^{\otimes m})$ is
complete with respect to the ideal $(p, v_1, \dots, v_{n-1})$, in view of the
$K(n)$-localization.
The algebraic fundamental group is thus invariant under quotienting by this
ideal. After we do this, we obtain precisely a presentation for the moduli
stack $M_{FG}^{n}$, so the Galois group of $L_{K(n)} \sp$ is that of this
stack. As we observed earlier, this is precisely the extended Morava stabilizer group.
\end{proof}
\subsection{Purity}
We next describe a ``purity'' phenomenon in the Galois groups of
$\e{\infty}$-rings in chromatic homotopy theory: they appear to depend only on
their $L_1$-localization. We conjecture below that this is true in general, and
verify it in a few special (but important) cases.
We return to the setup of \Cref{sec:dstack}.
Let $R$ be an $\e{\infty}$-ring that
arises as the global sections of the structure sheaf (``functions'') on a
derived stack $(\mathfrak{X}, \mathcal{O}^{\mathrm{top}})$ which is a refinement of a flat
map $X \to M_{FG}$.
Suppose further that $(\mathfrak{X}, \mathcal{O}^{\mathrm{top}})$ is \emph{0-affine}, i.e., the
natural functor $\mathrm{Mod}(\Gamma( \mathfrak{X}, \mathcal{O}^{\mathrm{top}})) \to \mathrm{QCoh}( \mathfrak{X})$
is an equivalence, and that $X$ is
\emph{regular}.
In this case, we have:
\begin{theorem}[$KU$-purity] \label{E1purity}
The map $R \to L_{KU} R$ induces an isomorphism on Galois groups. \end{theorem}
In order to prove this result, we recall the \emph{Zariski-Nagata purity theorem}, for
which a useful reference is
Expos\'e X of \cite{SGA2}.
\begin{theorem}[Zariski-Nagata] \label{ZN} Let $X$ be a
regular noetherian scheme and $U \subset X$ an open subset such that $X
\setminus U$ has codimension $\geq 2$ in $X$. Then the restriction functor
establishes an equivalence of categories between finite \'etale covers of $X$
and finite \'etale covers of $U$.
\end{theorem}
If $X$ is instead a regular Deligne-Mumford stack, and $U \subset X$ is an open
substack whose complement has codimension $\geq 2$ (a condition that makes
sense \'etale locally, and hence for $X$), then it follows from the above
and descent theory that finite \'etale
covers of $X$ and $U$ are still equivalent.
\begin{proof}[Proof of \Cref{E1purity}]
First we work localized at a prime $p$, so that $L_{KU} \simeq L_1$.
In this case, the result is a now a direct consequence of various results in the preceding sections
together with \Cref{ZN}.
Choose a derived stack $(\mathfrak{X}, \mathcal{O}^{\mathrm{top}})$ whose global sections give $R$;
suppose $\mathfrak{X}$ is an even periodic refinement of an ordinary
Deligne-Mumford stack $X$,
with a flat, affine map $X \to M_{FG}$.
Then $L_1 R$ can be recovered as the $\e{\infty}$-ring of functions on the open
substack of $(\mathfrak{X}, \mathcal{O}^{\mathrm{top}})$ corresponding to the open substack $U$ of $X$
complementary to closed substack cut out by the ideal $(p, v_1)$. The derived
version of $U$ is also 0-affine, as observed in \cite[Proposition 3.27]{MM}.
Now, in view of \Cref{galstack}, the Galois group of $L_1 R$ is that of the open
substack $U$, and the Galois group of $R$ is that of $X$. However, the
Zariski-Nagata theorem implies that the inclusion $U \subset X$ induces an
isomorphism on \'etale fundamental groups. Indeed, the complement of $U
\subset X$ has codimension $\geq 2$ as $(p, v_1)$ is a regular sequence on $X$
by flatness and thus cuts out a codimension two substack of $X$.
To prove this integrally, we need to piece together the different primes
involved.
Given any $\e{\infty}$-ring $A$, it follows from
descent theory that there is a sheaf $\mathrm{Gal}_G$ of (ordinary) categories on
the Zariski site of $\mathrm{Spec} \pi_0 A$, such that on a basic open affine $U_f
= \mathrm{Spec}
\pi_0 A[f^{-1}] \subset \mathrm{Spec} \pi_0 A$,
$\mathrm{Gal}_G(U_f)$ is the groupoid of $G$-Galois extensions of the
localization $A[f^{-1}]$. Thus we can prove:
\begin{lemma}
\label{galloc}
Fix a finite group $G$.
Let $R \to R'$ be a morphism of $\e{\infty}$-rings with the following properties:
\begin{enumerate}
\item $R \to R'$ induces an equivalence of categories $\mathrm{Gal}_G(R_{(p)}) \to
\mathrm{Gal}_G(R'_{(p)})$ for each $p$.
\item $R_{\mathbb{Q}}\to R'_{\mathbb{Q}}$
induces an equivalence of categories $\mathrm{Gal}_G(R_{\mathbb{Q}}) \to
\mathrm{Gal}_G(R'_{\mathbb{Q}})$.
\end{enumerate}
Then the natural functor $\mathrm{Gal}_G(R) \to \mathrm{Gal}_G(R')$ is an
equivalence of categories.
\end{lemma}
\begin{proof}
By the above, there is a sheaf $\mathrm{Gal}(G; R)$ (resp. $\mathrm{Gal}(G;
R')$) of categories on $\mathrm{Spec} \mathbb{Z}$, whose value
over an open affine $\mathrm{Spec} \mathbb{Z}[N^{-1}]$ is
the category of $G$-Galois extensions of $R[N^{-1}]$ (resp. of $R'[N^{-1}]$).
These are the pushforwards of the sheaves $\mathrm{Gal}_G$ on $\mathrm{Spec} \pi_0 R,
\mathrm{Spec} \pi_0 R'$
discussed above.
Now
\Cref{galcolim}, together with the hypotheses of the lemma, imply that
the map of sheaves $\mathrm{Gal}(G; R) \to \mathrm{Gal}(G'; R)$ induces an
\emph{equivalence} of categories on each stalk over every point of $\mathrm{Spec}
\mathbb{Z}$. It follows that the map induces an equivalence upon taking global
sections, which is the conclusion we desired.
\end{proof}
This lemma let us conclude the proof of \Cref{E1purity}. Namely, the map $R \to L_K R$
satisfies the two hypotheses of the lemma above, since in fact $R_{\mathbb{Q}}
\simeq (L_K R)_{\mathbb{Q}}$, and we have already checked the $p$-local case
above.
\end{proof}
Using similar techniques, we can prove a purity result for the Galois groups of
the $E_n$-local spheres.
\begin{theorem}
The Galois theory of $L_n S^0$ is algebraic and is given by that of $\mathbb{Z}_{(p)}$.
\end{theorem}
\begin{proof}
We can prove this using descent along the map $L_n S^0 \to E_n$.
Since this map admits descent, we find that
\[ \clg^{\mathrm{cov}}( L_n S^0) \simeq \mathrm{Tot}\left(
\clg^{\mathrm{cov}}( E_n) \rightrightarrows \clg^{\mathrm{cov}}(E_n \otimes E_n) \triplearrows \dots
\right).
\]
Now, $E_n \otimes E_n$ does not have a regular noetherian $\pi_0$. However, $\clg^{\mathrm{cov}}( E_n)$
is simply the ordinary category of finite \'etale covers of $\pi_0 E_n$, in
view of \Cref{etalegalois}. Therefore, we can replace the above totalization by
the analogous totalization where we only consider the \emph{algebraic} finite
covers at each stage (since the two are the same at the first stage).
In particular, since the cosimplicial (discrete) commutative ring
\[ \pi_0 (E_n) \rightrightarrows \pi_0 (E_n \otimes E_n) \triplearrows \dots , \]
is a presentation for the algebraic stack $M_{FG}^{\leq n}$ of formal groups
(over $\mathbb{Z}_{(p)}$-algebras) of
height $\leq n$, we find that the Galois theory of $L_nS^0$ is the Galois
theory of this stack. The next lemma thus completes the proof.
\end{proof}
\begin{lemma}
For $n \geq 1$,
the maps of stacks $M_{FG}^{\leq n} \to M_{FG} \to \mathrm{Spec} \mathbb{Z}_{(p)}$ induce
isomorphisms on
fundamental groups.
\end{lemma}
\begin{proof}
The moduli stack of formal groups $M_{FG}$ has a presentation in terms of the
map $\mathrm{Spec} L \to M_{FG}$, where $L$ is the \emph{Lazard ring} (localized at
$p$). $L$ is a polynomial ring on a countable number of generators over
$\mathbb{Z}_{(p)}$. Similarly, $\mathrm{Spec} L \times_{M_{FG}} \mathrm{Spec} L$ is a
polynomial ring on a countable number of generators over $\mathrm{Spec}
\mathbb{Z}_{(p)}$.
The \'etale fundamental group of $\mathbb{Z}_{(p)}[x_1, \dots, x_n]$ is that of
$\mathbb{Z}_{(p)}$,\footnote{Let $R$ be a regular, torsion-free ring. Then we
claim that the fundamental group of $\mathrm{Spec} R[x]$ and $\mathrm{Spec} R$ are isomorphic
under the natural map.
In fact, this is evident (e.g., by topology) if $R$ is a field of
characteristic zero. Now, if $K$ is the fraction field of $R$, then to give an \'etale cover of
$\mathrm{Spec} R[x]$ is equivalent to giving an \'etale cover of $\mathrm{Spec} K[x]$ (i.e.,
an \'etale $K[x]$-algebra $R_K'$) such that
the normalization of $R[x]$ in $R_K'$ is \'etale over $R[x]$, since \'etale
extensions preserve normality.
The \'etale $K[x]$-algebra $R_K'$ is necessarily of the form $L[x]$ where $L$
is a finite separable extension of $K$ (if it is connected, at least).
In order for this normalization to be \'etale over $R[x]$, the normalization of
$R$ in $L$ must be \'etale over $R$.} and by taking filtered colimits, the same follows for a
polynomial ring over $\mathbb{Z}_{(p)}$ over a countable number of variables.
Thus, the \'etale fundamental group $M_{FG}$ is that of $\mathrm{Spec}
\mathbb{Z}_{(p)}$. The last assertion follows because, again, the deletion of
the closed subscheme cut out by $(p, v_1)$ does not affect the \'etale
fundamental group in view of the Zariski-Nagata theorem (applied to the
infinite-dimensional rings by the filtered colimit argument).
\end{proof}
The above results suggest the following purity conjecture.
\begin{conj}
\label{purityconj} Let $R$ be \emph{any} $L_n$-local $\e{\infty}$-ring.
The map $R \to L_1 R$ induces an isomorphism on fundamental groups. \end{conj}
\Cref{purityconj} is supported by the observation that, although not every
$L_n$-local $\e{\infty}$-ring has a regular $\pi_0$ (or anywhere close),
$L_n$-local $\e{\infty}$-rings seem to built from such at least to some extent.
For example, the free $K(1)$-local $\e{\infty}$-ring on a generator is known to
have an infinite-dimensional regular $\pi_0$.
\begin{remark}
Conjecture~\ref{purityconj} cannot be valid for general $L_n S^0$-linear stable
homotopy theories: it is specific to $\e{\infty}$-rings. For example, it fails
for $L_{K(n)} \sp$.
\end{remark}
\bibliographystyle{alpha}
|
{
"redpajama_set_name": "RedPajamaArXiv"
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| 7,884
|
{"url":"https:\/\/stats.stackexchange.com\/questions\/62315\/what-is-lambda-in-an-elastic-net-model-penalized-regression","text":"# What is lambda in an elastic net model (penalized regression)?\n\nIn the language R there is the possibility to estimate the best $\\lambda$ for an elastic net model via a cross-validation, having set the value of $\\alpha$. However, being $\\alpha$ defined as $\\lambda_2\/(\\lambda_1+\\lambda_2)$, where $\\lambda_1$ and $\\lambda_2$ are the coefficients of the penalizations for the ridge and lasso terms, how is $\\lambda$ defined?\n\nYou're confused; $\\alpha$ and $\\lambda$ are totally different.\n$\\alpha$ sets the degree of mixing between ridge regression and lasso: when $\\alpha = 0$, the elastic net does the former, and when $\\alpha = 1$, it does the latter. Values of $\\alpha$ between those extremes will give a result that is a blend of the two.\nMeanwhile, $\\lambda$ is the shrinkage parameter: when $\\lambda = 0$, no shrinkage is performed, and as $\\lambda$ increases, the coefficients are shrunk ever more strongly. This happens regardless of the value of $\\alpha$.\n\u2022 My problem was that in my lecture notes the professor used the notation of $\\lambda_1$ and $\\lambda_2$ to identify the parameters of the ridge and the lasso regression, and from them he derives the generalization of the elastic net, setting $\\alpha$ like in the question. Hence, I thought $\\lambda$ of R was related to these parameters! :) \u2013\u00a0Pippo Jul 24 '13 at 12:24","date":"2019-07-23 03:49:49","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8622549176216125, \"perplexity\": 331.91456851698166}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2019-30\/segments\/1563195528687.63\/warc\/CC-MAIN-20190723022935-20190723044935-00452.warc.gz\"}"}
| null | null |
{"url":"https:\/\/mechanismsrobotics.asmedigitalcollection.asme.org\/offshoremechanics\/article-abstract\/124\/4\/212\/445872\/Comparing-Different-Test-Procedures-to-Determine?redirectedFrom=fulltext","text":"Maneuvering models for tanker based FPSOs are somewhat different from the classical maneuvering models. The reasons are zero or low forward speed (current), large mean drift angles, small values of rate of turn and relatively large low frequency (lf) transverse and yaw motions around the mean drift angle. A maneuvering model for a FPSO will be described in the paper. For a FPSO the maneuvering model must comply with both still water and a current field condition. Also the \u201ctwilight\u201d zone being defined as the transient from a current field to still water and from still water to a current field (tidal change current) must be considered. In a current field, the coefficients of such a model consist of added mass coefficients, stationary current coefficients and dynamic current coefficients. In still water the coefficients should consist of added mass coefficients and the still water dynamic coefficients. The added mass coefficients $\u03c9\u21920rad\/s$ can be determined by 3-D potential theory. For the stationary current coefficients, classical towing tests for different headings may be carried out. For the determination of the hydrodynamic reaction force coefficients in both still water and in current two methods can be distinguished. With both methods the tanker is connected to the towing carriage by means of the PMM (Planar Motion Mechanism). By running the carriage current can be simulated. The test methods are either the yaw-rotating test or the yaw-oscillatory test. The pure yaw-rotating test is a dynamic test exposing the hull to different low advance velocities while the model rotates with constant rate of turn. In this way the hull will be exposed to the current for the full circle of 360 degrees. The pure yaw-oscillatory test is a dynamic test exposing the hull under a number of headings to different low advance speeds. The model is subjected to a low frequency and a large amplitude yaw motion around the mean yaw heading with regard to the current direction. If the maneuvering model is provided with the dynamic coefficients obtained from either the yaw-rotating tests or the oscillatory tests the results may differ. Model tests have been carried out using both methods. Results will be shown illustrating the difference in the force\/moment components of the maneuvering models for a FPSO hull. In this paper the coefficients as used for the maneuvering model are derived from pure yaw-oscillatory tests. To validate the model recently PMM test series were carried for the combined sway and yaw modes of motion. The test series were performed in both still water and forward velocities. The formulation as derived from the pure yaw oscillating tests was applied to the combined yaw-sway motion and the results are presented.\n\n1.\nSierevogel, L. M., 1998, \u201cTime-domain Calculations of Ship Motions,\u201d PhD thesis, Delft University of Technology.\n2.\nAbkowitz, M. A., 1964, \u201cLectures on Ship Hydrodynamics, Steering and Maneuverability,\u201d Hy A Report Hy S.\n3.\nNorrbin, N. H., 1970, \u201cTheory and Observation on the Use of a Mathematical Model for Ship Manoeuvring in Deep and Confined Water,\u201d Proc. 8th Symposium on Naval Hydrodynamics.\n4.\nMunk, M., 1924, \u201cThe Aerodynamics of Airship Hulls,\u201d NACA Report No. 184.\n5.\nTakashina, J., 1986, \u201cShip Manoeuvring Motion due to Tugboats and Its Mathematical Model,\u201d Journal of the Society of Naval Architects of Japan, 160.\n6.\nSphaier, S. H., Fernandes, A. C., and Correa, S. H., 2000, \u201cManeuvering Model for the FPSO Horizontal Plane Behavior,\u201d ISOPE.\n7.\nWichers, J. E. W., 1988, \u201cA Simulation Model for a Single Point Moored Tanker,\u201d PhD thesis, Delft University of Technology.\n8.\nOCIMF 96, \u201cPrediction of Wind and Current Loads on VLCCs,\u201d London.","date":"2023-03-30 02:21:20","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 1, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.5255417227745056, \"perplexity\": 2365.3984540878996}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2023-14\/segments\/1679296949093.14\/warc\/CC-MAIN-20230330004340-20230330034340-00741.warc.gz\"}"}
| null | null |
{"url":"https:\/\/www.homeworklib.com\/qaa\/1372961\/how-do-you-simplify-3y-2-z-3-3-2x-y-4-z-3","text":"Question\n\n# How do you simplify (3y ^ { 2} z ^ { 3} ) ^ { 3} ( 2x y ^ { 4} z ^ { 3} )?\n\nHow do you simplify (3y ^ { 2} z ^ { 3} ) ^ { 3} ( 2x y ^ { 4} z ^ { 3} )?\n\nAnswer 1\n\n$= 162 x {y}^{10} {z}^{12}$\n\n#### Explanation:\n\n$\\left(3 {y}^{2} {z}^{3}\\right) \\times 3 \\left(2 x {y}^{4} {z}^{3}\\right)$\n\nRemove the brackets\n\n$\\rightarrow$ for the first one all the factors have go be cubed.\n$\\rightarrow$ for the second, multiply by $3$\n\n$= 27 {y}^{6} {z}^{9} \\times 6 x {y}^{4} {z}^{3} \\text{ } \\leftarrow$ now multiply as usual\n\nTo multiply in algebra:\n\n\u2022 multiply the signs\n\u2022 multiply the numbers\n\u2022 add the indices of like bases.\n\n$27 {y}^{6} {z}^{9} \\times 6 x {y}^{4} {z}^{3}$\n\n$= 162 x {y}^{10} {z}^{12}$\n\n#### Earn Coins\n\nCoins can be redeemed for fabulous gifts.\n\nSimilar Homework Help Questions","date":"2022-05-22 03:56:20","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 8, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.9969798922538757, \"perplexity\": 5189.036529762787}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 20, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2022-21\/segments\/1652662543797.61\/warc\/CC-MAIN-20220522032543-20220522062543-00000.warc.gz\"}"}
| null | null |
When you complete this quote form we will be able to send you a personally designed health or life insurance quote from a number of quality, major insurance companies. (Your email and text address will remain confidential).
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"redpajama_set_name": "RedPajamaC4"
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|
\section{\label{sec:level1}First-level heading:\protect\\ The linebreak was forced \lowercase{via} \textbackslash\textbackslash}
\section{\label{sec:intro}Introduction}
In such a complex contemporary society where elements -- people and events -- influence one another and feedback at different scales~\cite{parisi1999}, the application of tools set forth in Statistical Physics in order to cope with collective phenomena has gained prominence in other areas such as Biology and Medicine, Social Sciences, and Humanities, which have put quantitative tools in the methodologies they apply~\cite{thurner2018,stauffer2006biology,castellano2009statistical,de2013evolution,galam2008sociophysics,sen2014sociophysics}.
Accordingly, phenomena in which there is a change in the collective behavior displayed by a social system have turn into an appropriate field for the application of such techniques~\cite{pastor2015,arruda2018,wang2017}; among the several different instances we can find important contributions within the spreading of epidemics as well as opinion dynamics (see eg~\cite{wang2019coevolution} and Sec.~\ref{sec:litrev}).
In spite of the fact that the two subject-matters are not related at first, the dissemination of a causal relationship between neurological disorders and vaccinations~\cite{gasparini2015} has prompted an urban myth that ultimately has jeopardized the elimination of the disease in countries with a very high Human Development Index as the USA~\cite{feemster2020}.
Next the manuscript is organized as follows: in Sec.~\ref{sec:litrev}, we establish the state-of-the-art of the problem; in Sec.~\ref{sec:level1}, we introduce our model for the combined dynamics of opinion and contagion; in Sec.~\ref{sec:resudisc}, we discuss the results for the model; and in Sec.~\ref{sec:final}, we present our final observations on the work and future perspectives about it.
\section{\label{sec:litrev}Literature review}
Modular networks~\cite{2014nematzadehFFA}
are generated by an algorithm that leads to networks with an architecture of communities. A given node in each community can be connected to nodes of the same community (intracommunity links) and/or to nodes of the other community (intercommunity links).
The impact of the network modularity in spreading processes has been investigated in recent years. Since the results introduced in Ref.~\cite{2014nematzadehFFA}, a series of works were published regarding the subject of optimal network modularity; therein, the authors showed that modular structure may have counterintuitive effects on information diffusion. Indeed, it was discussed that the presence of strong communities in modular networks can facilitate global diffusion by improving local intracommunity spreading.
Still in relation to modular networks, it was recently found that an optimal community structure that maximizes spreading dynamics which can pave the way to rich phase diagrams with exhibiting first-order phase transitions~\cite{su2018optimal}. Within the same context, the authors in Ref.~\cite{wu2016optimal} discussed the impact of social reinforcement in information diffusion. They also found optimal multi-community network modularity for information diffusion, i.e., depending on the range of the parameters the multi-community structure can facilitate information diffusion instead of hindering it.
Regarding biological systems, it was recently found there is a nonlinear relation between modularity and global efficiency in animal networks, with the latter peaking at intermediate values of the former~\cite{romano2018social}. In addition, in neural networks there exists an optimal modularity for memory performance, where a balance between local cohesion and global connectivity is established, allowing optimally modular networks to remember longer~\cite{rodriguez2019optimal}.
The authors in Ref.~\cite{cui2018close} studied the importance of close and ordinary social contacts in promoting large-scale contagion and found an optimal fraction of ordinary contacts for outbreaks at a global scale. With respect to correlations in complex networks, it was found that constraining the mean degree and the fraction of initially informed nodes, the optimal structure can be assortative (modular), core-periphery or even disassortative \cite{curato2016optimal}. Other recent works leading with optimal modularity in networks can be found in \cite{nematzadeh2018optimal,PhysRevE.102.052316}.
In a recent work \cite{valdez2020epidemic}, it was proposed a model of disease spreading in a structural modular complex network and studied how the number of bridge nodes $n$ that connect communities affects disease spreading. It was verified that near the critical point as $n$ increases, the disease reaches most of the communities, but each community has only a small fraction of recovered nodes. Moreover, a combination of social networks with game theory was studied in Refs.~\cite{Nowak2011,Feng2019}.
Disease information can spark strong emotions like fear --- or even panic --- that would affect behavior during an epidemic. The authors in \cite{bi2019modeling} considered an agent-based model that assumes that agents can obtain a complete picture of the epidemic via information from local daily contacts or global news coverage. Those results helped conclude that such model can be used to mimic real-world epidemic situations and explain disease transmission, behavior changes, and distribution of prevalence panic. Game theory was also considered to reproduce the decision-making process of individuals during the evolution of a disease. In \cite{zhao2018risk} a spatial evolutionary game was coupled to a SIR model, and the results showed that protective behaviors decrease the numbers of infected individuals and delay the peak time of infection. The study also concluded that increased numbers of risk-averse individuals and preemptive actions can more effectively mitigate disease transmission; however, changes in human behavior require a high social cost (such as avoidance of crowded places leading to absences in schools, workplaces, or other public places).
A recent work considered a coupled behavior-change and infection in a structured population characterized by homophily and outgroup aversion~\cite{smaldino2020coupled}. It was found that homophily can either increase or decrease the final size of the epidemic depending on its relative strength in the two groups. In addition, homophily and outgroup aversion can also produce a `second wave' in the first group that follows the peak of the epidemic in the second group.
Models of opinion dynamics were applied in the context of opinions about vaccination (pro versus anti-vaccine) without coupling an epidemic process~\cite{galam2010public}. Later, kinetic opinion dynamics were coupled to classical epidemic models in order to study the feedback among risk perception, opinions about vaccination, and the disease spreading. In \cite{pires2017dynamics} it was found that the engagement of the pro-vaccine individuals can be crucial for stopping the epidemic spreading. On the other hand, the work \cite{2018piresOC} found counterintuitive outcomes like the fact that an increment in the initial fraction of the population that is pro-vaccine can lead to smaller epidemic outbreaks in the short term, but it also contributes to the survival of the chain of infections in the long term.
Recently, the anti-vaccine sentiment was treated as a cultural pathogen. The authors in \cite{mehta2020modelling} modeled it as a 'infection' dynamics. The authors showed that interventions to increase vaccination can potentially target any of three types of transitions - decreasing sentiment transmission to undecided individuals, increasing pro-vaccine decisions among undecided individuals, or increasing sentiment switching among anti-vaccine individuals.
We previously cited anti-vaccine opinions, thus it is important to mention some recent discussion about the global anti-vaccine movement. Since the online discussions dominate the social interactions in our modern world, the propagation of such anti-vaccine opinions is growing fast. A recent report noted that 31 million people follow anti-vaccine groups on Facebook, with 17 million people subscribing to similar accounts on YouTube \cite{burki2020online}. The authors in \cite{johnson2020online} recently pointed that if the current trends continue, anti-vaccine views will dominate online discussion in 10 years. The importance of anti-vaccine movement is fundamental for the evolution of COVID-19 outbreak. Indeed, the authors in \cite{buonomo2020effects} called attention to the fact that it is a key point to qualitatively assess how the administration of a vaccine could affect the COVID-19 outbreak, taking into account of the behavioral changes of individuals in response to the information available on the status of the disease in the community. According to a study published in August 2020, nearly one in four adults would not get a vaccine for COVID-19 \cite{boyon} and in some countries, more than half of the population would not get it, including Poland and France \cite{curielantivax}. In September 2020, it was verified that only 42 percent of Americans said \textit{yes} to receiving a future COVID-19 vaccine, across all political sides. It means that even in a best-case scenario where a future high performing vaccine is 95$\%$ effective in an individual, it would only impact 42x95$\approx 40\%$ of the
population, which is way below predicted thresholds for herd immunity \cite{johnsonnotsure}.
\begin{figure}[h]
\centering
\includegraphics[width=0.29\textwidth]{ER_mod_05.pdf}
\includegraphics[width=0.29\textwidth]{ER_mod_10.pdf}
\includegraphics[width=0.29\textwidth]{ER_mod_30.pdf}
\caption{Examples of modular networks with $N=100$, $\langle k \rangle = 10$ for different values of $\mu$. The parameter $\mu$ is the community interconnectivity: small values of $\mu$ means few intercommunities bridges which implies strong community structure, ie strong modularity/segregation. In these examples we can see the strengthening of the community structure for lower values of $\mu$.}
\end{figure}
\begin{figure}[h]
\centering
\includegraphics[width=0.49\textwidth]{fig-opi-epi-main.png}
\caption{Coupled vaccination and continuous opinion dynamics.}
\label{fig:fullmodel}
\end{figure}
\begin{figure*}[t
\centering
\includegraphics[width=0.85\textwidth]{IxL_mu_0.100000_w_0.200000.pdf}
\caption{ Steady-state for the spreading measure $I_i$ and collective opinion $m_i$ for each community $i=\{1,2\}$. Symbols are the steady-state outcome for each sample, i.e., each symbol is the result from each Monte Carlo realization. Results for $\mu=0.1$. For this high level of segregation, each community ends up preserving the sign of its initial opinion. Besides, the chain of contagion starts in the community $2$ and cannot become permanent in the community $1$.
}
\label{fig:steadystate-1}
\end{figure*}
\begin{figure*}[t
\centering
\includegraphics[width=0.85\textwidth]{IxL_mu_0.200000_w_0.200000.pdf}
\caption{Steady-state for the spreading measure $I_i$ and collective opinion $m_i$ for each community $i=\{1,2\}$. Symbols are the steady-state outcome for each sample, ie, each symbol is the result from each Monte Carlo realization. Results for $\mu=0.2$. For this intermediate level of segregation, there is the possibility for a switch of opinion in the community $2$ (seed). The epidemic spreading does not survive at the global and local levels.
}
\label{fig:steadystate-2}
\end{figure*}
\begin{figure*}[t
\centering
\includegraphics[width=0.85\textwidth]{IxL_mu_0.300000_w_0.200000.pdf}
\caption{Steady-state for the spreading measure $I_i$ and collective opinion $m_i$ for each community $i=\{1,2\}$. Symbols are the steady-state outcome for each sample, i.e., each symbol is the result from each Monte Carlo realization. Results for $\mu=0.3$. For this low level of segregation, there is the possibility for a switch of opinion in both communities. The epidemic dynamics can survive if the contagion is not too aggressive (intermediate values of $\lambda$) .}
\label{fig:steadystate-3}
\end{figure*}
\begin{figure*}[t
\centering
\includegraphics[width=0.85\textwidth]{IxM_l_0.800000_w_0.100000.pdf}
\caption{Steady-state for the spreading measure $I_i$ and collective opinion $m_i$ for each community $i=\{1,2\}$. Symbols are the steady-state outcome for each sample, i.e., each symbol is the result from each Monte Carlo realization. Results for $w=0.1$ and $\lambda=0.8$.}
\label{fig:steadystate-4}
\end{figure*}
\section{\label{sec:level1}Model}
\subsection{I: Opinion dynamics}
Even though payoff-based models have been employed to address the problem of vaccination dynamics (for instance see \cite{Nowak2011,Feng2019,wang2016statistical} and the references therein), there is an alternative approach that is based on the coupling of epidemic and psychosocial factors that have been provided a successful modelling of phenomena related to vaccination dynamics~\cite{salathe2008effect,wu2016dynamics,coelho2009dynamic,smaldino2020coupled,voinson2015beyond,mehta2020modelling,Feng2017}. In this work, we follow such second methodology. Specifically, based on Refs.~\cite{2018piresOC},\cite{2010lallouacheCCC} we consider an agent-based dynamics
in which the opinion about vaccination, $o_i\in [-1,1]$, of each agent, $i$, evolves with
\begin{equation}
o_i(t+1)=o_i(t)+\epsilon o_j(t)+wI_{n(i)}(t),
\label{eq:evol}
\end{equation}
A negative (positive) value of $o_i$ represents an individual $i$ supporting anti-vaccine (pro-vaccine) opinion. Equation~\eqref{eq:evol} takes into account the agent's opinion, $o_{i}(t+1)$, depends on multiple factors: (i) his previous opinion $ o_i(t)$; (ii) the peer pressure exerted by a randomly selected neighbor, $j$, modulated by a stochastic heterogeneity $\epsilon$, uniformly distributed in the interval $[0, 1]$; (iii) the proportion of infected neighbors, $I_{n(i)}(t)$, modulated by a risk perception parameter, $w$. Notice that, in Eq. \eqref{eq:evol}, if the value of the opinion exceeds (falls below) the value $1 (-1)$, then it adopts the extreme value $1 (-1)$ \cite{2010lallouacheCCC}.
The opinion dynamics regarding the vaccination campaign is coupled with the epidemic dynamics, due to the factor $I_{n(i)}(t)$ in Eq. \eqref{eq:evol}.
\subsection{II: epidemics-vaccination dynamics}
Based on \cite{pires2017dynamics,2018piresOC} (and references therein), we define the transitions among the epidemic compartments as follows:
\begin{itemize}
\item $S \stackrel{g_{i}}{\rightarrow} R$: a Susceptible agent $i$ becomes Vaccinated with probability $g_i$;
\item $S \stackrel{(1-g_{i})\lambda}{\rightarrow} I$: a Susceptible agent $i$ becomes Infected with probability $(1-g_i)\lambda$ if he is in contact with an Infected agent;
\item $I \stackrel{\alpha}{\rightarrow} S$: an Infected agent $i$ recovers with probability $\alpha$;
\item $R \stackrel{\phi}{\rightarrow} S$: a immune agent $i$ becomes Susceptible again with the resusceptibility probability $\phi$. We assume that Vaccinated and Recovered agents are in the same compartment\cite{zeng2005complexity,rao2019complicated,moneim2005threshold,lahrouz2012complete,doutor2016optimal}.
\end{itemize}
The vaccination probability $g_{i}$ of an agent $i$ is proportional to his opinion about vaccination $-1\leq o_i\leq1$:
\begin{align}
g_i(t) = \frac{1+o_{i}(t)}{2} \in [0,1]
\label{eq:gamma}
\end{align}
Despite the differences, the modeling of the coupling between disease and opinion evolution is still a open subject. In this work, we consider the two dynamics have the same time scale. An overview of our model is shown in Fig.\ref{fig:fullmodel}. An element in this problem which is still focus of debate concerns the timescale of each dynamics, epidemic and opinion. On the one hand, it is often assumed in the epidemiological literature~\cite{wu2016dynamics,voinson2015beyond,coelho2009dynamic,velasquez2017interacting} that the two timescales are equivalent. At first, this can be understood as a simplification it captures the mass vaccination campaigns governments swiftly implement in order to avoid disease outbreaks.
On the other hand, it is possible to assume different timescales of evolution of the diseases and opinions about the disease~\cite{ventura2021role,da2019epidemic}.
In this work we consider the first approach of equality between the two timescales.
\subsection{Community structure}
Based on Ref.~\cite{2019oestereichPC} and related literature, we start by picking the first $N_1=N/2$ of the $N$ nodes and attaching them to the community $1$, and assigning the other $N_2=N - N_1$ nodes to community $2$. We then proceed by randomly assigning $(1-\mu)M$ connections among pairs of nodes from the same community and $\mu M$ connections are randomly distributed among pairs of nodes that belong to distinct communities, where $M=N\,k/2$ and $k$ is the network average degree \cite{2019oestereichPC}.
The parameter $\mu$ regulates the community strength: large values of $\mu$ means more ties between the two communities consequently a weaker community organization. Another way to control the network structure -- especially in the formation of the echo chambers -- is by considering rewiring~\cite{Wang2020}.
\subsection{Initial condition}
We consider that community $1$ holds a positive stance on vaccination, whereas the community $2$ holds a negative opinion about that. We also assume the chain of infections starts in community $2$, because $o_i<0$ leads to a low propensity for the agents to get vaccinated, which is naturally more relevant. If the epidemic started in community $1$, pro-vaccine opinions, $o_i>0$, would induce a higher probability for an agent to get vaccinated that ultimately would end up disrupting the chain of contagions.
Let $U(a,b)$ be a single random value from a uniform distribution in the range $[a,b]$.
At $t=0$, we set:
\begin{itemize}
\item For i in $0 \ldots N/2-1$: (community 1: $o_i>0$; $0\%$ infected)
\begin{itemize}
\item $o_i \sim U(0,1) $
\item status(i) = S
\end{itemize}
\item For i in $N/2 \ldots N-1$: (community 2: $o_i<0$; $1\%$ of infected)
\begin{itemize}
\item $o_i \sim U(-1,0) $
\item status(i) = S with probability $0.99$
\item status(i) = I with probability $0.01$
\end{itemize}
\end{itemize}
\section{\label{sec:resudisc}Results and Discussion}
\begin{figure}[h]
\centering
\includegraphics[width=0.49\textwidth]{I1xLxMu_w_0.100000.pdf}
\includegraphics[width=0.49\textwidth]{I2xLxMu_w_0.100000.pdf}
\caption{Steady-state for the spreading measure $I_i$ for community 1, above, and 2, bellow. The colors indicate the average of non zero steady-state outcomes of all 200 samples. Results for $w=0.1$.}
\label{fig:new_results1}
\end{figure}
\begin{figure}[h]
\centering
\includegraphics[width=0.49\textwidth]{I1xLxMu_w_0.200000.pdf}
\includegraphics[width=0.49\textwidth]{I2xLxMu_w_0.200000.pdf}
\caption{Steady-state for the spreading measure $I_i$ for community 1, above, and 2, bellow. The colors indicate the average of non zero steady-state outcomes of all 200 samples. Results for $w=0.2$.}
\label{fig:new_results2}
\end{figure}
In this section, we present our results come from Monte Carlo simulations of networks with $N=10^4$ nodes and k=20.
In all simulations, we set $\alpha=0.1$ and $\phi=0.01$, without loss of generality.
In Figs.~\ref{fig:steadystate-1}-\ref{fig:steadystate-4}, we show the steady-state density of infected agents in the community $u$, $I_u$. We also depict the behavior of the stationary opinion in the community $u$, $m_u$. In turn, $I_{tot}$ and $m_{tot}$ refer to the global proportion of infected individuals and global mean opinion, respectively.
The results in Fig.~\ref{fig:steadystate-1} show that in the community $2$ --- the seed community --- there is a transition from the absorbing phase (extinction of the epidemic) to the epidemic survival phase.
In the community $1$, there is no survival of the chain of infections in the long term.
In this setting with $\mu=0.1$ -- which can be understood as yielding a weak modular structure because of the small value of the parameter -- the seed community remains with the negative opinion about vaccination, which weakens the vaccination campaign and thus facilitates the local permanence of the disease. Similarly, there is a persistence of the initial opinion in the community $1$, which in this case is pro-vaccine and therefore favors the vaccine uptake that makes the epidemic spreading unsustainable. This means that a low number of intercommunity ties hinders the change in the community stance over vaccination; that creates a strong distinction in the epidemic spread between both communities with community $1$ being unfavorable to epidemic spreading since $m_1>0$, and community $2$ being favorable since $m_2<0$.
In Fig.~\ref{fig:steadystate-2}, it is notable that an intermediate community strength leads to the elimination of the epidemic transmission in both communities even when there is a dominance of the negative opinion about vaccination in the community $2$. The epidemic contagion spreading is halted in the community $2$, even though the agents have a negative opinion about the vaccination, due to the intermediate number of bridges, $\mu=0.2$, to the other community. These bridges are just strong enough to drain the infected agents of the community $2$, but not strong enough to change its average opinion.
In Fig.~\ref{fig:steadystate-3}, with $\mu=0.3$ there is a high number of intercommunity links. This additional connectivity between communities weakens the initial epidemic spreading in the community $2$, but it is sufficient to introduce the possibility of a wide opinion change in the community $1$. The opinion change in the community $1$ facilitates the epidemic spreading in that community. This effect is limited because we can see for high infection probabilities $\lambda > 0.8$ the epidemic spread vanishes. So, we have a counterintuitive effect, because for higher transmissibility the epidemic spread vanishes. The reason behind this is the risk perception, $wI$ in Eq.~\eqref{eq:evol}, which promotes vaccination, so higher transmissibility leads to a bigger outbreak that in turn results in better opinions about vaccination which ends up stopping the epidemic outbreak.
The emergence of an intermediate range of $\mu$ that blocks the local and global epidemic spreading is visible in Fig.~\ref{fig:steadystate-4}. Regarding the opinion dynamics, an initial increase in $\mu$ leads to a decrease in $m_1$ and an increase in $m_2$, that is the collective
opinions tend to be less extremist for an initial rise in the amount of inter-communities routes.
Then a further increase in $\mu$ promotes a sudden rise in $m_1$ and $m_2$ which means a speed up in the switch of opinions in the community $2$.
A further rise in $\mu$ leads to a bistable behavior in both communities.
This intermediary range of inter-community connectivity that promotes a minimal epidemic spreading seems to also come from a perceived increment in the probability of an infected individual having a vaccinated neighbor. The increment of the bridges between communities the initially infected agents have a bigger probability of having a neighbor that was vaccinated because initially most of the infected people are in the community $2$ and most agents with a positive opinion about vaccination are in the community $1$. This effect does not persist for higher values of $\mu$ because then both communities tend to adopt the same average opinion about vaccination and this opinion can, in some cases, be negative. A negative global opinion about vaccines does not guarantee that the epidemic spread will persist, as can be seen in some cases for $\mu \approx 0.23$ where all samples had no infected individual but some of them had negative opinions about the vaccination. This can occur due to the fact that the number of infected agents can become zero before the negative global consensus about vaccines is reached.
While in Figs.~\ref{fig:steadystate-1}-\ref{fig:steadystate-2} there is a single stable steady-state (either extinction or persistence), Fig.~\ref{fig:steadystate-3} displays bistable solutions depending on the randomness 'embedded' in the dynamics.
Moreover, the results in Fig.~\ref{fig:steadystate-1} suggest the absorbing-active epidemic transition is continuous for strong communities (such as $\mu=0.1$) whereas the results shown in Fig.~\ref{fig:steadystate-3} signalize this extinction-persistence epidemic transition is discontinuous for weak communities (such as $\mu=0.3$). Therefore, the structural factors present in the modular networks can induce the emergence
of bistability in the epidemic-vaccination-opinion dynamics as well as a change in the nature of the absorbing-active transitions.
An overall look into Figs.~\ref{fig:steadystate-1}-\ref{fig:steadystate-4} reveals a sudden transition can emerge from structural factors (increasing $\mu$) or epidemiological factors (increasing $\lambda$).
The transitions from the Disease-Free phase to the active phase and vice-versa (epidemic resurgence) highlight the
nonmonotonic behavior of the full dynamics with the transmissibility $\lambda$.
Comparing with other works, we see that while in \cite{2014nematzadehFFA} there is an optimal modularity for enhancing information spreading, here there is an optimal modularity for hindering epidemic spreading.
In \cref{fig:new_results1,fig:new_results2} we can see a wide range of results for two different settings of risk perception, i.e. $w = 0.1$ and $w=0.2$. These results are similar but they show how increasing the risk perception reduces the range of parameters that present an endemic state. Other than that, we can also see that in community 1 the endemic state is more prevalent for higher values of modularity $\mu$, this is to be expected since initially only community 2 has infected agents. In community 2 the increment in modularity initially reduces the fraction of infected agents, but at a certain point when the endemic state appears in community 1 it surges back in community 2. This further reinforces that optimal modularity reduces the epidemic spreading.
\FloatBarrier
\section{\label{sec:final}Final Remarks}
In previous work, namely Ref.~\cite{salathe2008effect}, it was shown with a binary opinion dynamics that the spread of opinions against vaccination is one of the potential responsible for the large outbreaks of vaccine-preventable diseases in many high-income countries. In this work, we have gone farther afield to show the emergence of a networked SIRSV model that the spectrum of scenarios arising from the competition of pro- vs anti-vaccine views during an epidemic spreading is highly complex.
The several outcomes shown in Figs.\ref{fig:steadystate-1}-\ref{fig:new_results2} point out that our model produces a diverse
phenomenology where the social and biological scenarios exhibit a nonmonotonic dependence with spreading rate $\lambda$. From the
perspective of the dynamical systems, our results provide a new mechanism for bistability in a
biological-social setting. From a practical point of view, our work offers new perspectives for the development of novel strategies for halting epidemic spreading based on tuning the modularity to an optimal degree.
Some pro-vaccine strategies can have as side effect the segregation between individuals with conflicting views about the vaccines and clustering of similars. In \cite{kadelka2020effect} the authors found that in scenarios with effective vaccines, the impact of clustering and correlation of belief systems become stronger.
Alternatively, the authors in Ref.~\cite{bizzarri2021epidemic} shown that segregation of anti-vaxxers can potentially extend the duration of an epidemic spreading, whereas in Ref.~\cite{saad2020immune} it was found that an increase in the contact between vaccine refusers and the rest of the society can lead to a scenario where vaccination alone may not be able to prevent an outbreak. Here we show that too much or too low segregation of anti-vaxxers favors the chain of contagion, but an intermediate level of segregation disfavor the epidemic spreading. Therefore, our results indicate that vaccination campaigns should avoid strategies that have as a side effect too much informational segregation of anti-vaccine groups so that reliable pro-vaxx information can reach those groups whilst enforcing a minimum degree of physical distancing as it occurs in countries where childhood vaccination is required at some degree, namely school entry \cite{ourworldindata}.
Our work produces a thought-provoking analogy. In a small-world architecture, there is an intermediate number of long-range bridges that lead the full network to have unusual properties such as high clustering and low path lengths. Here, a structure with an intermediate number of inter-community ties leads the dynamics in the full network to produce an interesting outcome, namely the suppression of the epidemics. Thus, it would be interesting to consider further sophisticated network architectures, like multiplex networks.
Despite the rich phenomenology we observed in our model, some limitations can be discussed which can be targeted in future work. The structure social contacts' structure of modular networks, presenting communities, is relevant to study several dynamical processes \cite{2014nematzadehFFA}-\cite{valdez2020epidemic}. However, it could be more realistic to consider two distinct layers, one for the spreading of each dynamics (epidemic and opinion ones), but with each dynamics influencing the other. Such multiplex network structure can model better the coupled opinion-epidemic dynamics. Other rules for the opinion dynamics, distinct of the kinetic exchanges, could also be considered.
Besides, it will be worthwhile to consider the interplay between several sources of heterogeneity in agent's bias, namely plurality and polarization~\cite{oestereich2020hysteresis}.
\section*{Acknowledgments}
The authors acknowledge financial support from the Brazilian funding agencies Conselho Nacional de Desenvolvimento Cient\'ifico e Tecnol\'ogico (CNPq), Coordena\c{c}\~ao de Aperfei\c{c}oamento de Pessoal de N\'ivel Superior (CAPES) and Funda\c{c}\~ao Carlos Chagas Filho de Amparo \`a Pesquisa do Estado do Rio de Janeiro (FAPERJ).
\FloatBarrier
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{
"redpajama_set_name": "RedPajamaArXiv"
}
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\section{Introduction}
The idea that the flavor of a neutrino can change when traveling a macroscopic distance is quite old~\cite{pontecorvo}~\cite{mns}~\cite{bilenky}, and it is among the best examples showing us that we are in need of physics beyond the current Standard Model~\cite{minkowski}~\cite{mohapatra}, which does not embed neutrino masses. Despite this fact, a firm treatment for the probability of conversion between two neutrino flavors has now been set up, both in the vacuum~\cite{kayser}~\cite{giuntikimlee1}~\cite{giuntikimlee2}~\cite{giuntikimlee3}~\cite{lipkin}~\cite{grimus}~\cite{beuthe}~\cite{giunti}~\cite{giunti_review}~\cite{smirnov} and in matter~\cite{wolfenstein}~\cite{mikheyev}.
Neutrino oscillations in the presence of a gravitational field were pioneered by Stodolsky~\cite{stodolsky}, and it was later shown that the interaction of neutrinos with the gravitational field finds various applications both in cosmology and astrophysics, like the possible effects in the emissions occurring in type-II supernova events~\cite{ahluwalia96}~\cite{kojima96} or in the strong gravitational field of an active galactic nucleus~\cite{piriz96}.
The theory of neutrino flavor oscillations in a gravitational field has been further discussed in the Schwarzschild metric~\cite{ahluwalia97}~\cite{fornengo97}~\cite{cardall97}~\cite{ahluwalia98}~\cite{habib99}~\cite{fornengo99}~\cite{ahluwalia04}~\cite{crocker04}~\cite{maiwa04}~\cite{godunov09}, the Kerr metric~\cite{konno98}~\cite{wudka01}, the Lense-Thirring metric~\cite{lambiase05}, and the Hartle-Thorne metric~\cite{geralico12}. Also, neutrino spin oscillation in a gravitational field have been discussed in Refs.~\cite{dvornikov02}~\cite{dvornikov05}~\cite{dvornikov06}~\cite{dvornikov13}~\cite{alavi13}.
In this paper we derive the phase shifts for free-streaming neutrinos using a WKB approximation~\cite{anandan} of the solution to the Dirac equation in curved space-time. We apply our results to describe neutrino flavor oscillations in two well-known space-time metrics, namely the Kerr-Newman metric, which describes the spacetime around a charged and rotating black hole, and the Friedmann-Robertson-Walker (FRW) metric, which describes the cosmological expansion of a homogeneous and isotropic Universe. Notice that the electric charge of a Kerr-Newman black hole affects the trajectory of the neutrino, despite such particle being free of electric charge. This occurs because the energy density associated with the electromagnetic field around the black hole enters the equation of general relativity and influences space-time around the black hole itself.
To the best of our knowledge, the oscillation of neutrinos in the two metrics presented has not been explored before. After discussing the Dirac equation for a fermion propagating in a generic pseudo-Riemann manifold $\mathcal{M}$ in Sec.~\ref{sec_dirac_curved}, we apply this formalism to neutrino oscillations in Sec.~\ref{neutrinos}. We derive the expression for the probability of neutrino oscillations in the Kerr-Newman metric in Sec.~\ref{sec_kerr}, and in the FRW metric in Sec.~\ref{sec_FRW}.
\section{Approximation of the Dirac equation in curved space-time} \label{sec_dirac_curved}
\subsection{Review of Dirac equation on a curved space-time}
Before discussing the properties of neutrinos in the presence of gravity, we briefly review the basic tools for the Dirac equation on curved space-time. On a flat, Minkowski background, the Dirac equation for a spinor field $\psi(x)$ of mass $m$ reads
\begin{equation} \label{dirac}
i\,\gamma^a\,\partial_a\,\psi(x) = m\,\psi(x).
\end{equation}
Here, a Latin index $a \in\{0,1,2,3\}$ labels the coordinates in the Minkowski space-time, while the Dirac matrices $\gamma^a$ satisfy the Clifford algebra
\begin{equation}\label{clifford_flat}
\{\gamma^a,\gamma^b\} = 2\eta^{ab},
\end{equation}
where curly brackets indicate the anti-commutation operation. In the following, the convention for the flat metric is $\eta_{ab} = {\rm diag}(1,-1,-1,-1)$.
According to general relativity, gravitational effects are included by expressing the Dirac Eq.~(\ref{dirac}) on a suitable manifold. We consider a four-dimensional, torsion-free pseudo-Riemann manifold $\mathcal{M}$ equipped with a metric tensor $g_{\mu\nu}$, where Greek indices are used to refer to coordinates on $\mathcal{M}$. Indices for quantities on $\mathcal{M}$ are lowered with $g_{\mu\nu}$ and raised with the inverse of the metric tensor $g^{\mu\nu}$, which is defined by
\begin{equation}
g^{\mu\lambda}\,g_{\lambda\nu} = \delta_\mu^\nu.
\end{equation}
The metric tensor defines the torsion-free Levi-Civita connection on $\mathcal{M}$ as
\begin{equation}
\Gamma_{\mu\nu}^\sigma = \frac{1}{2}g^{\sigma\lambda}\left(\partial_\nu\,g_{\lambda\mu}+\partial_\mu\,g_{\nu\lambda}-\partial_\lambda\,g_{\mu\nu}\right),
\end{equation}
which appears in the parallel transport of vector quantities. For spinors, we define the spinor connection on $\mathcal{M}$ as
\begin{equation} \label{spinor_connection}
\Gamma_{\mu} = \frac{1}{8}\omega_{ab\mu}\left[\gamma^a,\gamma^b\right],
\end{equation}
where squared brackets indicate the commutation operation. We defined the gravity spin connection,
\begin{equation}
\omega_{ab\mu} = e_a^\nu\,\partial_\mu\,e_{b\nu} - e_a^\nu\,\Gamma^\sigma_{\mu\nu}\,e_{b\sigma},
\end{equation}
in terms of the tetrad $e_{a}^{\mu}$ satisfying
\begin{equation}
g_{\mu\nu}\,e^\mu_a \,e^\nu_b = \eta_{ab}.
\end{equation}
Finally, we define the covariant derivative for a spinor field as
\begin{equation}
\mathcal{D}_\mu \equiv \partial_\mu + \Gamma_\mu.
\end{equation}
Given the Dirac equation on the flat space-time, the recipe for expressing the equation on the manifold $\mathcal{M}$ consists in replacing all derivative operators with the covariant derivative,
\begin{equation}
\partial_a \to e_a^\mu\,\mathcal{D}_\mu,
\end{equation}
so that Eq.~(\ref{dirac}) with this prescription reads
\begin{equation}
i\,e^\mu_a\,\gamma^a\,\mathcal{D}_{\mu}\,\psi(x) = m\,\psi(x).
\end{equation}
Defining the Dirac matrices on the manifold $\gamma^\mu \equiv e^\mu_a\,\gamma^a$ and satisfying the algebra
\begin{equation}
\{\gamma^{\mu},\gamma^{\nu}\} = 2g^{\mu\nu},
\end{equation}
we obtain the Dirac equation for the massive spinor field on $\mathcal{M}$,
\begin{equation} \label{dirac_curved}
i\,\gamma^\mu\,\mathcal{D}_\mu\,\psi(x) = m\,\psi(x).
\end{equation}
The action associated to the Dirac Eq.~(\ref{dirac_curved}) is
\begin{equation}
S = \int d^4x\,\sqrt{g}\,\mathcal{L}_D,
\end{equation}
where $g = g^{\mu\nu}\,g_{\mu\nu}$, and we introduced the Lagrangian
\begin{equation}
\mathcal{L}_D = \frac{i}{2}\,\left[\bar{\psi}\,\gamma^\mu\,\mathcal{D}_\mu\,\psi - (\mathcal{D}_\mu\,\bar{\psi})\,\gamma^\mu\,\psi\right] - m\,\bar{\psi}\,\psi.
\end{equation}
\subsection{WKB approximation}
We seek for an approximate solution to the Dirac Eq.~(\ref{dirac_curved}) using a Wentzel-Kramers-Brillouin (WKB) approximation. In the literature, various forms of the WKB approximations have been proposed. Stodolsky~\cite{stodolsky} decomposes the complex spinor $\psi(x)$ into an amplitude $\chi = \chi(x)$ and a semi-classical phase $S = S(x)$, as
\begin{equation} \label{ansatz_stodolsky}
\psi(x) = e^{-iS(x)/\hbar}\,\chi(x).
\end{equation}
Anandan~\cite{anandan} and Maiwa and Naka~\cite{maiwa04} further decompose the complex spinor $\psi(x)$ into a power series in terms of $\hbar$, as
\begin{equation} \label{ansatz_anandan}
\psi(x) = e^{-iS(x)/\hbar}\,\sum_{k=0}^{+\infty}\, \left(\frac{\hbar}{i}\right)^k\,\chi_k(x).
\end{equation}
Here, we include an additional phase containing the spin connection $\Gamma_\mu$, as
\begin{equation} \label{ansatz}
\psi(x) = e^{-iS(x)/\hbar}\,e^{-\Gamma_\mu\,x^\mu}\,\sum_{k=0}^{+\infty}\, \left(\frac{\hbar}{i}\right)^k\,\chi_k(x).
\end{equation}
Substituting Eq.~\eqref{ansatz} into Eq.~(\ref{dirac_curved}) and equating terms with the same power of $\hbar$, a system of recurring equations for the amplitudes $\chi_k$ is obtained as
\begin{equation} \label{ansatz1.1}
\left(\slashed{\partial}\,S - m \right)\,\chi_0 = 0,\quad \hbox{and}\quad \left(\slashed{\partial}\,S - m \right)\,\chi_k = \slashed{\partial}\,\chi_{k-1},\quad\hbox{for $k \neq 0$}.
\end{equation}
Notice that, since $S(x)$ is a scalar function, the covariant derivative of this function has been replaced with the ordinary derivative. Since the spin connection can be written in terms of the parity-violating matrix $\gamma^5$~\cite{cardall97},
\begin{equation} \label{spin_connection_gamma5}
\Gamma_\mu = (-g)^{-1/2}\,\frac{\gamma_5}{2i}\,A_\mu,\quad \hbox{with} \quad A^\mu = \frac{(-g)^{1/2}}{4}\,\epsilon^{abcd}\,e_a^\mu\,\left(e_{b\nu,\sigma}-e_{b\sigma,\nu}\right)\,e_c^\nu\,e_d^\sigma,
\end{equation}
we conclude that the extra phase factor in Eq.~\eqref{ansatz} explicitly accounts for the interaction between the metric and the spin orientation of the spinor (see Refs.~\cite{ahluwalia96}~\cite{ahluwalia97} for a discussion on the effects of this interaction).
Multiplying the expression for $\chi_0$ on the right by $\gamma^\nu\,\partial_\nu\,S(x) - m$, we obtain the Hamilton-Jacobi (HJ) equation
\begin{equation} \label{HJ}
g^{\mu\nu}\,\partial_{\mu}\,S(x)\,\partial_{\nu}\,S(x) = m^2.
\end{equation}
Eq.~(\ref{HJ}) expresses the mass-shell condition for a massive particle in a curved space-time, and allows us to identify the phase $S(x)$ with the classical action for a particle of mass $m$ moving on $\mathcal{M}$, provided that the four-momentum of the particle is~\cite{stodolsky}
\begin{equation} \label{4momentum}
p_{\mu} = m \,g_{\mu\nu}\,\frac{dx^{\nu}}{d\tau},
\end{equation}
and where the proper time $\tau$ is given by
\begin{equation}
d\tau^2 = g_{\mu\nu}\,dx^\mu\,dx^\nu.
\end{equation}
Eq.~(\ref{HJ}) is equivalent to the mass-shell condition if we identify
\begin{equation}
p_\mu = \partial_\mu\,S(x),
\end{equation}
which is the Hamilton-Jacobi relation. A solution to Eq.~(\ref{HJ}) is then~\cite{stodolsky}
\begin{equation} \label{action}
S(x) = \int^x \,p_{\mu}\,dx^{\mu},
\end{equation}
with the Lagrangian describing the geodesic being
\begin{equation} \label{lagrangian_geodesic}
\mathcal{L} = \sqrt{g_{\mu\nu}\,\frac{dx^\mu}{d\tau}\,\frac{dx^\nu}{d\tau}}.
\end{equation}
In fact, the Euler-Lagrange equation applied to the Lagrangian in Eq.~(\ref{lagrangian_geodesic}) gives the geodesic equation
\begin{equation} \label{geodesics}
\frac{d}{d\tau}\left(g_{\mu\nu}\,\frac{dx^\nu}{d\tau}\right) - \frac{1}{2}\,g_{\alpha\beta,\mu}\,\frac{dx^\alpha}{d\tau}\,\frac{dx^\beta}{d\tau} = 0.
\end{equation}
\section{Neutrinos} \label{neutrinos}
\subsection{Probability of oscillation} \label{Probability of oscillation}
We now apply the general results presented in Sec.~\ref{sec_dirac_curved} to the theory of neutrino oscillations. For the $i$-th neutrino generation with mass eigenvalue $m_i$, we consider a neutrino mass eigenstate $\nu_i(x)$ propagating from the point $x_A$, where the source is placed, to the receiver at $x_B$. Neutrinos produced at the source can be described by a flavor state $\nu_{\alpha}(x)$ ($\alpha = e, \mu, \tau$) that is a linear combination of the mass eigenstates $\nu_i(x)$ as
\begin{equation}
\nu_{\alpha}(x) = \sum_i\,U_{\alpha i}^*\,\nu_i(x).
\end{equation}
The mixing matrix $U$, also known as the Maki-Nakagawa-Sakata-Pontecorvo (MNSP) matrix \cite{mns}, is the leptonic analogous of the Cabibbo-Kobayashi-Maskawa matrix that governs quarks mixing. For three generations of neutrinos, the MNSP matrix is parametrized by three mixing angles $\theta_i$, a phase $\delta$ describing CP-violation and two additional phases $\alpha_1$ and $\alpha_2$ that may differ from zero only if neutrinos are Majorana particles, while $\alpha_1=\alpha_2 = 0$ if neutrinos are Dirac particles.
The amplitude for the process in which a neutrino of flavor $\alpha$ at position $x_A$ is detected as a neutrino of flavor $\beta$ at position $x_B$ is given by
\begin{equation} \label{flat1}
\mathcal{A}_{\beta\alpha} = \langle\nu_{\beta}(x_B)|\nu_\alpha(x_A)\rangle = \sum_i \,U_{\alpha i}^*U_{\beta i}\,\langle\nu_i(x_B)|\nu_i(x_A)\rangle.
\end{equation}
We approximate the expression for the spinor $\nu_i(x)$ with the WKB in Eq.~\eqref{ansatz_stodolsky}, where both the action $S_i(x)$ for the $i$-th mass eigenstate and the spin connection $\Gamma_\mu$ appear. As discussed in Refs.~\cite{ahluwalia96}~\cite{ahluwalia97}~\cite{ahluwalia98}~\cite{ahluwalia04}, when discussing neutrino oscillation we might distinguish at least three different scenarios where neutrino oscillate in I) a flat spacetime, II) a curved spacetime in a non-rotating frame and III) a curved spacetime in a rotating frame. In Scenarios I) and II), the neutrino phase difference depends on $S(x)$ only, and not on the spin connection, so that the phase difference reads
\begin{equation} \label{action_stodolsky}
S(m_i,x_B - x_A) \equiv S_i(x_B) - S_i(x_A) = \int_{x_A}^{x_B} p_{\mu}\,dx^{\mu}.
\end{equation}
Since this phase difference is a scalar quantity, it is invariant in all frames.
In Scenario III), an extra contribution to the phase shift appears if two mixing eigenstates $\nu_i(x)$ have different spin orientation, as can be seen from the representation of the spin connection in Eq.~\eqref{spin_connection_gamma5}, where the parity-violating matrix $\gamma^5$ appears~\cite{cardall97}. This additional contribution might be seen as a gravitational analogue to the Zeeman effect~\cite{ahluwalia97}. In the following we will only consider the same spin orientation for the massive neutrinos and we will not treat this contribution. Since in this work we focus on neutrino flavor oscillations induced by the action $S(x)$, in the following we will consider the same spin orientation for the massive neutrinos only, neglecting the interaction of the neutrino spin with the metric resulting from $\Gamma_\mu$ (see Refs.~\cite{konno98}~\cite{dvornikov06}~\cite{alavi13} for additional discussion).
The expression for the probability amplitude of neutrino oscillations on a generic manifold is then
\begin{equation}
\mathcal{A}_{\beta\alpha} = \sum_i \,U_{\alpha i}^*U_{\beta i}\,e^{-i S(m_i, x_B-x_A)}.
\end{equation}
Indicating the phase difference between two mass eigenstates with
\begin{equation} \label{relative_phase}
\Phi_{ij} = S(m_i, x_B-x_A) - S(m_j, x_B-x_A),
\end{equation}
the probability of conversion from flavor $\alpha$ to $\beta$ is
\begin{equation} \label{probability}
\mathcal{P}_{\beta\alpha} = \left|\mathcal{A}_{\beta\alpha}\right|^2 = \sum_{ij} \,U_{\alpha i}^*U_{\beta i}U_{\alpha j}U_{\beta j}^*\,e^{-i \Phi_{ij}}.
\end{equation}
Eq.~(\ref{relative_phase}) can be specialized to the case of relativistic neutrinos, which is the case for various realistic situations. After all, the most stringent upper bound on the sum of the masses of the three known neutrinos species comes from cosmological consideration as $\sum_i m_i < 0.28$eV \cite{bernardis}, while neutrinos often take part in processes involving energies ranging from the keV to hundreds of GeVs.
Motivated by these considerations, we expand the neutrino action in powers of $m_i^2$ as
\begin{equation} \label{taylor_expansion}
S(m_i, x_B - x_A) = \sum_{k=0}^{+\infty} \,\frac{(m_i^2)^k}{k!}S^{(k)}(x_B-x_A),
\end{equation}
where
\begin{equation} \label{taylor_expansion}
S^{(k)}(x_B-x_A) = \frac{\partial^{(k)}\, S(m_i, x_B - x_A)}{\partial^{(k)}\,
m_i^2}\bigg|_{m_i^2=0}.
\end{equation}
For a similar treatment, see also Ref.~\cite{wudka01}. The phase difference in Eq.~(\ref{relative_phase}) reads
\begin{equation}\label{relative_phase_expanded}
\Phi_{ij} = \Delta m_{ij}^2 \,S^{(1)}(x_B - x_A) + \frac{1}{2}\,\Delta m_{ij}^4 \,S^{(2)}(x_B - x_A) + ...\,,
\end{equation}
with
\begin{equation}
\Delta m_{ij}^2 = m_i^2 - m_j^2,\quad \hbox{and}\quad \Delta m_{ij}^4 = m_i^4 - m_j^4 = \left(m_i^2 + m_j^2\right)\,\Delta m_{ij}^2.
\end{equation}
The term corresponding to $k=0$ in the Taylor expansion of Eq.~\eqref{taylor_expansion} is canceled in the difference in Eq.~\eqref{relative_phase} which defines the phase shift $\Phi_{ij}$.
\subsection{Two generations of neutrinos}
The result in Sec.~\ref{Probability of oscillation} can be applied to any number of neutrino generations and for any neutrino energy. However, in many cases of interest like the solar or atmospheric neutrino mixing, the probability of conversion to a specific neutrino flavor is suppressed. If this is the case the MNSP matrix reduces to an element of the SO(2) group and can be parametrized by one mixing angle only $\theta$ as
\begin{equation} \label{rotation_EM}
U =
\left( \begin{array}{cc}
\cos\theta & \sin\theta\\
-\sin\theta & \cos\theta\\
\end{array} \right).
\end{equation}
In the case of two effective neutrino generations, there is only one splitting in mass $\Delta m^2 = m_1^2-m_2^2$ (we assume $m_1 > m_2$), and $\Delta m^4 = m_1^4-m_2^4$. We thus suppress the lower indices in $\Phi = \Phi_{12}$. The probability of conversion is
\begin{equation}\label{probability_conversion}
\mathcal{P}_{\beta\alpha} = \begin{cases}
\sin^22\theta\,\sin^2\Phi,\quad\quad\quad \beta \neq \alpha,\\
1-\sin^22\theta\,\sin^2\Phi,\quad\beta = \alpha.
\end{cases}
\end{equation}
With the series expansion given in Eq.~(\ref{relative_phase_expanded}), Eq.~(\ref{probability_conversion}) reads
\begin{equation}\label{probability_conversion_approx}
\mathcal{P}_{\beta\alpha} = \begin{cases}
\sin^2\theta\,\sin^2 \left[S^{(1)}(x_B - x_A)\,\Delta m^2 + \frac{1}{2}\,S^{(2)}(x_B - x_A)\,\Delta m^4\right],\quad\quad \beta \neq \alpha,\\
1 - \sin^2\theta\,\sin^2 \left[S^{(1)}(x_B - x_A)\,\Delta m^2 + \frac{1}{2}\,S^{(2)}(x_B - x_A)\,\Delta m^4 \right], \quad \beta = \alpha.
\end{cases}
\end{equation}
This is the general expression for the probability of flavor conversion of one neutrino propagating from the source to the receiver. In the next section, we apply the procedure described to obtain the phase difference in some well-known metric spaces.
\section{Application to the Kerr-Newman metric} \label{sec_kerr}
\subsection{General treatment}
Space-time around a charged, rotating body of mass $M$, angular momentum $J$, and charge $Q$, is described by the Kerr-Newman metric,
\begin{equation} \label{kerr_metric}
ds^2 = \left(1-\frac{\Lambda}{\rho^2}\right)\,dt^2 + \frac{2\Lambda\,a\,\sin^2\theta}{\rho^2}\,dt\,d\phi- \frac{\rho^2}{\Delta}\,dr^2 - \rho^2\,d\theta^2 - \left[a^2+r^2 + \frac{a^2\,\Lambda\,\sin^2\theta}{\rho^2}\right]\,\sin^2\theta d\phi^2,
\end{equation}
where, in Planck units, we defined the lengths $r_s = 2M$, $a = J/M$, and $r_Q = Q^2$. The Kerr-Newman metric reduces to the Kerr metric for $r_Q = 0$, to the Reissner-Nordstrom metric for $a = 0$, and to the Schwarzschild metric for $a = r_Q = 0$. We also introduced $\Lambda = r_s\,r - r_Q^2$, $\Delta = r^2 + a^2 - \Lambda$, and $\rho^2 = r^2 + a^2\,\cos^2\theta$. The inverse metric tensor is
\begin{equation} \label{inverse_kerr}
g^{\mu\nu} =
\left( \begin{array}{cccc}
g^{tt} & 0 & 0 & g^{t\phi}\\
0 & -\frac{\Delta}{\rho^2} &0 & 0\\
0 & 0 & -\frac{1}{\rho^2} & 0\\
g^{t\phi} & 0 & 0 & g^{\phi\phi}\\
\end{array} \right),
\end{equation}
where
$$g^{tt} = \frac{\rho^2\,\left(a^2+r^2\right)+ a^2\,\Lambda\,\sin^2\theta}{\Delta\,\rho^2} = \frac{(r^2+a^2)^2}{\Delta\,\rho^2} - \frac{a^2\,\sin^2\theta}{\rho^2},$$
$$g^{t\phi} = \frac{\Lambda\,a}{\Delta\,\rho^2},$$
$$g^{\phi\phi} = -\frac{\Delta - a^2\,\sin^2\theta}{\Delta\,\rho^2\,\sin^2\theta}.$$
Being stationary and axisymmetric, the Kerr metric admits two Killing vector fields $\partial_t$ and $\partial_\phi$, thus, both the energy $E$ and the azymuthal angular momentum $L$ of a particle are conserved. For this reason, the action can be separated as
\begin{equation}
S = E\,t - L\,\phi - W_r(r) - W_\theta(\theta),
\end{equation}
and the HJ Eq.~(\ref{HJ}) for massive neutrinos reads
\begin{equation}
g^{tt} \,E^2 - 2\,g^{t\phi}\,E\,L+g^{\phi\phi}\,L^2 + g^{rr}\,\left(\frac{dW_r}{dr}\right)^2+ g^{\theta\theta}\,\left(\frac{dW_\theta}{d\theta}\right)^2=m^2.
\end{equation}
Since the HJ equation can be written as a sum of a function of $r$ only and of $\theta$ only, as
\begin{equation}
\frac{[(r^2+a^2)\,E - a\,L]^2}{\Delta} - m^2\,r^2 - \Delta\,\left(\frac{dW_r}{dr}\right)^2 = \left(a\,E\,\sin\theta - \frac{L}{\sin\theta}\right)^2 + \left(\frac{dW_\theta}{d\theta}\right)^2 + m^2\,a^2\,\cos^2\theta,
\end{equation}
both sides of the equation can be set equal to the same constant $K$,
\begin{equation}
\left(\frac{dW_\theta}{d\theta}\right)^2 = K - \left(a\,E\,\sin\theta - \frac{L}{\sin\theta}\right)^2 - m^2\,a^2\,\cos^2\,\theta,
\end{equation}
and
\begin{equation}
\left(\frac{dW_r}{dr}\right)^2 = \frac{[(r^2+a^2)\,E-a\,L]^2-\Delta\,(K + m^2\,r^2)}{\Delta^2}.
\end{equation}
The motion on a plane with fixed $\theta = \theta_0$ is possible by choosing the angle given by
\begin{equation}
\left(a\,E\,\sin\theta_0 - \frac{L}{\sin\theta_0}\right)^2 + \left(m\,a\,\cos\theta_0\right)^2 = K,
\end{equation}
in which case, the action reads
\begin{equation}
S = E\,t - L\,\phi - \int\,\frac{\sqrt{[(r^2+a^2)\,E-a\,L]^2-\Delta\,(K + m^2\,r^2)}}{\Delta}\,dr.
\end{equation}
According to Eq.~(\ref{taylor_expansion}), expanding the action to its second order in $m^2$ gives
\begin{equation}\label{S1_kerr}
S^{(1)} = \int\,\frac{r^2\,dr}{2\sqrt{[(r^2+a^2)\,E-a\,L]^2-\Delta\,K}},
\end{equation}
and
\begin{equation}\label{S2_kerr}
S^{(2)} = \int\,\frac{\Delta\,r^4\,dr}{4\left\{[(r^2+a^2)\,E-a\,L]^2-\Delta\,K\right\}^{3/2}}.
\end{equation}
When $Q\to 0$, the Kerr-Newman metric reduces to the Kerr metric describing a rotating, charge-less black hole. In this case, the expression for $S^{(1)}$ in Eq.~(\ref{S1_kerr}) reduces to that in Eq.~(14) of Ref.~\cite{wudka01}, where the expression for neutrino oscillations in a Kerr metric is obtained to its first order in $\Delta m^2$.
\subsection{Radial propagation}
We now deal with the case of radial propagation $L = K = 0$, where we find
\begin{equation} \label{radial_Kerr1}
S^{(1)} = \int\,\frac{r^2\,dr}{2E\,(r^2+a^2)} = \frac{1}{2E}\,\left[r_R-r_A - a\,\left(\arctan\frac{r_B}{a}-\arctan\frac{r_A}{a}\right)\right],
\end{equation}
and
$$S^{(2)} = \int_{r_A}^{r_B}\,\frac{(r^2-r\,r_s+a^2+r_Q^2)\,r^4\,dr}{4E^3\,(r^2+a^2)^3} = $$
\begin{equation} \label{radial_Kerr2}
= \frac{1}{32\,E^3}\,\left[8r + \frac{4 a^2 (r - 2 r_s)-5 \,r_Q^2 r}{a^2 + r^2} + \frac{2a^2\,(r_Q^2 r + a^2\,r_s)}{(a^2 + r^2)^2} - \frac{3 (4 a^2 - r_Q^2) \arctan\frac{r}{a}}{a} - 4 r_s\,\ln\left(a^2 + r^2\right)\right]_{r_A}^{r_B}.
\end{equation}
\subsection{Limits for small and large values of the angular momentum}
Since neither $r_Q$ nor $r_s$ are contained in the expression for the phase difference $\Phi$ at first order in Eq.~\eqref{radial_Kerr1}, we need to discuss limits of this term when $a \ll r_B - r_A$ or $a \gg r_B - r_A$ only.
For $a \ll r_B - r_A$, the phase difference expressed in the first-order term in Eq.~\eqref{radial_Kerr1} reduces to the result obtained in the flat geometry, while in the opposite limit $a \gg r_B - r_A$ we find an additional factor of two. In formulas,
\begin{equation}
S^{(1)} \approx \frac{|r_B - r_A|}{E}\,\begin{cases}
\frac{1}{2},\quad \hbox{for $a \ll |r_B - r_A|$},\\
1,\quad \hbox{for $a \gg |r_B - r_A|$}.
\end{cases}
\end{equation}
The second-order term in Eq.~\eqref{radial_Kerr2} contains all three parameters $r_s$, $r_Q$, and $a$. Here, we notice that for given $r_s$ and $r_Q$ and in the limit $a \ll r_s, r_Q, |r_B-r_A|$, we obtain
\begin{equation}
S^{(2)} \approx \frac{1}{4E^3}\,\bigg\{\left[\left(r_B - r_A \right)\,\left(1+\frac{r_Q^2}{r_A\,r_B}\right)- r_s\,\ln\frac{r_B}{r_A}\right] + a^2\,\frac{2 r_Q^2 + 4 r^2 - 3 r r_s}{2r^3}\bigg|_{r_A}^{r_B}\bigg\}.
\end{equation}
The term in the squared brackets corresponds to the second-order correction to the neutrino phase difference in the metric of a non-rotating charge black hole.
\subsection{Small values of the angular momentum and the charge}
We now work in the limit $a \sim r_Q \ll r_s \ll |r_B - r_A|$, which corresponds to a Lense-Thirring metric with a slowly-rotating and charged object at the center of the coordinates. Under these conditions, the expressions for the phase shift in Eqs.~\eqref{radial_Kerr1} and~\eqref{radial_Kerr2} reduces to
\begin{equation} \label{expression_small_kerr}
\Phi = \Phi^{\rm Sch} - \frac{\Delta m^2}{2 E}\,\frac{a^2}{r_A\,r_B}\,|r_B-r_A| + \frac{\Delta m^4}{8 E^3}\,\frac{r_Q^2 - 2a^2}{r_A\,r_B}\,|r_B-r_A|,
\end{equation}
where $\Phi^{\rm Sch}$ is the expression for the phase shift in the Schwarzschild metric previously obtained by Godunov and Pastukhov~\cite{godunov09},
\begin{equation}
\Phi^{\rm Sch} = \frac{\Delta m^2}{2E}\,\left|r_B - r_A\right| + \frac{\Delta m^4}{8E^3}\left(r_B - r_A - r_s\,\ln\frac{r_B}{r_A}\right).
\end{equation}
Notice that the gravitational effects due to the mass $r_s$ and the charge $r_Q$ enter the term proportional to $\Delta m^4$ only if the phase oscillation is written in terms of the coordinate difference $r_B - r_A$, while the effects of rotation also enter the first order term $S^{(1)}$.
\subsection{Proper length}
It is possible to write analytically the expression for the proper length in the Kerr-Newman metric along the plane $\theta = \pi/2$ as
\begin{equation}
L_p = \int_{r_A}^{r_B} \sqrt{-g_{rr}}\,dr' = \sqrt{r^2 - r_s\,r + a^2+r_Q^2}+ \frac{r_s}{2}\,\ln\left(2r-r_s + 2\sqrt{r^2 - r_s\,r + a^2+r_Q^2}\right)\bigg|_{r_A}^{r_B}.\end{equation}
We now work in the limit $a \sim r_Q \ll r_s \ll |r_B - r_A|$, in which
\begin{equation}
L_p = L_p^{\rm Sch} + \frac{a^2+r_Q^2}{r-r_s + \sqrt{r\,(r-r_s)}}\bigg|_{r_A}^{r_B} \approx L_p^{\rm Sch} - \frac{a^2+r_Q^2}{2\,r_A\,r_B}\,|r_B-r_A|.
\end{equation}
Here, we introduced the proper length in the Schwarzschild metric
\begin{equation}
L_p^{\rm Sch} = \sqrt{r^2 - r_s\,r} + \frac{r_s}{2}\,\ln\left(2r-r_s + 2\sqrt{r^2-r_s\,r}\right)\bigg|_{r_A}^{r_B} \approx r_B-r_A + \frac{r_s}{2}\,\ln\frac{r_B}{r_A}.
\end{equation}
The coordinate length is then written in terms of the proper length as
\begin{equation}
|r_B-r_A| \approx L_p\,\left(1 + \frac{a^2+r_Q^2}{2\,r_A\,r_B}\right) - \frac{r_s}{2}\,\ln\frac{r_B}{r_A}.
\end{equation}
Following Fornengo {\it et al.}~\cite{fornengo97}~\cite{fornengo99} and Crocker {\it et al.}~\cite{crocker04}, we introduce the local energy $E^{\rm loc}(r_B)$ measured by an observer at rest at the position $r_B$, as
\begin{equation}
E^{\rm loc}(r_B) = E/\sqrt{g_{tt}(r_B)} = \frac{r_B\,E}{\sqrt{r_B^2- r_s\,r_B + r_Q^2}}\approx E \,\left(1+\frac{r_s}{2r_B} - \frac{r_Q^2}{2r_B^2}\right).
\end{equation}
At first-order, the phase shift in Eq.~\eqref{expression_small_kerr} in the local coordinates introduced is then written as
\begin{equation} \label{expression_small_kerr1}
\Phi = \frac{\Delta m^2\,L_p}{2E^{\rm loc}(r_B)}\,\left[1 + \frac{r_Q^2\,L_p}{2r_A\,r_B^2} - \frac{a^2}{2\,r_A\,r_B} - \frac{r_s}{2}\,\left(\frac{1}{L_p}\ln\frac{r_B}{r_A} + \frac{1}{r_B}\right)\right],
\end{equation}
and the expression reduces to the ordinary result $\Phi = \Delta m^2\,L_p/2E^{\rm loc}(r_B)$ in the Schwarzschild limit $r_s = a = r_Q = 0$.
\section{Application to the Friedmann-Robertson-Walker metric} \label{sec_FRW}
We consider the line element for a flat, conformal FRW metric
\begin{equation}
ds^2 = a^2(\eta)\,(d\eta^2 - dr^2- r^2d\theta^2 - r^2\sin^2\theta\,d\phi^2),
\end{equation}
where $\eta$ is the conformal time. The scale factor $a = a(\eta)$ describes the expansion of the Universe through the Friedmann equation, see Eq.~(\ref{frieldmann_eq}) below, and it is normalized so that at present time it is $a(0) = 1$. Azymuthal angular momentum $L$ is a conserved quantity in the FRW metric, while the energy is not since $\partial_\eta$ is not a Killing vector of the FRW metric. We look for the additional invariants in the metric by writing the neutrino action as
\begin{equation}
S = W(\eta) - W_r(r) - W_\theta(\theta) - L\,\phi,
\end{equation}
and the HJ Eq.~(\ref{HJ}) is
\begin{equation}
\left(\frac{dW_\eta}{d\eta}\right)^2 -\left(\frac{dW_r}{dr}\right)^2 - \frac{1}{r^2}\,\left(\frac{dW_\theta}{d\theta}\right)^2 - \frac{L^2}{r^2\,\sin^2\theta} = m^2\,a^2(\eta).
\end{equation}
This differential equation is separable into a set of three equations as
$$\left(\frac{dW_\eta}{d\eta}\right)^2 = m^2\,a^2(\eta) + E^2,$$
$$\left(\frac{dW_r}{dr}\right)^2 = E^2 - \frac{K^2}{r^2},$$
$$\left(\frac{dW_\theta}{d\theta}\right)^2 = K^2 - \frac{L^2}{\sin^2\theta},$$
where we introduced two new constants $E$ and $K$. Fixing the plane in which the motion occurs by setting $\sin\theta = L/K$, the action is
\begin{equation}\label{action_FRW}
S = \int\,\sqrt{m^2\,a^2(\eta) + E^2}\,d\eta - \int\,\sqrt{E^2 - \frac{K^2}{r^2}}\,dr - L\,\phi.
\end{equation}
Eq.~(\ref{action_FRW}), expanded to the second order in $m^2$ according to Eq.~(\ref{taylor_expansion}), gives
\begin{equation}\label{FRW_expansion}
S^{(1)} = \int \frac{a^2\,d\eta}{2E},\quad\hbox{and}\quad S^{(2)} = \int \frac{a^4\,d\eta}{4E^3}.
\end{equation}
To simplify these integrals, we use the definition for the red-shift $z$ in terms of the conformal factor,
\begin{equation}
1+z = \frac{1}{a(\eta)},
\end{equation}
together with the Friedmann equation
\begin{equation} \label{frieldmann_eq}
H(z) = H_0\, f(z),
\end{equation}
where the Hubble rate is
\begin{equation} \label{friedmann}
H(z) = \frac{1}{a^2(\eta)}\,\frac{d\,a(\eta)}{d\eta} = -\frac{dz}{d\eta}.
\end{equation}
Here, $H_0 = H(z=0)$ is the present Hubble rate, and we defined the function
\begin{equation}
f(z) = \sqrt{\Omega_r\,(1+z)^4+\Omega_m\,(1+z)^3+\Omega_k\,(1+z)^2+\Omega_\Lambda},
\end{equation}
which accounts for the content of the Universe and the equations of state for radiation, cold matter, curvature, and dark energy, respectively. With these substitutions, the relative phase in Eq.~(\ref{relative_phase_expanded}) for two neutrino generations is
\begin{equation}\label{FRW_phase}
\Phi = \frac{\Delta m^2}{2E}\,d_1(z_1) + \frac{\Delta m^4}{8E^3}\,d_2(z_1),
\end{equation}
where $d_1(z_1)$ is the cosmological distance from the source, at redshift $z_1$, to the detector at $z=0$,
\begin{equation} \label{distance1}
d_1(z_1) = \frac{1}{H_0}\int_0^{z_1}\frac{dz}{(1+z)^2f(z)};
\end{equation}
we also defined the function
\begin{equation} \label{distance2}
d_2(z_1) = \frac{1}{H_0}\,\int^{z_1}_0\frac{dz}{(1+z)^4\,f(z)}.
\end{equation}
For close ($z_1 \ll 1$) astrophysical sources of neutrinos, we recover the usual formula
\begin{equation}
d_1(z_1) \approx d_2(z_1) \approx \frac{z_1}{H_0} = r_B-r_A.
\end{equation}
For more distant sources the curvature of the Universe affects measurements, as shown in Fig.~\ref{plot_distance} where we neglect the curvature and radiation terms $\Omega_k = \Omega_r = 0$, and we use $\Omega_m = 0.27$ and $\Omega_\Lambda = 1 - \Omega_m$. The plot in Fig.~\ref{plot_distance} shows that both $d_1(z_1)$ and $d_2(z_1)$ reach a constant value, thus the phase difference results constant for sources with redshift $z_1 > 2$. The constancy of the function $d_1(z_1)$ for large values of $z_1$ has also been noticed by Silk and Stodolsky~\cite{silk2006}, in the context of the dilution of the cosmological flux of weakly interacting particles.
\begin{figure}[h!]
\begin{center}
\includegraphics[width=10cm]{plot_distance.pdf}
\caption{The functions $d_1(z_1)$ (blue solid line) and $d_2(z_1)$ (red solid line), in units of $1/H_0$, computed from Eq.~(\ref{distance1}) and Eq.~(\ref{distance2}), respectively. }
\label{plot_distance}
\end{center}
\end{figure}
This behavior is retained even if we restrain from expanding the action in Eq.~(\ref{action_FRW}) in Taylor series. In fact, writing the action as
\begin{equation}
S = m\,d(z_1) - \int\,\sqrt{E^2 - \frac{K^2}{r^2}}\,dr - L\,\phi,
\end{equation}
where, setting $\epsilon = E/m$, we defined
\begin{equation} \label{distance_full}
d(z_1) = \frac{1}{H_0}\,\int_0^{z_1}\,\sqrt{\frac{1}{(1+z)^2} + \epsilon^2}\,\frac{dz}{f(z)},
\end{equation}
we obtain that the function $d(z_1)$ reaches a constant value when $z_1 \gg 1$, as shown in Fig.~\ref{plot_distance_full} for different values of $\epsilon$.
To the best of our knowledge, the expression for the phase difference in the oscillation of neutrino mass eigenstates over a FRW metric in Eq.~(\ref{FRW_phase}) has never been derived before.
\begin{figure}[h!]
\begin{center}
\includegraphics[width=10cm]{plot_distance_full.pdf}
\caption{The function $d(z_1)$, in units of $1/H_0$, computed from Eq.~(\ref{distance_full}) for $\epsilon = 0.5$ (green solid line), $\epsilon = 1$ (red solid line), and $\epsilon = 2$ (blue solid line). }
\label{plot_distance_full}
\end{center}
\end{figure}
\section{Concluding remarks}
In this paper we have reviewed the mathematics of the Dirac equation in a curved space-time and its application to neutrino oscillations. In particular, we have derived the method of calculating the phase shift in flavor neutrino oscillations by a Taylor-expansion of the action in orders of $m^2$.
In Sec.~\ref{sec_kerr}, we have applied this method by evaluating the correction to the phase difference of neutrino mass eigenstates due to the gravitational field produced by a rotating and charged black hole, described by the Kerr-Newman metric. We have shown that, for the case of radial propagation, the effects of the black hole rotation are present at the first order term in the mass splitting $\Delta m^2$ and dominate the phase difference with respect to the charge, which appear at the second order. For a charge-less and rotation-less black hole, we have recovered the results obtained in the previous literature.
In addition, in Sec.~\ref{sec_FRW} we have applied the Taylor series method to the case of cosmological neutrinos propagating in an expanding, flat Friedmann-Robertson-Walker metric. After discussing the equations for the invariants of motion, we have obtained an expression for the phase difference for neutrino mass eigenstates in a $\Lambda$-CDM model. We have shown that, for distant sources $z_1 \gg 1$, the phase difference is independent of distance, thus neutrino oscillations cannot be used to infer the nature of the beam. For close sources $z_1 \ll 1$, we have recovered the usual result that the phase difference is proportional to the distance itself.
\section*{Acknowledgments}
The author would like to thank Paolo Gondolo (U. of Utah) for useful discussions on neutrino oscillations.
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 6,435
|
Q: Fetch External Page and use JSON in it JQueryMobile I m using jquerymobile, I want to put content inside the page fetched by $.mobile.changePage('external.html') or page called directly when we clicked on link, like:
My app has two physical files, index.html and external.html.
Index.html anchor link call external.html, but during changing the view from index.html to external.html, I m getting json from another server that I want to use in that
$.mobile.changePage('external.html') is fetching page properly but display it imediately and ajax call is not even completed.
var ProductDetailEvent = function(){
thisProd = $(this);
$.mobile.showPageLoadingMsg();
Product.id = thisProd.attr('data-id');
Product.name = thisProd.find('h3').html();
$.mobile.changePage( "productView.html", {
transition: "pop",
reverse: false,
changeHash: false
});
}
////LOAD DATA FOR E PAGES::4
$(document).bind( "pageload", function( event, data ){
if(data.page[0].id != null)
switch(data.page[0].id)
{
case 'detailView':
var pageData = {
page: data.page,
header: Product.name,
url: 'pDetail&productId='+Product.id,
loadDataCB: function(_resp){
strHtml = '';
img = 'http://10.0.1.64/magento/media/catalog/product/' + _resp.image;
strHtml += '<div style="text-align:center"><img src="'+img+'" width="50%" /><br/><b>Description:</b>'+_resp.short_description;
strHtml += '</div><br/><input type="button" value="Add to Cart" data-role="button" /><br/><div class="ui-grid-a ui-bar-d">\
<div class="ui-block-a"><div class="ui-bar ui-bar-d" >Price</div></div>\
<div class="ui-block-b"><div class="ui-bar ui-bar-d" >'+_resp.price+'</div></div>\
<div class="ui-block-a"><div class="ui-bar ui-bar-d" >Weight</div></div>\
<div class="ui-block-b"><div class="ui-bar ui-bar-d" >'+_resp.weight+'</div></div>\
</div>';
return strHtml;
}
};
loadExternalView(pageData);
break;
case 'externalView':
break;
}
});
////Load List::Inner Pages///
var loadExternalView = function(_data)
{
var NPage = _data.page;
pHeader = NPage.find('.header h1').html(_data.header);
var pContent = NPage.find('.content');
ServerCall(_data.url,function(result){
var strHtml = _data.loadDataCB(result);
pContent.html(strHtml);
});
};
var ServerCall = function(_url,callback)
{
$.ajax({
type: "POST",
url: 'consumeservice/magentoapi.php?option='+_url,
data: '',
dataType:'json',
success:
function(result) {
callback(result);
},
error: function (data, status, e)
{
alert("error:"+e);
}
});
};
External Page HTML:
<!DOCTYPE html>
<html>
<head>
<meta charset="utf-8" />
</head>
<body>
<!-- Begin Page 4 -->
<div id="detailView" data-role="page">
<div class="header" data-role="header" data-icon="back" data-theme="a">
<h1></h1>
</div>
<div class="content" data-role="content">
<div class="ui-grid-a ui-bar-d">
<div class="ui-block-a"><div class="ui-bar ui-bar-d" >A</div></div>
<div class="ui-block-b"><div class="ui-bar ui-bar-d" >B</div></div>
</div>
</div>
</div>
<!-- End Page 4-->
</body>
</html>
I don't want to create too many internal pages b/c it will affect the performance and increase the page size.
When external page is called it immediately display the page on screen, I want to change it content and then render the page.
Thanks
A: Do you want to change the content BEFORE showing the page? If so, bind 'pagebeforecreate':
$('#pageID').live('pagebeforecreate',function(){
//Change content
});
Or do you want to show the page, then change the content and update the page? If so, use .trigger("create") on the div:
//Change content first
$('#pageID').trigger('create');
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 6,436
|
SiFi Networks to Build USA's Largest Privately Funded Open Access FiberCity™
International fiber optic network developer SiFi Networks (SiFi), whose aim is to revolutionize the North American telecoms market, will deliver the USA's largest privately funded open access FiberCity™ in Fullerton, California.
Fullerton is set to become the biggest network of its kind in America and will be funded by the Smart City Infrastructure Fund, a global investment fund managed by Whitehelm Capital and backed by APG, the largest pension delivery organization in the Netherlands.
SiFi aims to deliver more networks throughout the USA in the same manner. Fullerton will be the first FiberCity™ with several cities already in line to be next.
"We are excited to deliver our first FiberCity™ in the USA, an investment that sets the standard for fiber optic infrastructure as a core utility. We believe that our business model can transform the telecoms market in the USA. Privately funded, open access networks will not only benefit residents and businesses, but also provide citywide platforms for Smart City applications including 5G and more," stated Ben Bawtree-Jobson, CEO of SiFi Networks.
The network will provide a significant upgrade to internet speeds and accommodate the growing demand for data from next generation devices in households and businesses. It will also facilitate new Smart City initiatives in key government services such as traffic control, street lighting and emergency services. The network will also provide a platform for the future expansion of 4G and 5G cellular networks into the area.
"We are delighted to welcome SiFi Networks and its ISP partners Ting and GigabitNow to the city," stated Fullerton City Manager, Ken Domer. "Having a true fiber optic network passing every part of the city is an amazing opportunity for Smart City applications, bringing competition to the city's communication needs, and creating enhanced opportunities for economic development."
SiFi funds, builds and operates the network whilst partnering with Internet Service Providers who bring their marketing and customer service expertise to deliver retail services (internet, TV and voice) to residents and businesses throughout the entire city without demographic segmentation.
The Internet Service Providers in Fullerton will be GigabitNow and Ting, both exceptional providers with excellent customer service levels and competitive pricing.
"GigabitNow is pleased to be delivering true Gigabit Internet speeds at an affordable price to the residents and businesses of Fullerton," said Stephen Milton, CEO of GigabitNow. "Working with SiFi over the last several years to find ways to bring fast, reliable, Internet to cities across the United States has meshed perfectly with GigabitNow's overall goal of easy turnkey Internet solutions for communities of all sizes. We are eager to start providing awesome service to the community of Fullerton!"
Elliot Noss, Ting CEO said "Fullerton will be great for our business, and Ting will support a thriving economy and quality of life there. We are pleased to embark on a California footprint, and to see alternative business models emerging in the ongoing fiberization of America."
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 592
|
Q: UIButton State and progress of selector I am having a bit of trouble with displaying the progress of a longer mainthread action (needs to be in the main thread).
The action is called by pressing a button.
-(void)getCSVExport:(id)sender{
...
NSString *filePath = [path stringByAppendingPathComponent:fileName];
NSData *csvData = [NSData dataWithContentsOfFile:filePath];
if (nil == csvData) {
_progressView.hidden = NO;
[self.view bringSubviewToFront:_progressView];
_progressView.progress = 0;
csvData = [self generateCSVExportForMonth:_monthToExportInt];
[csvData writeToFile:filePath atomically:YES];
_progressView.hidden = YES;
}
...
}
within the funktion generateCSVExportForMonth: i am updating the progress with _progressView.progress = newValue.
i now have 2 problems:
1) when pressing the button that calls getCSVExport: the button remains highlighted until the call is finished.
2) the progressView does never show up, let alone update itself.
information: the call takes between .5 and 2 seconds depending on the device.
any ideas where i've gone wrong?
// EDIT: new version with backgroundThread:
[self.view bringSubviewToFront:_progressView];
_progressView.progress = 0;
[self performSelector:@selector(assignCSVData:) onThread:[NSThread new] withObject:csvData waitUntilDone:YES];
_progressView.hidden = YES;
and the time expensive call:
-(void)assignCSVData:(NSData*)data{
data = [self generateCSVExportForMonth:_monthToExportInt];
}
this results in a deadlock upon the performSelector call.
A: The problem is that your main thread is blocked. That's exactly the reason for using background threads for things that take longer, because you don't want the GUI to freeze.
I don't see why something like parsing a CSV file absolutely has to be on the main thread. You'll have to do it in the background (or live with the bad user experience of a frozen GUI).
You have a few options how to actually implement something like this.
*
*Use NSObject's performSelectorInBackground:withObject:
Put the parsing code in a separate method and start it on a background thread using:
[self performSelectorInBackground:@selector(parseMethod) withObject:csvData];
At the end of that method you call some method on the main thread to notify it that the parsing is finshed.
[self performSelectorOnMainThread:@selector(parsingDone:) withObject:result waitUntilDone:NO];
*Use Grand Central Dispatch (GCD) to run some code in the background using the block syntax. Also quite simply, but a little bit more complicated syntax and semantics wise, if you're used to Objective-C and the Cocoa APIs.
*Use NSOperation and NSOperationQueue. Probably a little bit of an overhead for your purpose. Though you can also easily add a new operation to a queue by calling addOperationWithBlock without subclassing NSOperation.
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 2,310
|
Q: how do I create a program in windows that can be activated by pressing short cut key instead of clicking? I need to create a GUI working on windows that can be activated by pressing short cuts.
1. is it possible without setup class?
2. if not possible, just achieve pressing hotkeys and activate my program--how should i code it out--would be enough
thanks (I am using Qt for vs2012 add in to do the GUI)
A: I put some code up that starts a thread that does this. It is windows specific, but it does the job.
Clipboard Shortcut/Hotkey binding with Qt outside of application
One alternative to all of this, is to go to a shortcut to your program, go to its Properties, and then click on the shortcut area and type your desired shortcut. As long as it doesn't overlap with existing hotkeys that are registered in windows, it should work, without a hidden presence of your app in the system tray or some other background thread.
Hope that helps.
A: libqxt offers a QxtGlobalShortcut class that does what you want.
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 5,715
|
@import SocketIO;
@interface Help : NSObject
@property (nonatomic,strong) SocketIOClient *socket;
@end
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 9,809
|
"You Okay, Sis?" #WorldSuicidePreventionDay
There are many falsehoods some black people believe, and that other people believe about us. But none such falsehood is more destructive than "Black people don't commit suicide. Only white people do that." Over the years, that stereotype has been challenged as we've witnessed high-profile black women succumb to their internal demons and bid the world adieu.
Remember Karyn Washington? The founder of For Brown Girls and #DarkSkinRedLip and advocate of black girls and women embracing their unique beauty and dark skin ushered herself out of this world on April 19, 2014.
We lost a staunch advocate in Karyn. What would the world be like if she would have held on? How much awesomeness did we miss out on because this beautiful young woman felt hopeless?
So many of us suffer in silence because we're told that black women aren't supposed to ever feel overwhelmed, depressed or anxious. I've literally been sitting in a pulpit when a preacher told the congregation that seeking psychological help is a expression of you lack of faith that God will deliver you. Would a cancer diagnosis also be an expression of a lack of faith?!
Little girls get mocked when they cry. White girls get hugs and huddles of people rushing to comfort them. We aren't allowed to be soft. That's for white girls. We're not supposed to suffer mental illness. Just say the Lord's Pray and read the 23 Psalms, turn around three times and ta-daa! By your faith you are healed.
Sometimes we surround ourselves with toxic people. Take Titi Branch, co-founder of Miss Jessie's. Her sociopath of a boyfriend, Anthony Spadafora, "used her as an atm" and took over $400,000 of her money to start his beard business, Maestro Classics (please, male readers and fans with beards, find another guy to buy your grooming products from). He also pulled money from her to work on his house, and got her to give him a $135,000 interest-free loan. After her suicide, Spadafora claimed that Branch rewrote her will to award him with 50% of everything. What a walking piece of stinking excreta.
Don't be afraid to appear weak. Don't be afraid to ask for help. Don't let ANYONE shame you about your mental wellness. It can be hard sometimes, I know. When I revealed my General Anxiety Disorder diagnoses, I was mocked by some so-called BWE women who should have known better. How are you going to tell people to seek therapy while simultaneously mocking people and calling them "crazy" and "mentally ill?!" WTF…
But I never let their judgements keep me from taking care of me, and you need to do that same. Thanks to Obamacare, mental health services are now available to everyone. Not to diss the church, but please don't use that as your sole source of counseling. There are many ways to overcome, and some may include intensive behavioral therapy and/or medication.
National Suicide Prevention Lifeline – 1‑800‑273‑TALK (8255) or Live Online Chat
If you or someone you know is suicidal or in emotional distress, contact the National Suicide Prevention Lifeline Site exit disclaimer. Trained crisis workers are available to talk 24 hours a day, 7 days a week. Your confidential and toll-free call goes to the nearest crisis center in the Lifeline national network. These centers provide crisis counseling and mental health referrals.
SAMHSA Treatment Referral Helpline – 1‑877‑SAMHSA7 (1‑877‑726‑4727)
Get general information on mental health and locate treatment services in your area. Speak to a live person, Monday through Friday from 8 a.m. to 8 p.m. EST.
Enjoying the Great Outdoors: Hiking and ...
2021: The Year BW Should Stay Home...
PSA: Actually, Bonnets Don't Belong On...
Pink Pill Spotlight: Naomi's Dating St...
Pink Pill Spotlight: Meet Naomi...
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 9,219
|
Top 10 People Named Linda
htoutlaws2012
1 Linda Ronstadt Linda Maria Ronstadt is an American popular music singer. She has earned 11 Grammy Awards, three American Music Awards, two Academy of Country Music awards, an Emmy Award, an ALMA Award, and numerous United States and internationally certified gold, platinum and multiplatinum albums.
The most beautiful woman of this world!
2 Linda Evangelista Linda Evangelista is a Canadian model. She is regarded as one of the most accomplished and influential models of all time, and has been featured on over 700 magazine covers.
3 Linda Fiorentino Linda Fiorentino is an American actress. She became known for her leading role in the 1985 coming-of-age drama film Vision Quest; then, in the same year she earned wide recognition for her role in the action film Gotcha!
4 Linda McMahon
5 Linda Blair
6 Linda Cardellini Linda Edna Cardellini is an American actress. She is known for playing Lindsay Weir on Freaks and Geeks, Samantha Taggart on ER, and Meg Rayburn on Bloodline.
7 Linda Hunt
8 Linda Chung
9 Linda Hamilton
10 Linda Chapman
11 Linda Davis
Best Linda Fiorentino Movies Best Linda Ronstadt Songs Best Linda Hamilton Movies of the '80s Best Linda Hamilton Movies of the '90s Best Linda Hamilton Movies of the '00s
1. Linda Ronstadt
2. Linda Evangelista
3. Linda Fiorentino
All Top Ten Lists9People
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|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 4,704
|
export default (grunt) => {
grunt.initConfig({})
grunt.registerTask("default", [])
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 8,365
|
\section{Introduction}
Trapping and cooling Bose-Fermi mixtures of dilute quantum gases has
opened a wide area of research in atomic physics. The interactions
between bosonic and fermionic species interconnect two systems of
fundamentally different quantum statistics. The diluteness of the
gaseous mixtures allows one to treat the interactions between particles
in terms of binary collisions. In consequence we can replace the real
inter-atomic potential by a pseudo-potential characterized by only
one parameter, the $s$-scattering length. The latter is experimentally\cite{ferlaino,gunter,ospelkaus,best}
tunable by exploiting optically or magnetically induced Feshbach resonances\cite{inouye}.
Despite its simplicity the interaction potential (mathematically ill
defined\cite{galindo}) of the ultra-cold multi-component gases confined
in optical lattices is responsible for a wealth of novel quantum phases\cite{lewenstein,albus}
including charge density waves (CDW)\cite{mering,mathey}, as well
as supersolid behavior\cite{buchler,titvinidze,orth}. The nature
of the phase transition and qualitative phase diagram for one-component
bosonic system can be inferred based on very simple arguments\cite{fisher}.
When tunneling between lattice sites of the bosons is suppressed,
compared with point-like interaction between them, the system can
undergo a quantum phase transition between a superfluid (SF) phase
(characterized by large number fluctuations at each lattice site),
and a Mott insulating (MI) phase where each lattice site is occupied
by precisely an integer number of bosons without any number fluctuations.
Adding to a bosonic system a fermionic ingredient and allowing for
the mutual repulsion or attraction between species of different statistics
strongly affects the equilibrium properties. Increasing the boson-fermion
repulsion drives the system towards spatial separation whereas attraction
gives rise to implosion\cite{capuzzi,akdeniz}. The dynamics underlying
the phase transitions in the Bose-Fermi mixtures is produced by the
small changes of the bosonic density which induce a modulation of
the fermionic density. As a consequence of the feedback of the fermionic
perturbation a shift of the bosonic energy occurs, thereby inducing
an additional attraction or repulsion that changes the original interaction
between bosons\cite{mazzarella}. In the case of deep optical lattices
and small densities, the coherent description of the system provided
by the Gross-Pitaevskii equation is not reliable due to rising effects
of correlation. The experimental data clearly demonstrated that adding
a fermionic cloud to strongly interacting bosons always results in
a decay of visibility of the interference pattern in time-of-flight
images\cite{best,gunter,ospelkaus}. Moreover, the scale of disappearance
of the coherence in the mixtures is different for attractive and repulsive
scattering lengths\cite{best}. To predict such behavior theoretically
one can include the more general, than one-component Bose-Hubbard
(BH), multi-band model. In mentioned approach if the higher-band renormalization
of the boson parameters is dominant over the fermion screening of
the interaction, the Mott-insulating lobes in the Bose-Hubbard phase
diagram are enhanced for either sign of the Bose-Fermi interactions\cite{lutchyn,tewari}.
On the other hand inclusions of the retardation effects\cite{akdeniz-1}
(which arises from the presence of very low energy excitations in
a Fermi sea) give rise to so-called orthogonality catastrophe\cite{refael}.
Another approach to quantum mixtures of particles of unequal masses,
when the difference in the tunneling amplitudes between heavy bosons
and light fermions is large enough to neglect quantum nature of the
bosons, provides to description of the system in Fermi-Bose version
of the Falicov-Kimball model\cite{iskin}. The mutual interactions
of bosons and fermions can affect the spectrum of collective excitations
in the collisionless regime as the mixture goes toward either demixing
or collapse\cite{capuzzi}. It has been shown that mode-mode coupling
effects may arise when sound velocity of the Bose gas is comparable
to the Fermi velocity of the fermions\cite{yip}. The energy spectra
of the bosonic and fermionic mixtures and phase diagram were also
obtained by the field theory methods\cite{han}, however calculated
phase boundary does not change the structure and only shifts the chemical
potential. The properly constructed effective theory lead to an effective,
fermion mediated, long-range interaction between bosons with alternating
sign that is the origin of the CDW and can explain the MI-CDW phase
separation\cite{mering}. There is also another possibility of the
analysis of the mixtures of atoms with different statistics where
the second species is strongly localized on random sites which can
lead to random shifts of the on-site energies and, in consequence,
the disorder with discrete probability distribution is created \cite{krutitsky}.
Recently the experiments \cite{catani} on a harmonically trapped
mixtures of atomic bose-bose gases show that the presence of relevant
fraction of the $^{41}$K bosonic species modifies the quantum phase
transition occurring in \emph{$ $}$^{87}$Rb inducing a significant
loss of coherence similarly to bose-fermi systems that can be explained
in the mean-field theory framework\cite{buosante}.
The aim of this work is to study the superfluid to Mott-insulator
zero-temperature phase transition by means of the Bose-Fermi-Hubbard
model in two- ($2D$) and three-dimensional ($3D$) optical condensates.
In order to find a phase boundary for BF mixtures very sophisticated
methods and calculations are required. Only several theoretical works
concentrated on the inherent difficulty of dealing with BF Hubbard
Hamiltonian originates from the non-perturbative nature of the model
and retardation effects. To elucidate the quantum phase transition
in optical lattices, where the kinetic energy scale is less than the
dominating repulsive energy and density-density coupling between species
with different statistics comes into play, we have adopted a theoretical
approach for strongly interacting fermions \cite{kopec} to the BF
Hubbard model in a way to include the effects of particle number fluctuations
and make the qualitative phase diagrams more quantitative \cite{polak}.
To facilitate this task, we employ a functional integral formulation
of the theory that enables to perform functional integration over
fields defined on different topologically equivalent classes of the
$\mathrm{U}\left(1\right)$ group, i.e., with different winding numbers.
An inclusion of the winding numbers (comes from periodicity of the
phase variables) is unavoidable in order to properly construct the
phase diagram and the Poisson re-summation formula turns out to be
very useful for derivation of the topological term of the partition
function. The quantum rotor representation method we use is deeply
rooted in the gauge symmetries of the model. We construct an invariant
theory introducing an appropriate $\mathrm{U}\left(1\right)$ gauge
transformation. In Sec. II we review the Hamiltonian for the system
and show the connections of the parameters to the experimentally measured
quantities in optical lattices. Sec. III contains description of the
method we use and can serve a guidance to obtain the critical line
equation presented in Sec. IV. Before showing the phase diagrams for
the Bose-Fermi Hubbard model in the quantum rotor description we make
some general remarks in Sec. V concern the phase boundary equation
and compare our results with the diagrammatic perturbation approach
to the one-component Bose-Hubbard model for experimentally accessible
densities of the particles. Sec. VI presents the discussion of the
ground state phase diagrams for the Bose-Fermi Hubbard Hamiltonian
calculated within quantum rotor approach. The Sec. VII. is devoted
to some concluding remarks. The appendixes contain the derivation
of relevant formulas of the main text and are introduced to keep the
text self-contained.
\section{Hamiltonian}
For bosons confined in optical lattices the two main energy scales
are set by the hopping amplitude proportional to $t_{b}$ (which sets
the kinetic energy scale for bosons) due to the particles tunneling,
and the on-site interaction $U_{b}>0$. For $t_{b}>U_{b}$ the phases
of the superfluid order parameter on individual lattice sites are
well defined. On the other hand, for sufficiently large repulsive
energy $U_{b}$, the quantum phase fluctuations lead to complete suppression
of the long-range phase coherence even at zero temperature. The competition
between the kinetic energy, which is gained by delocalizing bosons
over lattice sites and the repulsive interaction energy, which disfavors
having more than one particle at any given site, can be modeled by
quantum Bose-Hubbard Hamiltonian\cite{fisher}. The physics of the
bosonic and non-interacting spin-polarized (collisions in the $s$-wave
channel are forbidden by their statistics) fermionic mixtures with
density-density interaction between species $U_{bf}$ leads to Bose-Fermi-Hubbard
Hamiltonian \cite{albus}: \begin{eqnarray}
\mathcal{H} & = & \frac{U_{b}}{2}\sum_{i}n_{bi}^{2}-\sum_{\left\langle i,j\right\rangle }t_{bij}b_{i}^{\dagger}b_{j}-\bar{\mu}_{b}\sum_{i}n_{bi}\nonumber \\
& - & \sum_{\left\langle i,j\right\rangle }t_{fij}f_{i}^{\dagger}f_{j}-\mu_{f}\sum_{i}n_{fi}+U_{bf}\sum_{i}n_{bi}n_{fi},\label{hamiltonian}\end{eqnarray}
where $b_{i}^{\dagger}\left(f_{i}^{\dagger}\right)$ and $b_{i}\left(f_{i}\right)$
stand for the bosonic (fermionic) creation and annihilation operators
$n_{bi}=b_{i}^{\dagger}b_{i}$, $\left(n_{fi}=f_{i}^{\dagger}f_{i}\right)$
is the boson (fermion) number operator on the site $i$, and the reduced
chemical potential $\bar{\mu}_{b}=\mu_{b}+U_{b}/2$ controls the number
of bosons and $\mu_{f}$ fermions respectively. Here, $\left\langle i,j\right\rangle $
identifies summation over the nearest-neighbor sites. Furthermore,
$t_{bij}\left(t_{fij}\right)$ is the hopping matrix element for bosons
(fermions). For simplicity, we neglect the inhomogeneous magnetic
trap potential. If the on-site boson-fermion coupling strength $U_{bf}$
becomes very strong the dilute gaseous mixtures are unstable to phase
separation $\left(U_{bf}>0\right)$ or to collapse of the phase separated
configuration $\left(U_{bf}<0\right)$ \cite{viverit,gunter}. The
presence of the lattice will introduce kinetic energy scales $t_{b\left(f\right)}$
competing with $U_{bf}$ stabilizing the system. We assume that an
optical lattice created by the counter-propagating laser beams is
deep enough and we can restrict ourselves to the lowest Bloch bands.
The corresponding experimental parameters can be estimated by following
relations\cite{titvinidze}\begin{eqnarray}
t_{x} & \simeq & \frac{4}{\sqrt{\pi}}E_{r}^{x}\left(\frac{V_{0}}{E_{r}^{x}}\right)^{3/4}\exp\left[-2\left(\frac{V_{0}}{E_{r}^{x}}\right)\right],\\
U_{x} & \simeq & \sqrt{\frac{8}{\pi}}ka_{x}E_{r}^{x}\left(\frac{V_{0}}{E_{r}^{x}}\right)^{3/4},\end{eqnarray}
(subscript $x=\left\{ b,f\right\} $ means $b$ bosons and $f$ fermions
respectively) where boson-boson $a_{b}$, fermion-fermion $a_{f}$
and boson-fermion $a_{bf}$ \begin{equation}
U_{bf}\simeq\sqrt{\frac{8}{\pi}}ka_{bf}E_{r}^{b}\left(\frac{V_{0}}{E_{r}^{b}}\right)^{3/4}\frac{1+\frac{m_{b}}{m_{f}}}{\left(1+\sqrt{\frac{m_{b}}{m_{f}}}\right)^{3/2}}\label{ubfexp}\end{equation}
scattering lengths can be continuously tune in the experiments\cite{ospelkaus,ferlaino,gunter,best}
inducing attractive or repulsive interaction between species. The
$k=2\pi/\lambda$ is the wavelength of the laser and $E_{r}^{x}=\hbar^{2}k^{2}/2m_{x}$
is the recoil energy and $m_{x}$ is the atomic mass.
\section{Description of the method}
We write the partition function of the system switching from the particle-number
representation to the conjugate phase representation of the bosonic
degrees of freedom using the bosonic and fermionic path-integral over
the complex fields $a_{i}\left(\tau\right)$ and $f_{i}\left(\tau\right)$
depending on the {}``imaginary time'' $0\leq\tau\leq\beta\equiv1/k_{\mathrm{B}}T$
with $T$ being the temperature:\begin{equation}
\mathcal{Z}=\int\left[\mathcal{D}\bar{b}\mathcal{D}b\mathcal{D}\bar{f}\mathcal{D}f\right]e^{-\mathcal{S}\left[\bar{b},b,\bar{f},f\right]}.\end{equation}
The action $\mathcal{S}$ is given by\begin{equation}
\mathcal{S}=\mathcal{S}_{B}\left[\bar{b},b,\bar{f},f\right]+\int_{0}^{\beta}d\tau\mathcal{H\left(\tau\right)},\end{equation}
where\begin{eqnarray}
\mathcal{S}_{B}\left[\bar{b},b,\bar{f},f\right] & = & \sum_{i}\int_{0}^{\beta}d\tau\bar{b}_{i}\left(\tau\right)\frac{\partial}{\partial\tau}b_{i}\left(\tau\right)\nonumber \\
& + & \sum_{i}\int_{0}^{\beta}d\tau\bar{f}_{i}\left(\tau\right)\frac{\partial}{\partial\tau}f_{i}\left(\tau\right).\end{eqnarray}
In the next section we will integrate over the fermionic fields since
the action is quadratic in $f_{i}\left(\tau\right)$ variables. We
attempt to reduce the large number of degrees of freedom in the partition
function to the few which dominate the low energy physics.
\subsection{Integration over fermionic fields}
Before integrating out of the fermionic degrees of freedom we write
the action in the form:
\begin{eqnarray}
\mathcal{S}_{b}\left[\bar{b},b,n_{b}\right] & = & \int_{0}^{\beta}d\tau\left\{ \sum_{i}\left[\bar{b}_{i}\left(\tau\right)\frac{\partial}{\partial\tau}b_{i}\left(\tau\right)+\frac{U_{b}}{2}n_{bi}^{2}\left(\tau\right)\right]\right.\nonumber \\
& - & \left.\sum_{\left\langle i,j\right\rangle }t_{bij}\bar{b}_{i}\left(\tau\right)b_{j}\left(\tau\right)-\bar{\mu}_{b}\sum_{i}n_{bi}\left(\tau\right)\right\} ,\nonumber \\
\mathcal{S}_{f}\left[\bar{f},f,n_{f}\right] & = & \int_{0}^{\beta}d\tau\left[\sum_{i}\bar{f}_{i}\left(\tau\right)\frac{\partial}{\partial\tau}f_{i}\left(\tau\right)\right.\nonumber \\
& + & \left.\sum_{\left\langle i,j\right\rangle }t_{fij}\bar{f}_{i}\left(\tau\right)f_{j}\left(\tau\right)-\mu_{f}\sum_{i}n_{fi}\left(\tau\right)\right],\nonumber \\
\mathcal{S}_{\mathrm{int}}\left[n_{b},n_{f}\right] & = & U_{bf}\sum_{i}\int_{0}^{\beta}d\tau n_{bi}\left(\tau\right)n_{fi}\left(\tau\right).\end{eqnarray}
We notice that adding the inter-species interaction term to the fermionic
part of the action\begin{equation}
\mathcal{S}_{f+\mathrm{int}}=\sum_{i,j}\int_{0}^{\beta}d\tau d\tau'\bar{f}_{i}\left(\tau\right)\left[\hat{G}_{f+\mathrm{int}}\left(\tau,\tau'\right)\right]_{ij}f_{j}\left(\tau'\right).\end{equation}
allows one to integrate over fermionic fields, because the action
is Gaussian in $f_{i}\left(\tau\right)$ operators. Resulting partition
function takes the form\begin{equation}
\mathcal{Z}=\int\left[\mathcal{D}\bar{b}\mathcal{D}b\right]e^{-\mathcal{S}_{b}\left[\bar{b},b,n_{b}\right]}e^{\mathrm{Tr}\ln\hat{G}_{f+\mathrm{int}}^{-1}}.\label{partitionfunction1}\end{equation}
We will be looking for solutions obeying translational invariance
in the {}``imaginary time'' direction, i.e., such that the partition
function depends only on the difference $\left|\tau-\tau'\right|$.
Expanding the trace of the logarithm in Eq. (\ref{partitionfunction1})
we have \begin{eqnarray}
\mathrm{Tr}\ln\hat{G}_{f+\mathrm{int}}^{-1} & = & -\mathrm{Tr}\ln\hat{G}_{f}-\mathrm{Tr}\hat{G}_{\mathrm{int}}\hat{G}_{f}\nonumber \\
& - & \frac{1}{2}\mathrm{Tr}\left(\hat{G}_{\mathrm{int}}\hat{G}_{f}\right)^{2},\end{eqnarray}
with\begin{eqnarray}
\left[\hat{G}_{f}^{-1}\left(\tau,\tau'\right)\right]_{ij} & = & \left[\left(\frac{\partial}{\partial\tau}-\mu_{f}\right)\delta_{ij}-t_{fij}I_{ij}\right]\delta\left(\tau-\tau'\right),\nonumber \\
\left[\hat{G}_{\mathrm{int}}\left(\tau,\tau'\right)\right]_{ij} & = & U_{bf}\bar{b}_{i}\left(\tau\right)b_{j}\left(\tau'\right)\delta_{ij}\delta\left(\tau-\tau'\right).\end{eqnarray}
We defined $I_{ij}=1$ if $i,j$ are the nearest neighbors and equals
zero otherwise. Trace over first term of the expansion gives constant
contribution of the fermions, in the non-interacting system, to the
action. Second one induces a shift in the chemical potential of bosons.
The third term after exploiting Fourier-Matsubara transform\begin{equation}
b_{i}\left(\tau\right)=\frac{1}{N\beta}\sum_{\boldsymbol{k},\ell}b_{\boldsymbol{k}}\left(\omega_{\ell}\right)e^{-i\left(\omega_{\ell}\tau-\boldsymbol{k}\cdot\boldsymbol{r}_{i}\right)},\end{equation}
where $\omega_{\ell}=2\pi\ell/\beta$ ($\nu_{\ell}=\pi\left(2\ell+1\right)/\beta$)
with ($\ell=0,\pm1,\pm2,...$) are Bose(Fermi)-Matsubara frequencies
respecting periodic (anti-periodic) boundary conditions of the bosonic
(fermionic) field operator, reduces to\begin{eqnarray}
\mathrm{Tr}\ln\hat{G}_{f+\mathrm{int}}^{-1} & = & \frac{U_{bf}^{2}}{2}\sum_{\boldsymbol{q},\ell}\Lambda_{\boldsymbol{q}}\left(\omega_{\ell}\right)\nonumber \\
& \times & \chi\left(\boldsymbol{q},i\nu_{\ell},\mu_{f},\beta\right)\Lambda_{-\boldsymbol{q}}\left(-\omega_{\ell}\right),\label{trace}\end{eqnarray}
where $\Lambda_{\boldsymbol{q}}\left(\omega_{\ell}\right)=\bar{b}_{\boldsymbol{q}}\left(\omega_{\ell}\right)b_{\boldsymbol{q}}\left(\omega_{\ell}\right)$
and $\chi\left(\boldsymbol{q},i\nu_{\ell},\mu_{f},\beta\right)$ is
called Lindhard functio
\begin{figure}
\includegraphics[scale=0.9]{Fig1}\caption{(Color online) Real $t_{f}\chi'\left(\omega\right)$ and imaginary
$t_{f}\chi''\left(\omega\right)$ part of the local dynamic Lindhard
function for square ($2D$) and cubic lattice ($3D$), in the low-temperature
limit, as a function of frequency, where the normalized fermionic
potential $\mu_{f}/t_{f}=0$ is equal zero. The normalized value of
the critical frequency $\omega_{\mathrm{crit}}^{2D,3D}$ shows where
induced, frequency-dependent, effective part of the interaction $U_{bf}^{2}\chi'\left(\omega_{\mathrm{crit}}\right)$
changes character from attractive to repulsive.}
\label{fig1}
\end{figure}
\begin{equation}
\chi\left(\boldsymbol{q},i\nu_{\ell},\mu_{f},\beta\right)=\sum_{\mathbf{k}}\frac{f\left[t_{f\boldsymbol{k}},\mu_{f},\beta\right]-f\left[t_{f\boldsymbol{k}+\boldsymbol{q}},\mu_{f},\beta\right]}{t_{f\boldsymbol{k}}-t_{f\boldsymbol{k}+\boldsymbol{q}}-i\nu_{\ell}}.\label{lindhard}\end{equation}
In the above $f\left[t_{f\boldsymbol{k}},\mu_{f},\beta\right]=1/\left\{ \exp\left[\beta\left(t_{f\boldsymbol{k}}-\mu_{f}\right)\right]+1\right\} $
is the Fermi distribution function and $t_{f\boldsymbol{k}}$ is the
fermionic dispersion relation. To stay in the local (momentum integrated)
regime we perform $\boldsymbol{q}$ and \textbf{k} integration over
the first Brillouin zone and in the $T\rightarrow0$ limit using an
analytic continuation $i\nu_{\ell}\rightarrow$$\omega+i\epsilon$
we obtain imaginary part $\chi''\left(\omega,\mu_{f}\right)\equiv\mathrm{Im}\chi\left(\omega,\mu_{f}\right)$
of the local dynamic Lindhard function (see Appendix for details)\begin{eqnarray}
\chi''\left(\omega',\mu_{f}\right) & = & \int_{-\infty}^{+\infty}dx\left[\Theta\left(x-\omega'-\mu_{f}\right)-\Theta\left(x-\mu_{f}\right)\right]\nonumber \\
& \times & \rho\left(x\right)\rho\left(x-\omega'\right)\end{eqnarray}
that satisfies sum rule which is just the conservation of the number
of particles. In the above $\rho\left(\xi\right)=N^{-1}\sum_{\mathbf{k}}\delta\left[\xi-t_{f\boldsymbol{k}}\right]$
is the density of states and $\Theta\left(x\right)$ is the unit step
function. Therefore, the corresponding real part $\chi'\left(\omega,\mu_{f}\right)\equiv\mathrm{Re}\chi\left(\omega,\mu_{f}\right)$
can be easily deduced from Kramers-Kr\"{o}nig relation \begin{equation}
\chi'\left(\omega,\mu_{f}\right)=\frac{2}{\pi}\int_{0}^{+\infty}\frac{\omega'\chi''\left(\omega',\mu_{f}\right)}{\omega'^{2}-\omega^{2}}d\omega'.\end{equation}
Later, without any loss of generality, we drop the chemical potential
dependence writing $\chi'\left(\omega,\mu_{f}=0\right)\equiv\chi'\left(\omega\right)$
and $\chi''\left(\omega,\mu_{f}=0\right)\equiv\chi''\left(\omega\right)$.
Finally the {}``imaginary-time'' partition function with integrated
out fermionic degrees of freedom, in the local approximation (see
Appendix for details), can be written as:\begin{equation}
\mathcal{Z}=\int\left[\mathcal{D}\bar{b}\mathcal{D}b\right]e^{-\mathcal{S}_{\mathrm{eff}}\left[\bar{b},b\right]}\end{equation}
with the effective action \begin{eqnarray}
\mathcal{S}_{\mathrm{eff}}\left[\bar{b},b\right] & = & \int_{0}^{\beta}d\tau\left\{ \sum_{i}\bar{b}_{i}\left(\tau\right)\frac{\partial}{\partial\tau}b_{i}\left(\tau\right)\right.\nonumber \\
& + & \frac{U_{\mathrm{eff}}}{2}\sum_{i}n_{bi}^{2}\left(\tau\right)-\sum_{\left\langle i,j\right\rangle }t_{bij}\bar{b}_{i}\left(\tau\right)b_{j}\left(\tau\right)\nonumber \\
& - & \left.\bar{\mu}_{b}\sum_{i}n_{bi}\left(\tau\right)\right\} \label{effective action}\end{eqnarray}
expressed in terms of bosonic degrees of freedom only. We want to
emphasize that applying a local, in the Matsubara-imaginary time,
approach we neglect any dissipation effects. Whereas locality in real
space rules out some parts of interesting physics such as the charge
density wave, namely an insulating phase with modulated density or
the supersolid phase, presenting the coexistence of superfluidity
and a periodic spatial modulation of the density, different from that
of the lattice. On the other hand, the long-range character of the
fermion mediated interaction between bosons with the fermion-induced
mean field potential can lead to spatially homogeneous regions of
commensurate CDW \cite{mering}. The motivation of the local approximation
was the idea that response of an interacting system can be pictured
as the response of a non-interacting system to an effective self-consistent
fi{}eld, that depends on global properties such as the particle densities.
A question of both fundamental and practical interest is, to what
extent can the physics of the exact non-local interaction be captured
by an approximate local theory? It seems that local approximations
often work surprisingly well, yielding energies very accurately, without
suffering from some of the characteristic drawbacks of non-locality
\cite{giuliani}.
From Eq. (\ref{effective action}) it is concluded that there is a
striking resemblance to the one-component Bose-Hubbard action with
the original repulsive interaction replaced now by \begin{equation}
U_{b}\rightarrow U_{\mathrm{eff}}=U_{b}+U_{bf}^{2}\chi'\left(\omega,\mu_{f}\right)\label{u effective}\end{equation}
which is the induced, frequency-dependent, effective interaction between
bosons. From Eq. (\ref{u effective}) we see that integrating out
fermionic field from BF Hubbard Hamiltonian provides an additional
interaction among bosons, which is \emph{not affected} by the attractive
or repulsive nature of the inter-species interaction $\pm U_{bf}$.
Before we proceed with further calculations let us make some remarks.
The substitution we introduced in Eq. (\ref{u effective}) is deceptively
simple and can lead to the assumption that the phase diagram of the
BFH model can be easily derived from the critical line of the one-component
BH Hamiltonian, which already has been obtained in several approximations.
Unfortunately, as we will see in the next section, $U_{bf}^{2}\chi'\left(\omega,\mu_{f}\right)$
is \emph{not} the only one ingredient to the final equation for the
critical line. The additional part, which influences the phase boundary
line condition, comes from the inter-species interaction and number
of fermions added to the system has an impact on amplitude of the
order parameter. Moreover, the chemical potential for fermions $\mu_{f}/t_{f}$
is shifted (we postpone calculations of it now and show proper formula
later) because of the induced effective interaction between them.
\begin{figure}
\includegraphics[scale=0.7]{Fig2}\caption{(Color online) Imaginary $t_{f}\chi''\left(\omega,\mu_{f}\right)$
part of the local dynamic Lindhard function for cubic lattice in the
space of the parameters: normalized frequency $\omega/t_{f}$ and
fermionic chemical potential $\mu_{f}/t_{f}$ in the zero-temperature
limit.}
\label{fig2}
\end{figure}
\begin{figure}
\includegraphics[scale=0.7]{Fig3}\caption{(Color online) Real $t_{f}\chi'\left(\omega,\mu_{f}\right)$ part
of the local dynamic Lindhard function for cubic lattice in the space
of the parameters: normalized frequency $\omega/t_{f}$ and fermionic
chemical potential $\mu_{f}/t_{f}$ in the zero-temperature limit.}
\label{fig3}
\end{figure}
Next step in the calculations depends on the ratio $m_{b}/m_{f}$
of the masses of bosons and fermions which can be seen from Eq. (\ref{ubfexp}).
Consequence of the latter is the fact that the speed of the Bogoliubov
sound $c{}_{b}$ for bosons differs from the first sound $v_{f}$
of the ideal Fermi gas. In typical experimental realizations $^{40}\mathrm{K}$-$^{87}\mathrm{Rb}$
systems the acoustic long-wavelength (boson) $c_{b}$ and fermion
$v_{f}$ velocities are comparable or $c_{b}/v_{f}<1$ (boson mass
is larger than fermion). Therefore we do not restrict our calculations
to the static limit but consider also local dynamical response function
(thus including the retardation effects). If $c_{b}$ is much larger
than $v_{f}$ (in the $^{40}\mathrm{K}$-$^{23}\mathrm{Na}$ species
we have $c_{b}/v_{f}\sim5$) the resulting interaction between bosons
is \emph{instantaneous} and \emph{always} attractive (with $U_{bf}^{2}\chi'\left(\omega,\mu_{f}\right)<0$)
so using the static approximation is justified with an error which
involves the small parameter $v_{f}/c_{b}$.
The imaginary part of the Lindhard response function rises to a broad
peak before falling and the real part takes zero when changes in $\chi''\left(\omega\right)$
are the biggest (see Fig. \ref{fig1}). The real part $\chi'\left(\omega\right)$
is negative for the frequencies $\omega/8t_{f}<0.4710=\omega_{\mathrm{crit}}^{2D}$
for square and $\omega/12t_{f}<0.3525=\omega_{\mathrm{crit}}^{3D}$
for cubic lattice (see Fig. \ref{fig1}). We normalized the frequency
by the width of the band for non-interacting fermions to show the
scale of the energy. Nevertheless, for higher values of the normalized
frequency $\omega>\omega_{\mathrm{crit}}$ the induced part of the
interaction $U_{bf}^{2}\chi'\left(\omega\right)$ can be \emph{positive}
and \emph{increase} the effective interaction between bosons, in consequence
provide stronger localization these species on lattice sites. In the
case of large fermion hopping and commensurate filling with the lattice
the effective long-range density-density interaction between bosons
has alternating sign and is the origin of the charge density-wave
phases \cite{mering}. The higher values of the normalized chemical
potential for the fermions $\mu_{f}/t_{f}$ decreases the values of
both (Fig. \ref{fig2} and Fig. \ref{fig3}) real and imaginary part
of the local Lindhard function. That leads to the situation where
the terms containing explicitly the average density of fermions $n_{\mathrm{F}}$
will acquire more significance than terms with exclusively the inter-species
interaction $U_{bf}$.
\subsection{Static and periodic bosonic fields and gauge transformation}
Unfortunately the effective action is not quadratic in bosonic fields
$b_{i}$ and we have to decouple the effective interaction term in
Eq. (\ref{effective action}) by a Gaussian integration over the auxiliary
scalar potential fields \begin{equation}
V_{i}\left(\tau\right)=V_{i0}+V_{i}'\left(\tau\right),\end{equation}
with static \begin{equation}
V_{i0}=\frac{1}{\beta}V_{i}\left(\omega_{\ell=0}\right)\end{equation}
and periodic part \begin{equation}
V'_{i}\left(\tau\right)=\frac{1}{\beta}\sum_{\ell=1}^{+\infty}V_{i}\left(\omega_{\ell}\right)e^{i\omega_{\ell}\tau}+\mathrm{c.c},\label{periodic part V}\end{equation}
where $\omega_{\ell}$ is the Bose-Matsubara frequency. We observe
now that effective BF Hubbard Hamiltonian has a local $\mathrm{U}\left(1\right)$
gauge symmetry, when expressed in terms of the underlying boson variables.
This points out a possibility of an emergent dynamical $\mathrm{U}\left(1\right)$
gauge field as a fluctuating complex field attached to bosonic variables,
which is dynamically generated, by interacting bosons. Thus, the periodic
part $V'_{i}\left(\tau\right)\equiv V'_{i}\left(\tau+\beta\right)$
couples to the local particle number through the Josephson-like relation
$\dot{\phi}_{i}\left(\tau\right)=V'_{i}\left(\tau\right)$, where
\begin{equation}
\dot{\phi}_{i}\left(\tau\right)\equiv\frac{\partial\phi_{i}\left(\tau\right)}{\partial\tau}=e^{-\phi_{i}\left(\tau\right)}\frac{1}{i}\frac{\partial}{\partial\tau}e^{\phi_{i}\left(\tau\right)}.\end{equation}
The quantity $\phi\left(\tau\right)$ is the $\mathrm{U}\left(1\right)$
\textit{phase} field and satisfies the periodicity condition $\phi_{i}\left(\beta\right)=\phi_{i}\left(0\right)$
as a consequence of the periodic properties of the $V'_{i}\left(\tau\right)$
field in Eq. (\ref{periodic part V}). Next, we perform the local
gauge transformation to the new bosonic variables\begin{equation}
\left[\begin{array}{c}
b\left(\tau\right)\\
\bar{b}_{i}\left(\tau\right)\end{array}\right]=\left[\begin{array}{cc}
e^{i\phi_{i}\left(\tau\right)} & 0\\
0 & e^{-i\phi_{i}\left(\tau\right)}\end{array}\right]\left[\begin{array}{c}
a_{i}\left(\tau\right)\\
\bar{a}_{i}\left(\tau\right)\end{array}\right]\end{equation}
that removes the imaginary term $-i\int_{0}^{\beta}d\tau\dot{\phi}_{i}\left(\tau\right)n_{bi}\left(\tau\right)$
from all the Fourier modes except at zero frequency. From the above
we deduce bosons have a composite nature made of bosonic part $a_{i}\left(\tau\right)$
and attached {}``flux'' $\exp\left[i\phi_{i}\left(\tau\right)\right]$.
Due to such $\mathrm{U}\left(1\right)$ gauge invariance, the fluctuations
and the phase have the dynamics of $\mathrm{U}\left(1\right)$ gauge
field.
\subsection{Gauge group $\mathrm{U\left(1\right)}$ governed phase only action}
By integrating out the auxiliary static field $V_{i0}$ we calculate
the partition function with an effective action expressed in the form
of the propagator $\hat{G}$\begin{equation}
\mathcal{Z}=\int\left[\mathcal{D}\phi\right]e^{-\sum_{i}\int_{0}^{\beta}d\tau\left[\frac{1}{2U_{\mathrm{eff}}}\dot{\phi}_{i}^{2}\left(\tau\right)+\frac{1}{i}\frac{\bar{\mu}_{b}}{U_{\mathrm{eff}}}\dot{\phi}_{i}\left(\tau\right)\right]+\mathrm{Tr}\ln\hat{G}^{-1}},\label{partition function propagator}\end{equation}
where $\bar{\mu}_{b}/U_{b}=\mu_{b}/U_{b}+1/2$ is the shifted reduced
bosonic chemical potential. In the above $\exp\left(-\mathrm{Tr}\ln\hat{G}^{-1}\right)\equiv\det\hat{G}$
and the determinant takes the form\begin{eqnarray}
\det\hat{G} & = & \int\left[\mathcal{D}\bar{a}\mathcal{D}a\right]\exp\left\{ -\sum_{\left\langle i,j\right\rangle }\int_{0}^{\beta}d\tau\right.\nonumber \\
& \times & \bar{a}_{i}\left(\tau\right)\left[\left(\frac{\partial}{\partial\tau}+\bar{\mu}_{b}\right)\delta_{ij}\right.\nonumber \\
& - & \left.\left.e^{i\phi_{i}\left(\tau\right)}t_{bij}e^{-i\phi_{j}\left(\tau\right)}\right]a_{i}\left(\tau\right)\right\} .\end{eqnarray}
We parametrize the boson fields $a_{i}\left(\tau\right)=a_{0}+a_{i}^{'}\left(\tau\right)$
and incorporate fully our calculations to the phase fluctuations governed
by the gauge group $\mathrm{U}\left(1\right)$. Assuming nonfluctuating
amplitude at low temperatures $a_{i}\left(\tau\right)=a_{0}$, we
drop the corrections, which was proved to be justified in the large
$U_{b}/t_{b}$ limit we are interested in \cite{polak,kampf}. The
amplitude fluctuations are massive one and do not play important role
in the low energy scales. It is very convenient to define the order
parameter \begin{equation}
\Psi_{\mathrm{B}}\equiv\left\langle b_{i}\left(\tau\right)\right\rangle =\left\langle a_{i}\left(\tau\right)\exp\left[i\phi_{i}\left(\tau\right)\right]\right\rangle =a_{0}\psi_{\mathrm{B}},\label{order parameter definition}\end{equation}
which signals the emergence of the superfluid phase and vanishes in
the Mott-insulator state. The SF state is characterized by spontaneously
breaking of the $\mathrm{U\left(1\right)}$ symmetry of Bose-Fermi-Hubbard
Hamiltonian. Note, that a nonzero value of the amplitude $a_{0}$
in Eq. (\ref{order parameter definition}) is \emph{not sufficient}
for superfluidity. To achieve this, also the phase variables $\phi$
in Eq. (\ref{order parameter definition}), must become stiff and
coherent, which implies $\psi_{\mathrm{B}}\neq0$. As we see in the
next sections the presence of the fermions and density-density interactions
$U_{bf}$ between species of different statistics can also change
the amplitude of the order parameter. After mentioned assumption the
inverse of the propagator becomes\begin{equation}
\hat{G}^{-1}=\hat{G}_{0}^{-1}-\hat{T}=\hat{G}_{0}^{-1}\left(1-\hat{T}\hat{G}_{0}\right).\end{equation}
The explicit value of the amplitude $a_{0}$ in Eq. (\ref{order parameter definition})
can be obtained from minimization of the Hamiltonian $\partial\mathcal{H}\left(a_{0}\right)/\partial a_{0}=0$.
Therefore, we write\begin{eqnarray}
\hat{G}_{0} & = & a_{0}^{2}\equiv\frac{\sum_{\left\langle i,j\right\rangle }t_{bij}+\bar{\mu}_{b}}{U_{b}}-\frac{U_{bf}}{U_{b}}n_{\mathrm{F}}.\label{zero mode}\\
\hat{T} & = & e^{i\phi_{i}\left(\tau\right)}t_{bij}e^{-i\phi_{j}\left(\tau\right)}.\label{hopping}\end{eqnarray}
Expanding the trace of the logarithm in Eq. (\ref{partition function propagator})
and making use the above we obtain up to the second order in the amplitude
of the order parameter Eq. (\ref{order parameter definition}) \begin{eqnarray}
\mathrm{Tr}\ln\hat{G}^{-1} & = & -\mathrm{Tr}\ln\hat{G}_{0}-\mathrm{Tr}\hat{T}\hat{G}_{0}\nonumber \\
& - & \frac{1}{2}\mathrm{Tr}\left(\hat{T}\hat{G}_{0}\right)^{2}.\end{eqnarray}
Trace over first term of the expansion, as previously, not containing
any fluctuating field variables, gives an inessential constant contribution
to the action. Let us consider the second order term in more detail\begin{eqnarray}
\mathrm{Tr}\left(\hat{T}\hat{G}_{0}\right) & = & \sum_{\left\langle i,j\right\rangle }\tilde{t}_{bij}\int_{0}^{\beta}d\tau d\tau'\nonumber \\
& \times & e^{-i\left[\phi_{i}\left(\tau\right)-\phi_{j}\left(\tau'\right)\right]}\delta\left(\tau-\tau'\right),\end{eqnarray}
where\begin{equation}
\tilde{t}_{bij}=a_{0}^{2}t_{bij}=\left(\frac{\sum_{\left\langle i,j\right\rangle }t_{bij}+\bar{\mu}_{b}}{U_{b}}-\frac{U_{bf}}{U_{b}}n_{f}\right)t_{bij},\end{equation}
the hopping matrix elements are re-normalized by the amplitude of
the order parameter. We see that in comparison to pure bosonic case
there is an additional shift $-U_{bf}n_{\mathrm{F}}/U_{b}$ that depends
on the average of the fermion concentration and normalized inter-species
interaction. The above was also obtained in the effective bosonic
model and recognized as a mean-field contribution \cite{mering}.
Finally, the partition function Eq. (\ref{partition function propagator})
becomes\begin{eqnarray}
\mathcal{Z} & = & \int\left[\mathcal{D}\phi\right]e^{-\mathcal{S}_{\mathrm{phase}}\left[\phi\right]}\end{eqnarray}
with an effective action expressed \emph{only} in the \emph{phase}
fields variable\begin{eqnarray}
\mathcal{S}_{\mathrm{phase}}\left[\phi\right] & = & \int_{0}^{\beta}d\tau\left\{ \sum_{i}\left[\frac{1}{2U_{\mathrm{eff}}}\dot{\phi_{i}^{2}}\left(\tau\right)+\frac{1}{i}\frac{\bar{\mu}_{b}}{U_{\mathrm{eff}}}\dot{\phi_{i}}\left(\tau\right)\right]\right.\nonumber \\
& - & \left.\tilde{t}_{b}\sum_{i,j}e^{\phi_{i}\left(\tau\right)}I_{ij}e^{-\phi_{j}\left(\tau\right)}\right\} ,\label{action only phase}\end{eqnarray}
where $\tilde{t}_{b}=\left(\sum_{\left\langle i,j\right\rangle }t_{bij}+\bar{\mu}_{b}-U_{bf}n_{\mathrm{F}}\right)t_{b}/U_{b}$.
The total time derivative Berry phase imaginary term in Eq. (\ref{action only phase})
is nonzero due to topological phase field configurations with $\phi_{i}\left(\beta\right)-\phi_{i}\left(0\right)=2\pi m_{i}$
($m_{i}=0,\pm1,\pm2...$) that results in topological ingredients
to the correlator we will see below. Therefore, we concentrate on
closed paths in the {}``imaginary time'' $\left(0,\beta\right)$
labeled by the integer winding numbers $m_{i}$. The path-integral
\begin{equation}
\int\left[\mathcal{D}\phi\right]...\equiv\sum_{\left[m_{i}\right]}\int_{0}^{2\pi}\left[\mathcal{D}\phi\left(0\right)\right]\int_{_{\phi_{i}\left(0\right)}}^{\phi_{i}\left(\tau\right)+2\pi m_{i}}\left[\mathcal{D}\phi\left(\tau\right)\right]...,\end{equation}
includes a summation over $m_{i}$ and in each topological sector
the integration goes over the gauge potentials. Therefore, we do not
ignore the compactness of the gauge fields.
To proceed, we replace the phase degrees of freedom by the uni-modular
scalar complex field $\psi$ which satisfies the quantum periodic
boundary condition $\psi_{i}\left(\beta\right)=\psi_{i}\left(0\right)$.
This can be conveniently done using the Fadeev-Popov method with Dirac
delta functional resolution of unity, where we take $\psi$ as a continuous
but constrained (on the average) variable to have the uni-modular
value. We introduce \begin{eqnarray}
1 & = & \int\left[\mathcal{D}\psi\mathcal{D}\psi^{*}\right]\delta\left(\sum_{i}\left|\psi\left(\tau\right)\right|^{2}-N\right)\nonumber \\
& \times & \delta\left(\psi_{i}-e^{i\phi_{i}\left(\tau\right)}\right)\delta\left(\psi_{i}^{*}-e^{-i\phi_{i}\left(\tau\right)}\right)\end{eqnarray}
and\begin{eqnarray}
\delta\left(\sum_{i}\left|\psi_{i}\left(\tau\right)\right|^{2}-N\right) & = & \frac{1}{2\pi i}\int_{-i\infty}^{+i\infty}d\lambda\nonumber \\
& \times & e^{\int_{0}^{\beta}d\tau\lambda\left(\sum_{i}\left|\psi_{i}\left(\tau\right)\right|^{2}-N\right)},\end{eqnarray}
where $N$ is the number of lattice sites. Introducing the Lagrange
multiplier $\lambda$, which adds the quadratic terms (in the $\psi$
fields) to the action we can solve for the constraint. The partition
function can be rewritten to the form\begin{eqnarray}
\mathcal{Z} & = & \frac{1}{2\pi i}\int_{-i\infty}^{+i\infty}e^{-\lambda N}d\lambda\int\left[\mathcal{D}\psi\mathcal{D}\psi^{*}\right]\nonumber \\
& \times & \exp\left\{ -\sum_{i,j}\int_{0}^{\beta}d\tau d\tau'\psi_{i}\left[\left(\tilde{t}_{b}I_{ij}+\lambda\delta_{ij}\right)\delta\left(\tau-\tau'\right)\right.\right.\nonumber \\
& + & \left.\left.\gamma_{ij}\left(\tau,\tau'\right)\right]\psi_{j}^{*}\right\} ,\end{eqnarray}
where \begin{equation}
\gamma_{ij}\left(\tau,\tau'\right)=\left\langle \exp\left\{ -i\left[\phi_{i}\left(\tau\right)-\phi_{j}\left(\tau'\right)\right]\right\} \right\rangle \end{equation}
is the two-point phase correlator associated with the order parameter
field, where $\left\langle \cdots\right\rangle $ denotes averaging
with respect to the action in Eq. (\ref{action only phase}). Because
the values of the phases $\phi$ which differ by $2\pi$ are equivalent
we decompose phase field in terms of a periodic field and term linear
in $\tau$:\begin{equation}
\phi_{i}\left(\tau\right)=\varphi_{i}\left(\tau\right)+\frac{2\pi}{\beta}m_{i}\tau\end{equation}
with $\phi_{i}\left(\beta\right)=\phi_{i}\left(0\right).$ As a result
the phase correlator factorizes as the product of a topological term
depending on the integers $m_{i}$ and non-topological one:\begin{equation}
\gamma_{ij}\left(\tau,\tau'\right)=\gamma_{ij}^{T}\left(\tau,\tau'\right)\gamma_{ij}^{N}\left(\tau,\tau'\right).\end{equation}
Performing the Poisson re-summation formula in \begin{equation}
\gamma_{ij}^{T}\left(\tau,\tau'\right)=\frac{\sum_{\left[m_{i}\right]}e^{-i\frac{2\pi}{\beta}\left(\tau-\tau'\right)m_{i}}e^{-\frac{2\pi}{\beta}\sum_{i}\left[\frac{\pi}{U_{\mathrm{eff}}}m_{i}^{2}+\frac{\beta}{i}\frac{\bar{\mu}_{b}}{U_{\mathrm{eff}}}m_{i}\right]}}{\sum_{\left[m_{i}\right]}e^{-\frac{2\pi}{\beta}\sum_{i}\left[\frac{\pi}{U_{\mathrm{eff}}}m_{i}^{2}+\frac{\beta}{i}\frac{\bar{\mu}_{b}}{U_{\mathrm{eff}}}m_{i}\right]}}\end{equation}
and the functional integration over the phase variables \begin{equation}
\gamma_{ij}^{N}\left(\tau,\tau'\right)=\frac{\int\left[\mathcal{D}\varphi\right]e^{-i\left[\varphi_{i}\left(\tau\right)-\varphi_{j}\left(\tau'\right)\right]}e^{-\sum_{i}\frac{1}{2U_{\mathrm{eff}}}\int_{0}^{\beta}d\tau\dot{\varphi_{i}^{2}}\left(\tau\right)}}{\int\left[\mathcal{D}\varphi\right]e^{-\sum_{i}\frac{1}{2U_{\mathrm{eff}}}\int_{0}^{\beta}d\tau\dot{\varphi_{i}^{2}}\left(\tau\right)}}\end{equation}
the final formula of the correlator takes the form \begin{eqnarray}
\gamma_{ij}\left(\tau,\tau'\right) & = & \frac{\vartheta\left(\pi\frac{\bar{\mu}_{b}}{U_{\mathrm{eff}}}+\pi\frac{\tau-\tau'}{\beta},e^{-\frac{1}{U_{\mathrm{eff}}}\frac{2\pi^{2}}{\beta}}\right)}{\vartheta\left(\pi\frac{\bar{\mu}_{b}}{U_{\mathrm{eff}}},e^{-\frac{1}{U_{\mathrm{eff}}}\frac{2\pi^{2}}{\beta}}\right)}\nonumber \\
& \times & \exp\left(\frac{U_{\mathrm{eff}}}{2}\left|\tau-\tau^{'}\right|-\frac{\left(\tau-\tau'\right)^{2}}{\beta}\right),\end{eqnarray}
where $\vartheta\left(z,q\right)$ is the Jacobi theta function, which
comes from the topological contribution - summation over integer winding
numbers. The function $\vartheta\left(z,q\right)$ is defined by \begin{equation}
\vartheta\left(z,q\right)=1+2\sum_{n=1}^{+\infty}\cos\left(2nz\right)q^{n^{2}}\end{equation}
and is $\beta$-periodic in the {}``imaginary time'' as well in
the variable $\bar{\mu}_{b}/U_{\mathrm{eff}}$ with the period of
unity which emphasizes the special role of its integer values. After
Fourier transforming one obtains
\begin{equation}
\gamma_{ij}\left(\omega_{\nu}\right)=\frac{1}{\mathcal{Z}_{0}}\frac{4}{U_{\mathrm{eff}}}\sum_{\left[m_{i}\right]}\frac{e^{-\frac{U_{\mathrm{eff}}\beta}{2}\sum_{i}\left(m_{i}+\frac{\bar{\mu}_{b}}{U_{\mathrm{eff}}}\right)^{2}}}{1-4\left(\sum_{i}m_{i}+\frac{\bar{\mu}_{b}}{U_{\mathrm{eff}}}-i\frac{\omega_{\ell}}{U_{\mathrm{eff}}}\right)^{2}},\label{topological contribution}\end{equation}
where\begin{equation}
\mathcal{Z}_{0}=\sum_{\left[m_{i}\right]}e^{-\frac{U_{\mathrm{eff}}\beta}{2}\sum_{i}\left(m_{i}+\frac{\bar{\mu}_{b}}{U_{\mathrm{eff}}}\right)^{2}}\end{equation}
is the partition function for the set of quantum rotors. The action
Eq. (\ref{action only phase}), with the topological contribution
Eq. (\ref{topological contribution}), after Fourier transform, is
written as \begin{equation}
\mathcal{S}_{\mathrm{eff}}\left[\psi,\bar{\psi}\right]=\frac{1}{N\beta}\sum_{\mathbf{k},\ell}\bar{\psi}_{\mathbf{k}}\left(\omega_{\ell}\right)\mathrm{\Gamma}_{\mathbf{k}}^{-1}\left(\omega_{\ell}\right)\psi_{\mathbf{k}}\left(\omega_{\ell}\right),\end{equation}
where $\mathrm{\Gamma}_{\mathbf{k}}^{-1}\left(\omega_{\ell}\right)=\lambda-t_{b\mathbf{k}}+\gamma^{-1}\left(\omega_{\ell}\right)$
is the inverse of the propagator and $t_{b\boldsymbol{k}}$ is the
Fourier transform of the bosonic hopping matrix elements for two-
$t_{b\boldsymbol{k}}^{2D}=2t_{b}\left(\cos k_{x}+\cos k_{y}\right)$
and three-dimensional $t_{b\boldsymbol{k}}^{3D}=2t_{b}\left(\cos k_{x}+\cos k_{y}+\cos k_{z}\right)$
lattice.
\section{Critical Line}
Within the phase coherent state the order parameter $\psi_{B}$ is
evaluated in the thermodynamic limit $N\rightarrow\infty$ by the
saddle point method $\delta\mathcal{F}/\delta\lambda=0$ and the uni-modular
condition of the $\mathrm{U}\left(1\right)$ phase variables translates
into the equation\begin{equation}
1-\psi_{\mathrm{B}}^{2}=\lim_{N\rightarrow\infty}\frac{1}{N\beta}\sum_{\mathbf{k},\ell}\Gamma_{\boldsymbol{k}}\left(\omega_{\ell}\right),\label{critical line}\end{equation}
with\begin{equation}
\Gamma_{\boldsymbol{k}}^{-1}\left(\omega_{\ell}\right)=\tilde{t}_{b\mathbf{k}=0}-\tilde{t}_{b\mathbf{k}}+\frac{1}{U_{\mathrm{eff}}}\bar{\mu}_{b}^{2}-\frac{1}{U_{\mathrm{eff}}}\left(\bar{\mu}_{b}-i\omega_{\ell}\right)^{2}.\end{equation}
The phase boundary is determined by the divergence of the order parameter
susceptibility $\Gamma_{\mathbf{k}=0}\left(\omega_{\ell=0}\right)=0$\begin{equation}
\lambda_{0}-t_{b\boldsymbol{k}=0}^{\mathrm{max}}+\gamma^{-1}\left(\omega_{\ell=0}\right)=0\label{lagrange 0}\end{equation}
which determines the critical value of the Lagrange parameter $\lambda=\lambda_{0}$
and stays constant in the whole global coherent phase. To proceed,
it is desirable to introduce the density of states \begin{equation}
\rho\left(\xi\right)=\frac{1}{N}\sum_{\boldsymbol{k}}\delta\left(\xi-\frac{t_{b\boldsymbol{k}}}{t_{b}}\right)\label{DOS definition}\end{equation}
because the analytical expressions we use can be advantageous in evaluating
sums over momenta. The corresponding formulas for square lattice can
be written as\begin{equation}
\rho^{2D}\left(\xi\right)=\frac{1}{2\pi^{2}t_{b}}\mathbf{K}\left(\sqrt{1-\left(\frac{\xi}{4t_{b}}\right)^{2}}\right)\Theta\left(1-\left|\frac{\xi}{4t_{b}}\right|\right),\end{equation}
and for simple cubic geometry takes form \begin{eqnarray}
\rho^{3D}\left(\xi\right) & = & \frac{1}{2\pi^{3}t_{b}}\int_{a_{1}}^{a_{2}}\frac{d\epsilon}{\sqrt{1-\epsilon^{2}}}\Theta\left(1-\frac{\left|\xi\right|}{6t_{b}}\right)\nonumber \\
& \times & \mathbf{K}\left(\sqrt{1-\left(\frac{\xi}{4t_{b}}+\epsilon\right)^{2}}\right)\end{eqnarray}
with $a_{1}=\mathrm{min}\left(-1,-2-\xi/2t_{b}\right)$ and $a_{2}=\mathrm{max}\left(1,2-\xi/2t_{b}\right)$;
$\mathbf{K}\left(x\right)$ is the elliptic function of the first
kind.\cite{abramovitz}. After summation over Bose-Matsubara frequency
and for zero temperature limit $\beta\rightarrow\infty$ we can rewrite
the critical line equation to the form that represents solution of
the BF Hubbard model in terms of re-normalized pure Bose-Hubbard Hamiltonian
in the quantum rotor approach:
\begin{widetext}\begin{eqnarray}
1-\psi_{\mathrm{B}}^{2} & = & \frac{1}{2}\int_{-\infty}^{+\infty}\frac{\rho\left(\xi\right)d\xi}{\sqrt{2\left(\xi_{\mathrm{max}}-\xi\right)\left(2z\frac{t_{b}}{U_{b}}+\frac{\mu_{b}}{U_{b}}-\eta+\frac{1}{2}\right)\frac{1}{\alpha}\frac{t_{b}}{U_{b}}+\upsilon^{2}\left(\frac{1}{\alpha}\frac{\mu_{b}}{U_{b}}\right)}}\label{critical line-1}\end{eqnarray}
\end{widetext}In the above $\upsilon\left(\mu_{b}/\alpha U_{b}\right)=\mathrm{frac}\left(\mu_{b}/\alpha U_{b}\right)-1/2,$
where $\mathrm{frac}\left(x\right)=x-\left[x\right]$ is the fractional
part of the number and $\left[x\right]$ is the floor function which
gives the greatest integer less than or equal to $x$; $\xi_{\mathrm{max}}$
stands for the maximum value of the bosonic dispersion spectrum $t_{b\boldsymbol{k}}$
and $z$ is the lattice coordination number. The renormalization parameters
are defined as: \begin{eqnarray}
\alpha & = & 1+\frac{U_{bf}^{2}}{U_{b}}\chi'\left(\omega,\mu_{f}\right)\label{parameters1}\\
\eta & = & \frac{U_{bf}}{U_{b}}n_{\mathrm{F}}\label{parameters2}\end{eqnarray}
and allow us to see how adding free fermions to strongly interacting
bosons confined in optical lattice influences the phase boundary.
\section{Phase Diagrams - BH model}
The zero-temperature phase diagram of the Bose-Fermi-Hubbard model
Eq. (\ref{hamiltonian}) can be calculated from Eq. (\ref{critical line-1})
and usually is plotted as a function of $t_{b}/U_{b}$, with the density
of the bosons controlled by a chemical potential $\mu_{b}/U_{b}$.
The presence of the fermions implicates two additional different parameters
that can by varied namely $\alpha$ and $\eta$ in Eq. (\ref{parameters1})
and Eq. (\ref{parameters2}). The strength of the inter-species interaction
influences both of them, however the sign of $U_{bf}$ and the average
density of fermions $n_{\mathrm{F}}$ added to the system affects
only $\eta$. Besides, in the local dynamic approach the sign of the
density-density interaction depends also on the normalized frequency
$\omega/t_{f}$. For a general choice of parameters, Eq. (\ref{critical line-1})
is easy to solve, however considerations of special cases can provide
more insights into the solution of the problem. In discussion we will
follow the scheme\begin{eqnarray}
\eta\begin{array}{c}
\nearrow\\
\searrow\end{array} & \begin{array}{cccc}
\alpha<1 & \mbox{and} & \begin{array}{c}
c_{b}/v_{f}>1\\
c_{b}/v_{f}\thicksim1\end{array} & \begin{array}{c}
\mbox{for \ensuremath{\omega=0}}\\
\mbox{for \ensuremath{\omega<\omega_{\mathrm{crit}}}}\end{array}\\
\\\alpha>1 & \mbox{and} & c_{b}/v_{f}\thicksim1 & \mbox{for \ensuremath{\omega>\omega_{\mathrm{crit}}}}\end{array}\end{eqnarray}
firstly choosing the sign of the $\eta$ and later $\alpha$ in the
static ($\omega=0$) or dynamic ($\omega\neq0$) limit (see Fig. \ref{fig1}).
Before we proceed with analysis let us introduce the notation for
the maximum of the critical value for parameter $t_{b}/U_{b}$ (as
a function of the normalized chemical potential $\mu_{b}/U_{b}$)
at the tip of the $n$th ($n_{\mathrm{B}}=n$) MI lobe for different
lattice geometries and model parameters $\alpha$ and $\eta$ as follows
\begin{equation}
x_{n}\left(\alpha,\eta\right)\equiv{\rm max}\left\{ \left(\frac{t_{b}}{U_{b}}\right)_{{\rm crit}}\right\} _{\alpha,\eta}^{2D,3D}.\end{equation}
\begin{figure}
\includegraphics[scale=0.85]{Fig4}\caption{(Color online) Phase diagrams ($t_{b}/U_{b}$-$\mu_{b}/U_{b}$) for
the square ($2D$) lattice for different $\alpha=0.5$ (higher panel,
$\omega<\omega_{\mathrm{crit}}$), $\alpha=1.5$ ($\omega>\omega_{\mathrm{crit}}$)
and $\eta=-2$ (negative scattering length $a_{bf}<0$). Dashed line
stands for the phase boundary of one-component Bose-Hubbard model.
Within the lobes the Mott insulator phase takes place with $\Psi_{\mathrm{B}}=0$.\label{fig4}}
\end{figure}
\begin{figure}
\includegraphics[scale=0.85]{Fig5}\caption{(Color online) Phase diagrams ($t_{b}/U_{b}$-$\mu_{b}/U_{b}$) for
the cubic ($3D$) lattice for different $\alpha=0.5$ (higher panel,
$\omega<\omega_{\mathrm{crit}}$), $\alpha=1.5$ ($\omega>\omega_{\mathrm{crit}}$)
and $\eta=-2$ (negative scattering length $a_{bf}<0$). Dashed line
stands for the phase boundary of one-component Bose-Hubbard model.
Within the lobes the Mott insulator phase takes place with $\Psi_{\mathrm{B}}=0$.\label{fig5}}
\end{figure}
The above determines when the transition from MI to SF occurs. Values
$\alpha=1$ and $\eta=0$ stand for the one-component bosonic case.
In Table \ref{comparison} we show comparison of $x_{n}\left(1,0\right)$
for higher densities of the particles calculated in the quantum rotor
approach (QRA) to very accurate, recently developed, diagrammatic
perturbation approach\cite{teichmann} to Bose-Hubbard Hamiltonian.
The results for $3D$ BH model obtained in both theories are very
close and also comparison to quantum Monte-Carlo (QMC) numerical calculations\cite{capogrosso-sansone}
indicates that methods we use are able to properly catch the interesting
physics of strongly interacting systems. However, we want to analyze
the phase boundary for number of particles per lattice sites higher
than one $n_{\mathrm{B}}>1$ that adds another dimension to the analysis
and is difficult for the QMC to catch. The phase boundary for square
lattice shows that QRA works well also in low-dimensional geometries,
especially for higher densities. Nevertheless, the structure of Eq.
(\ref{critical line-1}) can cause some problems when \emph{both}
$\alpha$ and $\eta$ are nonzero and the number of bosons is equal
one per lattice sites. We expect that for $\eta>1$ some artificial
effects may arise for values of the normalized chemical potential
$\mu_{b}/U_{b}\approx0$ close to zero.
\begin{table}
\begin{tabular}{c|c|c|c|c|c}
$2D$ & $n_{\mathrm{B}}=1$ & $2$ & $3$ & $4$ & $10$\tabularnewline
\hline
DPT & $0.0590934$ & $0.0348009$ & $0.0247350$ & $0.0191986$ & $0.0082079$\tabularnewline
\hline
QRA & $0.0671998$ & $0.0439387$ & $0.0317523$ & $0.0246185$ & $0.0093296$\tabularnewline
\hline
$3D$ & $n_{\mathrm{B}}=1$ & $2$ & $3$ & $4$ & $10$\tabularnewline
\hline
DPT & $0.0340685$ & $0.0200755$ & $0.0142709$ & $0.0110779$ & $0.0047362$\tabularnewline
\hline
QRA & $0.0321429$ & $0.0194846$ & $0.0136102$ & $0.0103755$ & $0.0042086$\tabularnewline
\end{tabular}\caption{Comparison of the maximum of the critical value for $\left(t_{b}/U_{b}\right)_{\mathrm{crit}}$
(as a function of the normalized bosonic chemical potential $\mu_{b}/U_{b}$)
at the tip of the $n$th ($n_{\mathrm{B}}=1\div4$ and $10$) Mott
insulator lobe for the square ($2D$) and cubic ($3D$) lattice in
the one-component Bose-Hubbard model: DPT - diagrammatic perturbation
theory\cite{teichmann}), QRA - our calculations using quantum rotor
approach).}
\label{comparison}
\end{table}
\section{Bose-Fermi-Hubbard phase diagram}
\begin{figure}
\includegraphics[scale=0.8]{Fig6}\caption{(Color online) Maximum value of the $\left(t_{b}/U_{b}\right)_{\mathrm{max}}$
for different $\alpha$ and $\eta=0.001$ (very small amount of fermions)
for square ($2D$) and cubic ($3D$) lattice with $n_{\mathrm{B}}=1$.
Vertical solid line stands for the $\left(t_{b}/U_{b}\right)_{\mathrm{max}}$
obtained in one-component Bose-Hubbard model with one particle per
lattice site. Above the curves the superfluid phase takes place with
$\Psi_{\mathrm{B}}\neq0$.\label{fig6}}
\end{figure}
In the experiments\cite{best} for a degenerate mixtures of $4\times10^{5}$
$^{87}\mathrm{Rb}$ bosons and $3\times10^{5}$ $^{40}\mathrm{K}$
fermions the scattering length $a_{bf}$ (and in consequence interaction
$U_{bf}$, see Eq. (\ref{ubfexp})) can be continuously tune between
$-170a_{0}\div+800a_{0}$ below and between $-800a_{0}\div-200a_{0}$
above Feshbach resonance, where $a_{0}$ is the Bohr radius. The form
of the parameters we choose Eq. (\ref{parameters1}) and Eq. (\ref{parameters2})
allows for its interpretation. The periodicity of the phase diagram
can be easily deduced from the periodic properties of the propagator
Eq. (\ref{topological contribution}) and strongly depends on $\alpha$
however, the interaction between species does not generate additional
Mott lobes in the phase diagram. The above is in contrast to the strong
coupling expansion and exact diagonalization method applied to the
system of two alkali-metal atoms with different masses where (for
very small lattice sizes and quenched disorder) the MI phases with
integer filing factors disappear for boson-impurity interaction energy
larger than on-site atom-atom interaction energy itself and also the
MI phase exists for incommensurate bosonic filling \cite{krutitsky}.
If we fix the number of fermions $n_{\mathrm{F}}$ and inter-species
interaction $U_{bf}$ in Eq. (\ref{parameters2}) still there is a
dynamic part of the local Lindhard function $\chi'\left(\omega,\mu_{f}\right)$
we have to take into account. In the static limit $\omega/t_{f}\rightarrow0$
(where the Lindhard response function is purely real) there is nothing
unexpected in the behavior of the critical line (see discussion below).
However, we must stress that even we left the frequency dependence
apart, there is still very interesting part of physics remained, because
the Lindhard response function for the system with regular density
of states shows logarithmic divergence as temperature goes to zero.
These singularities give rise to instabilities in the system towards
two new ground states a phase separated state or a supersolid phase
\cite{buchler,buechler1}. On the other hand the oscillation of the
induced effective interaction between bosons is the origin of the
formation of charge density waves \cite{mering}.
Taking $\omega<\omega_{\mathrm{crit}}$ we recover the previous theoretical
results where, after adding fermions to the system, the effective
interaction $U_{\mathrm{eff}}$ becomes smaller than repulsive energy
$U_{b}$ for bosons only (see Fig. \ref{fig4} and Fig. \ref{fig5})
and superfluid phase increases. The above is best shown on Fig. \ref{fig6}
where for very small amount of fermions $n_{\mathrm{F}}$ the parameter
$\alpha<1$ causes decreasing the Mott insulator region of the phase
diagram in comparison to the pure bosonic case. However, in the local
dynamic limit, when $\omega>\omega_{\mathrm{crit}}$ the Mott insulator
phase is becoming stronger and bosons tend to localize on the lattice
sites in both $2D$ and $3D$ cases (see Fig. \ref{fig6}, Fig. \ref{fig7}
and Fig. \ref{fig8}).
\begin{figure}
\includegraphics[scale=0.85]{Fig7}\caption{(Color online) Phase diagrams ($t_{b}/U_{b}$-$\mu_{b}/U_{b}$) for
the square ($2D$) lattice for different $\alpha=0.5$ (higher panel,
$\omega<\omega_{\mathrm{crit}}$), $\alpha=1.5$ ($\omega>\omega_{\mathrm{crit}}$)
and $\eta=1$ (positive scattering length $a_{bf}>0$). Dashed line
stands for the phase boundary of one-component Bose-Hubbard model.
Within the lobes the Mott insulator phase takes place with $\Psi_{\mathrm{B}}=0$.\label{fig7}}
\end{figure}
\begin{figure}
\includegraphics[scale=0.85]{Fig8}\caption{(Color online) Phase diagrams ($t_{b}/U_{b}$-$\mu_{b}/U_{b}$) for
the cubic ($3D$) lattice for different $\alpha=0.5$ (higher panel,
$\omega<\omega_{\mathrm{crit}}$), $\alpha=1.5$ ($\omega>\omega_{\mathrm{crit}}$)
and $\eta=1$ (positive scattering length $a_{bf}>0$). Dashed line
stands for the phase boundary of one-component Bose-Hubbard model.
Within the lobes the Mott insulator phase takes place with $\Psi_{\mathrm{B}}=0$.\label{fig8}}
\end{figure}
\begin{figure}
\includegraphics[scale=0.8]{Fig9}\caption{(Color online) The maximum of the critical value for the parameter
$\left(t_{b}/U_{b}\right)_{\mathrm{max}}$ with $n_{\mathrm{B}}=1$
for different $\alpha=4$, $3$, $2$, $1$, $0.75$, $0.5$, $0.25$,
$0.1$ for square ($2D$) and cubic ($3D$) lattice. Vertical solid
line stands for the $\left(t_{b}/U_{b}\right)_{\mathrm{max}}$ obtained
in the one-component Bose-Hubbard model with one particle per lattice
site. Above the curves the superfluid phase takes place with $\Psi_{\mathrm{B}}\neq0$.\label{fig9}}
\end{figure}
One may argue that the Lindhard response function depends not only
on the frequency $\omega/t_{f}$ but also on the chemical potential
$\mu_{f}/t_{f}$ for fermions and so far we did not restrict ourselves
to any particular value of it. In many approaches it is a little tricky
to handle because despite of the absence of any direct interaction
between fermions $U_{ff}=0$ the density-density fluctuations can
indeed induce some effective interaction between fermionic species
\cite{illuminati}. Therefore problem becomes complex and many theories
just take half-filled band with $n_{\mathrm{F}}=1$ so that $\mu_{f}/t_{f}=0$.
Alternative approach comes from partial particle-hole symmetry Hamiltonian
Eq. (\ref{hamiltonian}) possesses. To make our approach self-consistent
we can calculate how does a particular value of the fermionic chemical
potential change in the effectively interacting system. We remind
that the amplitude of the order parameter was obtained from minimization
condition, assuming nonfluctuating bosonic amplitude at low temperatures.
By operating a similar procedure we get a shift of the chemical potential
for fermions \begin{equation}
\mu_{f}\rightarrow\mu_{f}-U_{bf}\left(2z\frac{t_{b}}{U_{b}}+\frac{\mu_{b}}{U_{b}}-\eta+\frac{1}{2}\right),\label{shift}\end{equation}
that in the non-interacting case $U_{bf}=0$ reduces to that of free
particles obeying fermionic commutation relations (see also Appendix).
There is the limit where the system containing gaseous mixtures has
the same value of $x\left(\alpha,\eta\right)$ as in the case of only
bosons confined in optical lattice (see Fig. \ref{fig9}). Again,
we take advantage of the choice of the parameters, that suits well
our goal, and make notation of the condition very simple. If $\eta=1-\alpha$
we have\begin{equation}
x_{n}\left(1,0\right)=x_{n}\left(\alpha,1-\alpha\right).\label{condition}\end{equation}
The above, in terms of the original variables, leads to $U_{bf}n_{\mathrm{F}}/U_{b}=U_{bf}^{2}\chi'\left(\omega,\mu_{f}\right)/U_{b}$.
For cubic lattice the formula Eq. (\ref{condition}) seems to not
hold (Fig. \ref{fig9}) however is accurate with a numerical error
less than $0.17$ percent. Therefore, if the number of fermions added
to the system is equal to the inter-species interaction then bosons
behaves as if were unaffected by the presence of fermions. As a matter
of fact we have to remember about sign of the scattering length $a_{bf}$
and normalized frequency $\omega/t_{f}$ that also modifies the introduced
condition. The recent experiment\cite{best} shows that there is an
asymmetry in profiles of visibility of the interference pattern (recorded
by absorption imaging) versus the inter-species scattering length
that increases with lattice depth. Presented data indicate that visibility
shows a maximum at the position consistent with $a_{bf}=0$. Besides,
there is an asymmetry in a shift of the MI to SF transition boundary.
Our calculations can reproduce latter however if the sign of the inter-species
interaction is negative the MI phase diminishes and quite oppositely
for positive scattering length and, as we expected, some anomaly appears
at the point with $\mu_{b}/U_{b}=0$ (see Fig. \ref{fig7} and Fig.
\ref{fig8}). There is no physical reason for the phase boundary to
change a position where the chemical potential for bosons is zero
and the repulsive interactions are very strong $U_{b}\rightarrow\infty$.
Moreover, in that case the value obtained from Eq. (\ref{critical line-1})
at mentioned point ($\mu_{b}/U_{b}=0$ and fixed $\eta>0$) is constant
in whole nonzero range of the parameter $\alpha$ and depends only
on the considered topology of the system. The similar to fermion-boson
loss of coherence for the boson-boson species was found using the
Gutzwiller mean-field approach \cite{buosante}. The main effect of
the addition different species of the same statistics is that the
new structure of wedding cake appear but the oscillatory behavior
of the relevant condensate fraction does not necessarily result in
increase of the overall coherence of other species. The later is limited
exclusively to the shallow lattice depth and was never observed in
the experiments.
We want to stress that one have to be careful with the analysis of
the phase diagrams. The summary of our results for square lattice
(we omit qualitatively similar results for cubic geometry) is presented
on Fig (\ref{fig10}) and Fig (\ref{fig11}). For the static and dynamic
limit, but below the critical frequency $\omega<\omega_{\mathrm{crit}}$
the Mott insulator region on the phase diagram broadens only when
the scattering length is positive (the part of the surface above the
plane of the critical value of $x_{1}\left(1,0\right)$ for the one-component
BH model). When we must take into account the difference in the inter-species
masses $m_{b}/m_{f}\neq1$ the sign of the real part of the local
Lindhard response function may become positive and, in consequence,
$\alpha$ parameter takes values above one Fig. (\ref{fig11}) leading
to higher repulsive energy between bosons even if measured scattering
length is negative. In that case for $\alpha>1-\eta$ there is always
a shift for higher values for the parameter $x_{n}\left(\alpha,\eta>1-\alpha\right)$
results in stronger localization of the bosons after adding fermions
to the system.
\begin{figure}
\includegraphics[scale=0.8]{Fig10}\caption{(Color online) The maximum of the critical value for the parameter
$\left(t_{b}/U_{b}\right)_{\mathrm{max}}$ with the negative real
part of the local dynamic Lindhard function $ $$\chi'\left(\omega\right)<0$
($\omega<\omega_{\mathrm{crit}}$), for cubic ($3D$) lattice in the
space of the dimensionless parameters $\alpha-\eta$ with $n_{\mathrm{B}}=1$.
The flat surface stands for $x_{1}^{3D}\left(1,0\right)$ (see also
Eq. \ref{condition}) in case of the one-component Bose-Hubbard model
with one particle per lattice site. The dashed line stands for the
condition where the system of gaseous mixtures has the same value
$\left(t_{b}/U_{b}\right)_{\mathrm{max}}$ as only bosons confined
in optical lattice. Above the surfaces the superfluid phase takes
place with $\Psi_{\mathrm{B}}\neq0$.}
\label{fig10}
\end{figure}
\begin{figure}
\includegraphics[scale=0.8]{Fig11}\caption{(Color online) The maximum of the critical value for the parameter
$\left(t_{b}/U_{b}\right)_{\mathrm{max}}$ with the positive value
of the real part of the local dynamic Lindhard function $ $$\chi'\left(\omega\right)>0$
($\omega>\omega_{\mathrm{crit}}$), for cubic ($3D$) lattice in the
space of the dimensionless parameters $\alpha-\eta$ with $n_{\mathrm{B}}=1$.
The flat surface stands for $x_{1}^{3D}\left(1,0\right)$ (see also
Eq. \ref{condition}) in case of the one-component Bose-Hubbard model
with one particle per lattice site. The dashed line stands for the
condition where the system of gaseous mixtures has the same value
$\left(t_{b}/U_{b}\right)_{\mathrm{max}}$ as only bosons confined
in optical lattice. Above the surfaces the superfluid phase takes
place with $\Psi_{\mathrm{B}}\neq0$.}
\label{fig11}
\end{figure}
\section{Conclusions}
It is well known that the ground state of a system of repulsively
interacting bosons confined in a periodic potential can be either
in a superfluid or in a Mott-insulting state, characterized by integer
boson densities. Because the phase of the order parameter and the
particle number, as conjugate variables, are subject to the uncertainty
principle $\Delta\phi\Delta n\sim\hbar$, so the bosons can either
be in the eigenstate of particle number or phase. The eigenstate of
phase is a superfluid and that of particle number is a localized Mott
insulator. Therefore, the quantum MI-SF phase transition takes place
as the particle density is shifted thus facilitating emergence of
the superfluid from the Mott insulating state. Adding to bosons particles
of different statistics and allowing for the mutual repulsion or attraction
between species strongly affects the equilibrium properties. We presented
a field-theoretic study of the ground-phase diagram in quantum two-
and three-dimensional gaseous Bose-Fermi condensates where mentioned
emulation takes place. We calculated the phase diagram using the quantum
rotor approach that can reproduce the asymmetry in a shift of the
MI to SF transition boundary for positive and negative inter-species
scattering length. Analysis of the local dynamic Lindhard function
revealed the critical value of the frequency for the collective excitations,
where the real part of the response function (and in consequence the
interaction between bosons and fermions) alters sign. The choice of
the parameters of the model led to simple condition for the experimentally
accessible parameters within the phase diagram for Bose-Fermi mixtures
is qualitatively the same as for one-component repulsively interacting
Bose system. We also compared the maximum of the critical value for
$t_{b}/U_{b}$ parameter (as a function of the normalized chemical
potential $\mu_{b}/U_{b}$) at the tip of the $n$th MI lobe for square
and cubic lattice with numerical diagrammatic method and found them
in a good agreement especially for higher, experimentally realizable,
filling factors. The nice feature of presented approach, described
in details above, is that all the expressions and handling are analytic.
It is also worth to notice that provided local approximation can be
very useful in various situations whenever the retardation effects
has to be taken into account and we are not interested in effects
caused by non-locality.
|
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In yesterday's post, I argued that the instinct to scale programs is not, despite wide-ranging concerns about the concept from nonprofit practitioners, the enemy. This is an important topic for PhilanthroMedia because, frankly, trepidation usually comes in response to donors who want to either scale initiatives they have helped launch or only to invest in programs that have the capacity to scale. In other words, if I may be so bold as to generalize, investments with the potential for national impact are valued more highly by some than those that only have the potential to benefit an individual community.
I'm not waving the flag for Walmart when I state my support for instincts that seek to gain maximum leverage for charitable investments. In fact, that is largely the topic with which this blog concerns itself. As someone who has spent most of my professional lifetime in the nonprofit sector, I'd like to state two personal examples for why I believe the trends described in yesterday's post point the way to greater dollar-per-dollar impact.
Example #1: I ran a small (average $350k annual income) youth agency for years and know what it is like to raise money a nickel and dime at a time. I started there at $18,000 in 1988 and two days later, when the leading candidate for executive director declined the job, it was mine with a raise to $28,000. I was 26 years old and knew nothing about running a youth agency, nothing about the town to which I had just moved and nothing about fundraising. But they could afford me.
While we had much success over my eight-year tenure, inexperience coupled with inadequate resources meant that we sorely lacked basic systems and capacities. Even so, we never talked about merging with any other organization or shifting to do only what we did best (which was to run an award-winning, citywide teen newspaper and video program.) We assumed that what we did was by any means better than nothing so we limped along. And almost twenty years after I took the job, that agency is still scrambling each month to cover costs and to hold together an idea whose vibrancy, in this new media age, faded long ago.
Example #2: In 1996, I left my position as head of the Children, Youth and Families Initiative at the Chicago Community Trust, to move off the grid (only felt like it) to a tiny little town in Southwest, Michigan. Almost immediately I was roped, by the people of that fair town, on to a planning committee of individuals who were trying to launch a Boys and Girls Club (BGC.) Great folks, great instincts, but together we couldn't plan our way out of a paper bag.
Before I joined, they had already identified a drafty old barn for the site and decided that they wanted to become an official member of that national organization in order to secure the wide range of resources that came with membership. I remember the BGC rep coming to several of our meetings to assist us with meeting their requirements. I recall how we could never quite pull it all together to gain buy-in from the diverse constituents needed to ensure the club's sustainability. Eventually the initiative failed and the club never came to fruition. You could blame the BGC for their requirements, put in place to ensure consistent quality across their efforts to scale. Or, as I did, you could recognize that if we had gone ahead with the money we might scrap together, the club would have failed just a little further down the road. But fail it would have.
Obviously, since I am a consistent variable in both examples and others that come to mind as I write, it is possible that I am the one to blame. But neither I nor any individual is powerful enough to overcome the, in many ways fundamentally flawed, dynamics of the nonprofit marketplace. And yet we try. We give our heart and soul to keeping precious, local, small, organic social entities alive in the bloody red ocean of competition. While I don't fault those who do, after a couple of decades of experience, I now gravitate to those that have the potential to gain momentum and the resources that come with it. While I love a start-up as much as the next social entrepreneur, my start-ups now start up with an eye toward that momentum.
Scale may not be the holy grail, but it ain't bad.
P.S. In response to yesterday's post, Bruce Trachtenberg wrote: "Obviously we need scale, especially to get those programs that work in more places where they can do more good. But we also have to guard against spreading too thinly. For more "real life" adventures of what it's like for youth serving organizations to attempt to go to scale, readers might enjoy this Bridgespan report."
Copyright © 2006 Philanthromedia. All Rights Reserved.
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{"url":"http:\/\/www.physicsforums.com\/showpost.php?p=4289441&postcount=1","text":"View Single Post\n P: 38 Hello! In the study of electric and magnetic fields, two equations are called the constitutive relations of the medium (the vacuum, for example): $\\mathbf{D} = \\mathbf{\\epsilon} \\cdot \\mathbf{E}\\\\ \\mathbf{B} = \\mathbf{\\mu} \\cdot \\mathbf{H}$ But in a generic medium (non linear, non isotropic, non homogeneous) $\\mathbf{\\epsilon}$ and $\\mathbf{\\mu}$ are tensors. Now, why not matrices with dimension 3x3? $\\mathbf{E}$ and $\\mathbf{H}$ are \"simple\" three-dimensional vectors. I know that a matrix is a particular case of a tensor, but so why do we never use the term \"matrix\" in this context? A matrix could exist only if a particolar system of coordinates is defined, whereas a tensor can always exist: is it the reason for calling $\\mathbf{\\epsilon}$ and $\\mathbf{\\mu}$ tensors and not just matrices? Thank you anyway! Emily","date":"2014-08-23 15:22:35","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.637456476688385, \"perplexity\": 521.3147741604381}, \"config\": {\"markdown_headings\": false, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": false}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2014-35\/segments\/1408500826259.53\/warc\/CC-MAIN-20140820021346-00233-ip-10-180-136-8.ec2.internal.warc.gz\"}"}
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Khukhrains.com - Official Website of Khukhrain Biradari - Chandragupta: Maurya or Anand?
Chandraguptawas born in 340 BC was the founder of the Maurya Dynasty. In Greek he is known as Sandrokuptos, Sandrokottos or Androcottus.
King Padam Anand was killed by Chandragupt, at that time the kingdom was divided among the eight brothers. Thus Magadha was disintegrated and became weak and vulnerable. Besides, Dhan Anand and his seven brothers were too weak to maintain peace in their territories.
Getting benefit of the deteriorate situation, the old deserted General of King Padamanand's army known as Chandragupta Anand captured the Magadha Empire in 322 B.C. and became the King.
Chandragupta Anand was the son of ANAND royal family of Magadha, but his mother was a maid name as MURA. When he became the King, he adopted his Surname as MAURIYA after his mother's name MURA DEVI.
That's why Ashoka renamed Mauriya Dynasty on the name of his ancestors as Anand Dynasty which was earlier mispronounced as Nanda Dynasty.
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\section{Introduction}
\label{sec:intro}
\setcounter{footnote}{1}
In January 1993 \citet{Guedel} detected microwave radiation from the
nearby solar-type dwarf $\kappa$~For. Its source was located
$0\farcs23$ south of the star. At that time it was already known that
$\kappa$~For is a spectroscopic binary. So, the authors suggested
that the radio emission comes from the secondary companion, presumably
a low-mass flaring dwarf. As we show below, the secondary is in fact a
tight pair of M dwarfs. Despite the old age of this triple system
(4 to 6~Gyr), fast axial rotation of the M-dwarfs (hence high
activity) is maintained by synchronization with the orbit.
Kappa Fornaci (HIP~11072, HD~14802, HR~895, GJ~97,
$\alpha_{2000}=$2:22:32.54, $\delta_{2000}=-$23:48:58.8) is located at
a distance of 22\,pc from the Sun according to the original {\it
Hipparcos} catalog \citep{HIP} and its new reduction
\citep{HIP2}. The {\it Hipparcos} satellite detected a large
acceleration of 19.4\,mas~yr$^{-2}$ presumably caused by the invisible
(astrometric) companion \citep{MK05}. \citet{Gontcharov2001}
collected historical astrometric data spanning half a century and
suggested that the orbital period is around 26.5\,yr. Later
\citet{GK02} published the elements of the astrometric orbit with this
period and with a relatively large semi-major axis of $\alpha =
0\farcs26$, noting that the ``dark companion'' is massive.
Radial velocity (RV) of $\kappa$~For was monitored both at Lick and at
La Silla in search of planetary companions. None was found so far, but
the RV trend caused by the stellar companion was obvious.
\citet{Nidever02} noted the trend, while \citet{Endl02} published a
preliminary spectroscopic orbit with a 21\,yr period. \citet{Abt06}
added their own observations and revised the orbit slightly, although
the full orbital cycle was not yet covered. Neither of these
publications mentions the astrometric results.
The astrometric and spectroscopic companion was first resolved by
\citet{LAF2007} in 2005 and, independently, by \citet{TC08} in 2007.
For this reason it received two confusing ``discoverer'' codes LAF~27
and TOK~40 in the Washington Double Star Catalog
\citep{WDS}.\footnote{The WDS keeps outdated tradition of assigning
discoverer codes even when the duplicity was actually discovered
before the first position measurement, as in the case of
$\kappa$~For} By using all resolved measures and fixing the orbital
period and eccentricity to those of the Gontcharov's orbit,
\citet{HTM12} computed the first visual orbit of grade 4. Here we add
new observations and derive the combined interferometric/spectroscopic
orbit which agrees with the astrometric orbit.
SIMBAD lists 187 references to date and provides basic data on the
primary companion, such as spectral type G1V, magnitudes $V=5.19$,
$B-V=0.60$, $K_s=3.741$, and near-solar metallicity
\citep[see the full compilation of stellar parameter measurements
in][]{PASTEL}. The star is located above the Main Sequence in the
$(V, B-V)$ color-magnitude diagram (CMD), being obviously evolved.
\citet{N04} estimate the age of 6\,Gyr by isochrone fitting.
\citet{Nielsen10} cite indirect age estimates of 4\,Gyr and 6.3\,Gyr
from the lithium line strength and rotation, respectively. The star
was observed by {\it Spitzer} and found to have no debris disk
\citep{Trilling08}. Yet, \citet{Nakajima2012} claimed recently that
$\kappa$~For is young and belongs to the IC~2391 moving group. In
calculating the kinematic parameters they overlooked the companion and
used the {\it Hipparcos} proper motion (PM), biased by the orbit. We
calculate the heliocentric Galactic velocity components of
$\kappa$~For from the center-of-mass PM \citep{Gontcharov2001} and the
new $\gamma$-velocity to be $[U,V,W] = [-19.5, -16.2,
-9.6]$\,km~s$^{-1}$ ($U$ is positive towards the Galactic center).
\begin{figure*}
\plotone{fig1.eps}
\caption{Combined orbit of $\kappa$~For AB. Left panel: orbit in the
plane of the sky, scale in arcseconds. The insert shows the $K$-band
image taken at Gemini-S on 2012.67. Right panel: the RV curve with
early measures plotted as crosses.
\label{fig:orbit}
}
\end{figure*}
In Section~2 we derive the updated orbit of the outer system AB. Then
in Section~3 we evaluate the parameters of the companions and show
that the secondary B is over-massive, being itself a close
binary. This hypothesis is confirmed in Section~4 by direct
spectroscopic detection of Ba and Bb. In the last Section~5
we discuss the implications of this finding for multiplicity
statistics and exo-planet searches.
\section{The orbit of AB}
\label{sec:orb}
So far, spectroscopic, astrometric, and visual orbits of $\kappa$~For
were determined almost independently of each other. We add fresh
measures and combine available data in the single orbital solution
presented in Fig.~\ref{fig:orbit}. The orbital elements and their
formal errors are obtained by the unconstrained least-squares fit with
weights inversely proportional to the measurement errors. The elements
are listed in Table~\ref{tab:orbits} together with the previously
published orbits. We have not used the astrometric data of
\cite{GK02}, so the good match between spectro-interferometric and
astrometric orbits speaks to their veracity. This is not the case of
spectroscopic orbits which have a too short period. \citet{Abt06}
mention that they used ``some older measures'' in the orbit derivation
but do not specify their source. In the future, with better RV and
positional coverage, the elements will be determined to a much higher
precision than here, but they will no longer be revised beyond the
stated errors. The new orbit and the {\it Hipparcos} parallax of
45.53$\pm$0.82\,mas \citep{HIP2} correspond to the semi-major axis of
11.44\,AU and to the mass sum of 2.25$\pm$0.13\,$M_\odot$ (the
uncertainty comes mostly from the parallax error).
\begin{deluxetable*}{ ccc ccc ccc l }
\tabletypesize{\scriptsize}
\tablecaption{Orbits of $\kappa$~For AB
\label{tab:orbits}}
\tablehead{
$P$ & $T$ & $e$ & $a$ & $\Omega_A$ & $\omega_A$ & $i$ & $K_1$ & $\gamma$ &
Ref. \\
(yr) & (BY) & & ($''$) & $^\circ$ & $^\circ$ & $^\circ$ & km~s$^{-1}$ & km~s$^{-1}$
& }
\startdata
26.5$\pm$2 & 1983.6$\pm$2.3 & 0.2$\pm$0.1 & 0.26$\pm$0.01 & 133$\pm$6 & 202$\pm$31 & 56$\pm$4 & \ldots & \ldots & a \\
21.46$\pm$0.09 & 1967.26$\pm$1.9 & 0.30$\pm$0.04 & \ldots & \ldots & 263$\pm$12 & \ldots & 3.95$\pm$0.26 & 18.13$\pm$0.66 & b \\
26.5 * & 2015.69 & 0.20 * & 0.493 & 131.6 & 275.5 & 44.8 & \ldots & \ldots & c \\
25.81$\pm$0.15 &1988.89$\pm$0.17 & 0.339$\pm$0.013 & 0.521$\pm$0.004 &
139.8$\pm$1.4 & 266.3$\pm$1.0 & 50.4$\pm$0.5 & 5.23$\pm$0.13 &
16.67$\pm$0.06 & d
\enddata
\tablenotetext{}{References: a -- astrometric \citep{GK02}; b -- spectroscopic
\citep{Abt06}; c -- visual \citep{HTM12}; d -- combined, this work}
\end{deluxetable*}
\begin{deluxetable}{l ccc l}
\tabletypesize{\scriptsize}
\tablewidth{0pt}
\tablecaption{Radial velocities and residuals of $\kappa$~For A
\label{tab:RV}}
\tablehead{JD & RV & $\sigma$ & O$-$C & Ref. \\
+2400000 & km~s$^{-1}$ & km~s$^{-1}$ & km~s$^{-1}$ & }
\startdata
19378.67 & 18.6 & 2.0 & 1.08 & a \\
19649.90 & 19.9 & 2.0 & 0.58 & a \\
19762.62 & 17.4 & 2.0 & -2.52 & a \\
21152.78 & 17.8 & 10.0 & -3.69 & a \\
49000.0 & 21.82 & 0.2 & 0.04 & b \\
50000.0 & 20.74 & 0.2 & 0.00 & b \\
50800.0 & 19.36 & 0.2 & -0.05 & b \\
51170.080 & 18.824 & 0.1 & 0.06 & c \\
51884.735 & 17.71 & 0.1 & 0.23 & d \\
\ldots & \ldots & \ldots & \ldots & d \\
53001.665 & 15.46 & 0.1 & 0.04 & d \\
55979.533 & 11.53 & 0.5 & -0.055 & e \\
55983.528 & 11.54 & 0.5 & -0.052 & e \\
56165.830 & 12.001 & 0.01 & -0.005 & e \\
56167.865 & 12.019 & 0.01 & 0.007 & e \\
56171.797 & 12.032 & 0.01 & 0.008 & e \\
56182.861 & 12.048 & 0.01 & -0.009 & e \\
56194.830 & 12.095 & 0.01 & 0.002 & e \\
56200.834 & 12.111 & 0.01 & -0.001 & e
\enddata
\tablenotetext{}{References: a -- \citep{Lick}; b -- \citep{Endl02}, zero-point 20.36\,km~s$^{-1}$;
c -- \citep{Nidever02}; d -- \citep{Abt06}; e -- this work.}
\end{deluxetable}
\begin{deluxetable}{l rrr c c l}
\tabletypesize{\scriptsize}
\tablewidth{0pt}
\tablecaption{Positional measures and residuals of $\kappa$~For AB
\label{tab:speckle}}
\tablehead{$t$ & $\theta$ & $\rho$ & $\sigma$ &
\multicolumn{2}{c}{(O$-$C)$_\theta, \rho$} & Ref. \\
yr & $^\circ$ & mas & mas & $^\circ$ & mas & }
\startdata
2005.6348 & 267.1 & 469 & 5 & 0.4 & -2 & a\\
2007.8130 & 285.9 & 542 & 100 & -1.7 & 44 & b \\
2008.6282 & 294.8 & 502 & 2 & -0.2 & 0 & c\\
2008.6936 & 295.3 & 501 & 2 & -0.3 & -1 & c\\
2008.8549 & 296.7 & 502 & 2 & -0.4 & 0 & c\\
2010.9655 & 317.8 & 464 & 2 & 0.6 & 3 & d\\
2012.8300 & 343.0 & 345 & 2 & 0.1 & 0 & e
\enddata
\tablenotetext{}{References: a -- \citep{LAF2007}; b -- \citep{TC08};
c -- \citep{TMH10}; d -- \citep{HTM12}; e -- this work.}
\end{deluxetable}
Radial velocities used in the orbit calculation are listed in
Table~\ref{tab:RV}. \citet{Endl02} did not publish the RVs; three
points from their Fig.~6 (1993--1998) are nevertheless included in
the present solution by assuming that the zero velocity in their plot
corresponds to 20.36\,km~s$^{-1}$. In this case their data match well the
single measurement in 1999 published by \citet{Nidever02} and the
velocities from \citep{Abt06}, of which we list here only the first
and the last points. The latest RV measures are obtained by the author
in 2012 (see Section~\ref{sec:chiron}). We also use the RVs measures
made in Santiago in 1911--1916 with the 2-prism spectrometer
\citep{Lick}. Although the precision of these early data (crosses in
Fig.~\ref{fig:orbit}, right) is low, they help in constraining the orbital period.
Positional measures of $\kappa$~For AB and their residuals to the new
orbit are listed in Table~\ref{tab:speckle}. The first measure is
performed with adaptive optics, the remaining data come from speckle
interferometry at the SOAR telescope in Chile.
The latest speckle measure was made at SOAR on October
29, 2012. The first speckle resolution is given a low weight,
considering uncertain calibration in that early experimental work.
\section{Properties of the components}
\label{sec:Bab}
The component A ($V=5.19$~mag, $B-V=0.60$) is located $\sim 1.5^m$ above
the Main Sequence in the $(M_V, B-V)$ CMD, as noted by \citet{N04}. By
fitting isochrones, these authors estimated the mass of the main star
$M_{\rm A}$ to be between 1.12 and 1.18\,$M_\odot$. We checked this
against the isochrones of \citet{Girardi} and found that the mass of A
can be as high as 1.25\,$M_\odot$ if its age is 4\,Gyr (it is just
leaving the Main Sequence). It is safe to assume that $M_{\rm A} =
1.20 \pm 0.05\,M_\odot$.
\begin{deluxetable}{l | c c c c}
\tabletypesize{\scriptsize}
\tablecaption{Photometry of the resolved components
\label{tab:ptm} }
\tablehead{Parameter & $V$ & $I$ & $H$ & $K_s$ \\
& mag & mag & mag & mag }
\startdata
$m_{\rm A+B}$ & 5.19 & 4.51 & 3.712 & 3.741 \\
$m_{\rm B} - m_{\rm A}$ & 5.02$\pm$0.04 & 3.69$\pm$0.05 & (2.46) & (2.14) \\
$m_{\rm B}$ & (10.21) & (8.23) & 6.3$\pm$0.2 & 6.0$\pm$0.2
\enddata
\end{deluxetable}
The photometric data are collected in Table~\ref{tab:ptm}. The
magnitude difference in the Str\"omgren $y$ and Cousins $I$ filters
was determined by speckle interferometry at SOAR (6 and 5 independent
measures respectively); we list here the average values and their
formal errors and assume $\Delta V \approx \Delta y$. The derived
quantities are listed in brackets.
The flux ratio in the 1.54-1.65\,$\mu$m band (which is close to $H$)
was estimated by \citet{LAF2007} as $\Delta H = 2.7 \pm 0.2$~mag. On 2012
September 2 (2012.6706) the binary was resolved with the NICI adaptive
optics instrument \citep{Chun08}, see Fig.~\ref{fig:orbit}. As the
primary companion was heavily saturated, the position measurement
($340.5^\circ$, 0\farcs342) is not very accurate (it is not included
in Table~\ref{tab:speckle}), and no relative photometry could be made.
However, the flux from the well-resolved companion B (after halo
subtraction) was estimated by comparing it to stars HIP~8674 and
HIP~12425 observed before and after this target at nearly the same
airmass. The $H$ and $K_s$ magnitudes of those two stars from 2MASS
were used to determine the zero point (the actual wavelength of the
narrow-band filters was 1.587\,$\mu$m and 2.272\,$\mu$m). In this way
we obtained crude estimates of the companion's infrared magnitudes
$H=6.0\pm0.2$~mag and $K_s = 6.3\pm0.2$~mag.
The magnitudes and colors of the companion B are thus established
reasonably well, $(V - I)_{\rm B} = 1.98 \pm 0.06$ and $(V - K_s)_{\rm
B} = 4.2 \pm 0.2$. Standard relations match those colors for a dwarf
star of $\sim$0.48\,$M_\odot$, but the component B is located about
$1.5^m$ above the Main Sequence in the $(M_V, V-I)$ and $(M_V, V-K)$
CMDs; its luminosity corresponds to a single dwarf of
$\sim$0.65\,$M_\odot$. This discrepancy is caused by the binary
nature of B.
Large total mass of the companion B follows from the orbital
parameters. Motion of the photo-center is characterized by the
semi-major axis $\alpha$ of the astrometric orbit. Its ratio to the
semi-major axis $a$ of the visual orbit is related to the mass ratio
$q = M_{\rm B}/M_{\rm A}$ and to the light ratio $r$ as
\begin{equation}
\phi = \frac{\alpha}{a} = \frac{q - r}{(q+1)(r+1)}.
\label{eq:phi}
\end{equation}
In our case we can neglect the companion's light because $r \approx
0.01$. The orbit of AB derived here and the astrometric orbit of
\citet{GK02} correspond to $\phi = 0.50$ and $q = \phi/(1 - \phi) =
1.0$. The companion B is therefore as massive as A while being
$\sim$100 times fainter at optical wavelengths. This finding agrees
with the large orbital mass sum.
Another argument for the high companion's mass is furnished by radial
velocities. Using the formula $a_1 \sin i = 0.01375 K_1 P (1 -
e^2)^{0.5}$ ($a$ in $10^6$km, $K_1$ in km~s$^{-1}$, $P$ in days) we
obtain $a_1= 5.53$\,AU and $\phi=a_1/a = 0.48$, leading to $q=0.93$.
The {\em Hipparcos} astrometry agrees very well with the new orbit if
we adopt the companion's masses inferred from the photometry, $M_{\rm
A}= 1.20\,M_\odot$ and $M_{\rm B}= 0.96\,M_\odot$, or $q=0.80$ and
$\phi = 0.43$. Using this $\phi$, we compute the photo-center motion
during the {\it Hipparcos} mission (mean epoch 1991.25, duration
3.2\,yr). Table~\ref{tab:hip} shows that the orbital proper motion of
the photo-center $\Delta \mu$ and its acceleration $\dot{\mu}$ match
the ephemeris in both magnitude and direction. In 1991.25 the
companion moved mostly to the South (see the circle in
Fig.~\ref{fig:orbit}, left), the photo-center moved to the North. The
measured $\Delta \mu$ is the difference between the {\it Hipparcos}
PM of $(+197, -5)$\,mas~yr$^{-1}$ and the long-term PM
of $(+196, -60)$\,mas~yr$^{-1}$ derived by \citet{Gontcharov2001} from
the combination of all ground-based data. The {\it Hipparcos}
astrometry thus confirms the orbit and the fact that B is massive.
\begin{deluxetable}{l | c c | c c}
\tabletypesize{\scriptsize}
\tablecaption{Hipparcos astrometry and the orbit
\label{tab:hip} }
\tablehead{Parameter & \multicolumn{2}{c|}{ \it Hipparcos} &
\multicolumn{2}{c}{Orbit ($\phi = 0.43$)} \\
& RA & Dec & RA & Dec }
\startdata
$\Delta \mu$, mas~yr$^{-1}$ & 1 & +55 & $-$9 & +56 \\
$\dot{\mu}$, mas~yr$^{-2}$ & +13.0$\pm$2.0 & $-$14.4$\pm$1.8 & +17.7 & $-$9.2
\enddata
\end{deluxetable}
\section{Spectroscopy}
\label{sec:chiron}
\subsection{Observations}
Knowing that the companion B must be a close binary, we tried to
detect this sub-system spectroscopically, despite its small
contribution to the combined light. Optical spectra with resolution
$\lambda/\Delta \lambda = 80\,000$ were recorded with the fiber-fed
CHIRON echelle spectrometer installed at the 1.5-m telescope at CTIO
\citep{CHIRON} and operated in service mode. The object was observed
in 2012 six times, on August 25, 27, 31 and September 11, 23, 29
(hereafter nights 1 to 6). On each visit, two 300-s exposures with
the image slicer were taken, accompanied by the comparison spectrum of
the thorium-argon (ThAr) lamp. During this period, the position of
the ThAr spectrum remained stable on the CCD to better than 1 pixel.
Moreover, on the first night the star HIP~14086 was observed as a RV
reference.
Extracted and wavelength-calibrated spectra were delivered by the
pipeline running at the Yale University. They contain 59 echelle
orders (central wavelengths from 4605\AA~ to 8713\AA) of 3200 pixels
each (1.0768\,km~s$^{-1}$ per pixel). As red orders with $\lambda >7000$\AA~
suffer from extraction and calibration problems (too few thorium
lines), they are not used here. The maximum intensity in the spectra
varies from night to night with a total range of two times (from 25 to
50 thousand electrons per pixel). This corresponds to a S/N from 160
to 220.
\subsection{Radial velocities}
\begin{figure}[ht]
\epsscale{1.0}
\plotone{fig2.ps}
\caption{ Radial velocity of the component A vs. time. The dashed
line shows a linear fit with a slope of 2.9\,m~s$^{-1}$ per day.
\label{fig:RV}}
\end{figure}
Radial velocities of $\kappa$~For were derived by cross-correlating
the spectra with a binary mask which equals one in the lines of the
solar spectrum and zero otherwise. The mask was constructed from the
digital solar spectrum \citep{Arcturus}\footnote{NOAO data archive:
\url{ftp://ftp.noao.edu/catalogs/arcturusatlas}}, binary-clipped at
0.6 of the continuum level. The cross-correlation is computed in the
wavelength range from 4600\AA ~to 6500\AA, thus avoiding the
contamination by telluric lines at longer wavelengths. Regions within
$\pm 0.5$\AA~ of the hydrogen Bahlmer lines are excluded from the
mask. The minimum in the cross-correlation function (CCF) is
approximated by a Gaussian curve, its center is taken to be the
apparent stellar radial velocity, which is then corrected to the
barycenter of the solar system in the standard way. This procedure
relies on the wavelength calibration of the reduced spectra. We
attempted to refine the velocity zero point by cross-correlating red
orders with the mask of telluric lines, but did not obtain any
trustworthy results, probably because of the poor wavelength
calibration in the red.
Figure~\ref{fig:RV} shows the RVs derived from 12 individual spectra
as a function of time (the average RV for each night is listed in
Table~\ref{tab:RV}). The linear trend of 2.9\,m~s$^{-1}$ per day is caused by the
orbital motion. The rms scatter of RV around this line is 6.8\,m~s$^{-1}$,
the rms residual to the orbit is 6.7\,m~s$^{-1}$. As measures from the two
nightly spectra agree well, most of the scatter can be attributed to
the wavelength calibration based on the ThAr lamp. The mean FWHM of
the Gaussian fits to the CCF is 12.96\,km~s$^{-1}$, their equivalent width is
5.59\,km~s$^{-1}$.
The same procedure applied to HIP~14086 gives an RV of $+39.14$\,km~s$^{-1}$.
According to \citet{Nidever02} the RV of this star is constant at
$+42.718$\,km~s$^{-1}$, but \citet{N04} list a quite different value of
$+38.0$\,km~s$^{-1}$ (while SIMBAD lists the wrong RV of $-38.4$\,km~s$^{-1}$). Apparently,
this star is a yet unrecognized slow spectroscopic binary, unsuitable
as a RV standard. However, we use our RV measure of HIP~14086 to
derive the RV of $\kappa$~For from the two spectra taken in February
2012 during CHIRON tests (those spectra lack wavelength calibration).
These two measures with a somewhat uncertain zero point are given low
weight in the orbit solution by adopting errors of 0.5\,km~s$^{-1}$.
\subsection{Variability of the hydrogen line profile}
We detect a tiny variability of the H$\alpha$ profile presumably
caused by the moving emission of Ba and Bb. This is achieved by
subtracting the template obtained by averaging all spectra together.
Although the spectrometer was very stable during these observations,
the spectrum moved on the CCD by 12\,km~s$^{-1}$ owing to the variable
barycentric correction. The template was constructed by shifting the
nightly-averaged spectra (with a 3-pixel median smoothing of each
spectrum to remove the cosmic-rays spikes) to match the night 1,
normalizing them in intensity, and adding together. Obviously, the
telluric lines do not move together with the stellar lines and
therefore show up in the residuals between the individual spectra and
the template. The rms residuals after template subtraction are 0.7\%
in the order 37 containing H$\alpha$ and 0.5\% in the blue orders
which are free from the telluric lines.
\begin{figure}[ht]
\epsscale{1.0}
\plotone{fig3a.ps}
\plotone{fig3b.ps}
\caption{Variable features in the H$\alpha$ line on the night 1 (top
panel) and on the night 5 (bottom panel). In each panel the upper
curves show the continuum-normalized spectrum scaled by 0.1, with a
Gaussian fit to the H$\alpha$ (dashed line). The lower curves show
the residuals after template subtraction.
\label{fig:Ha}}
\end{figure}
We see a clear residual signal in the H$\alpha$ line on the nights 1
and 5, while on the remaining nights the residuals are close to zero
(Fig.~\ref{fig:Ha}). Similar features of lower amplitude are also seen
in the H$\beta$ line, confirming their reality. The single
``emission'' peak on the night 5 can be approximated by Gaussian
curves. Their amplitude is 2.1\% and 1.3\% for H$\alpha$ and H$\beta$
respectively, and they are shifted relative to the stellar spectrum by
$+0.28$\AA~ and $+0.23$\AA~ which corresponds to $+12.8$\,km~s$^{-1}$
and $+14.2$\,km~s$^{-1}$. If the emission originated on the
slowly-rotating primary companion A ($V \sin i = 4$\,km~s$^{-1}$), it
would be centered on the stellar line rather than shifted. We show
below that on the night 5 the lines of Ba and Bb were superimposed
near their center-of-mass velocity which should be displaced by
$+9.2$\,km~s$^{-1}$ relative to the RV of A according to the orbit
(the masses of A and Ba+Bb being near-equal). The double peak on the
night 1 also matches the expected position of the emission from Ba and
Bb. The non-detection of emission features on the other four nights
could possibly be explained by variable activity of the M-dwarfs.
\subsection{Retrieval of the Ba and Bb signature by cross-correlation}
We detect the signature of absorption lines belonging to Ba and
Bb by correlating the residual spectra (after subtracting the
template, see above) with the solar or Arcturus masks (the latter is
analogous to the solar binary mask but uses the digital Arcturus
spectrum from the same source). Only wavelengths shorter than 6500\AA~
are used in the correlation. The resulting CCF has a weak narrow
feature centered on the RV of A (Fig.~\ref{fig:res1}). This
feature originates because the resolution of the template spectrum is
slightly less than the resolution of the nightly spectra owing to
small residual alignment errors in the template creation. The sign
and intensity of this feature depend on the relative degree of
smoothing applied to the spectra and the template.
\begin{figure}[ht]
\epsscale{1.0}
\plotone{fig4.ps}
\caption{Correlation functions of residuals with the Arcturus mask for
6 nights (from bottom up, displaced by 0.0015 per night). The
horizontal axis corresponds to the heliocentric RV. The upper curve
is correlation with the template to which a fake companion of 0.5\%
intensity and +100\,km~s$^{-1}$ RV shift is added. The dashed and
dotted lines show suggested positions of the dips corresponding to
Ba and Bb components respectively moving on a 3.7-d orbit. Numbers
on the left are Julian dates, numbers on the right are the nights.
\label{fig:res1}}
\end{figure}
Apart from the central feature, we see additional dips with variable
position and intensity, presumably produced by Ba and Bb. Gaussian
approximations of the strongest dips have FWHM between 15 and
23\,km~s$^{-1}$ and equivalent width of about 0.0017\,km~s$^{-1}$.
The star gives a CCF with equivalent width of 3.54\,km~s$^{-1}$ for
the Arcturus mask, so the dip ratio corresponds to the flux difference
on the order of $5.8^m$ (we neglect here the different match of the
Arcturus mask with the late-type spectrum of Ba on one hand and with
the G0V spectrum of A on the other hand). A fake companion of 0.5\%
relative intensity ($5.75^m$ fainter than the primary) is readily
detectable by this method (see the upper curve in
Fig.~\ref{fig:res1}).
The curves in Fig.~\ref{fig:res1} give an impression of secondary
lines moving with an amplitude of $\sim$80\,km~s$^{-1}$. We found a
tentative circular orbit of Ba,Bb with a period of 3.666\,d,
semi-amplitude $K_1 = K_2 = 83$\,km~s$^{-1}$, $\gamma$-velocity
+26\,km~s$^{-1}$, and initial epoch (RV maximum) JD~2456166.45.
The data at hand are not sufficient for the orbit determination and
the above elements are a guess only. The dashed and dotted lines in
Fig.~\ref{fig:res1} are Gaussian dips corresponding to the Ba and Bb
components respectively and positioned according to this tentative
orbit (not fitted to the CCF). The assumed amplitudes of both
Gaussians are $-$0.0007, their FWHM is 16\,km~s$^{-1}$. On the night
1 we clearly see both dips. On the nights 3 and 4 the CCFs of
residuals look almost identical, the dips are near the maximum
separation.
Remember that the template includes the average spectrum of Ba and Bb,
so their lines near maximum separation (the most frequent situation)
are partially subtracted, leaving only small residuals. On the night
5 the dips overlap near the $\gamma$-velocity.
\begin{figure}[ht]
\epsscale{1.0}
\plotone{fig5.ps}
\caption{Correlation functions of residuals with the M-star synthetic
spectrum for 6 nights (from bottom up), similar to
Fig.~\ref{fig:res1}.
\label{fig:res3}}
\end{figure}
The reality of the detection of Ba and Bb was checked by correlating
the residuals with the synthetic spectrum of a late-type dwarf. We
used the $R=500\,000$ spectrum from
\citep{Bertone08}\footnote{\url{http://www.inaoep.mx/\~{}modelos/bluered/documentation.html}}
with parameters $T_e = 4000$\,K, $\log g = 5.0$, and solar
metallicity. The resulting CCF should have a peak corresponding to
the velocity of the secondary. Indeed, we see in Fig.~\ref{fig:res3}
positive features at approximately same velocities as the dips in
Fig.~\ref{fig:res1}. To highlight these features, we again over-plot
fiducial Gaussians with an amplitude of +0.00007 and velocities
predicted by the tentative Ba,Bb orbit.
The case of the component B being a binary is very strong. Its high
mass, position in the CMD, variable emission, and moving absorption
lines all confirm this hypothesis. The RV semi-amplitude in a
spectroscopic binary with a circular edge-on orbit of period $P$ days
is $A_0 = 213 P^{-1/3} M_2 (M_1 + M_2)^{-2/3}$\,km~s$^{-1}$, or 69\,km~s$^{-1}$ for
$P=3.7$\,d, assuming $M_1 = M_2 = 0.5 M_\odot$. The RV amplitude of
our tentative Ba,Bb orbit is therefore in qualitative agreement with
its period.
\section{Discussion}
\label{sec:disc}
The triple system $\kappa$~For consists of the main slightly evolved
(age 4--6\,Gyr) component A of 1.2\,$M_\odot$, and a pair of M-dwarfs
of $\sim$0.5\,$M_\odot$ each on a tight orbit with a tentative period of
3.7\,d. The masses of A and Ba+Bb are nearly equal.
Further spectroscopic observations of $\kappa$~For are needed to
confirm the tentative period of Ba,Bb and to determine its orbit and
mass. High-resolution spectroscopy in the near-infrared where the
contrast of Ba,Bb is more favorable will help in this endeavor
\citep[e.g.][]{Bender2008}. Given the short period, eclipses in
Ba,Bb are likely, but their photometric detection presents a challenge
because of the small (sub-percent) amplitude in the combined visible
light. Precise photometry will eventually detect flares on the active
M dwarfs. Long-term monitoring of both orbits will lead to the
accurate measurement of the distance and the masses of all three
stars.
Until now, the triple nature of $\kappa$~For was not recognized
despite its closeness to the Sun. The survey of \citet{Raghavan10}
lists it only as a binary. The question is how many more such systems
are we missing? This relates to the ways of discovering sub-systems in
the faint secondary companions.
The binarity of B was revealed by its unusually high mass.
Over-massive companions can be detected by astrometry quite easily,
comparing the photo-center axis $\alpha$ with the estimated full axis
$a$ (see eq.~\ref{eq:phi}), if the astrometric orbit and parallax are
known. However, reliable astrometric orbits are rare. Acceleration
measured by {\it Hipparcos} can also be used to estimate the mass
ratio in binaries with reliably known visual or astrometric orbits.
On the other hand,
an excess of the total mass in orbital visual binaries with known
parallax is a less promising way of finding such sub-systems because
of the typically large uncertainties in both measured and modeled
masses. Over-massive (binary) secondaries also can be detected by
a high minimum mass inferred from a spectroscopic orbit, as e.g. in
the case of the quadruple system HD~27638 \citep{TG01,Torres2006}.
Over-massive but invisible companions could be white dwarfs;
distinguishing them from tight pairs of red dwarfs usually requires
some sort of photometry. When the resolved photometry of the
secondary companion in two colors is available (e.g. from speckle
interferometry), it can be placed on the CMD and detected as a binary
by an excess in luminosity. Last but not least, spatial resolution of
the sub-systems is the most direct and powerful method; if the period of
Ba,Bb were longer than $\sim$0.5\,yr (semi-major axis $>30$\,mas), it
would have been resolved at SOAR.
Statistical modeling done by \citet{NICI} hints that 10\% to 20\% of
nearby solar-type astrometric binaries found by {\it Hipparcos} could
have ``massive'' secondaries (sub-systems or white dwarfs).
This conclusion, however, depends on several assumptions in the model.
The detection techniques outlined above can be applied systematically
to nearby binaries to better constrain the fraction of massive
secondaries without making any assumptions. If sub-systems in the
secondary companions are indeed as frequent as in the primaries, the
known number of hierarchical triples will be nearly doubled, changing
the multiplicity statistics dramatically.
Origins of multiple stars are still actively researched and debated,
and different theories are tested by their predictions about
multiplicity. For example, chaotic $N$-body dynamics rarely produces
pairs of low-mass stars revolving around more massive primaries;
rather, the primary itself is likely to end up in a close pair while
the least massive body is ejected into a distant orbit around it
\citep{DD03}. Fragmentation of rotating cores makes the opposite
prediction where the sub-systems in primary or secondary components
are equally likely to form, being a natural sink of the angular
momentum. In this paradigm, stars are often born as quadruples, but
some inner sub-systems subsequently merge. Originally $\kappa$~For
could have consisted of two pairs of similar 0.5-$M_\odot$ stars. One
pair had merged long time ago and became the present-day primary,
while the other pair Ba,Bb is still here.
Binary secondary companions such as the one of $\kappa$~For have
implications for the search of exo-planets. If the period of Ba,Bb
were few months or years, the weak secondary lines would always blend
with the lines of A and create a small periodic RV signal that could
be mistaken for an exo-planet signature, as e.g. in HD~19994
\citep{Roell}.
\acknowledgments I thank M.~Giguere for scheduling this program at
CHIRON and running the data-reduction pipeline. The design and
construction of CHIRON was supported by the National Science
Foundation under the ARRA AST-0923441.
This work used the SIMBAD service operated by Centre des Donn\'ees
Stellaires (Strasbourg, France) and bibliographic references from the
Astrophysics Data System maintained by SAO/NASA.
{\it Facilities:} \facility{SOAR},\facility{CTIO:1.5m}, \facility{Gemini-S}
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 7,532
|
__author__ = 'Glenn'
import unittest
from tictactoe_symmetry import *
class testSymmetry(unittest.TestCase):
def testApplySymmetries(self):
boardString = 'XO '
canon_string = canonical_board(boardString)
self.assertEqual('XO ', apply_symmetry(boardString, IDENTITY))
self.assertEqual(' X O ', apply_symmetry(boardString, ROT90))
self.assertEqual(' OX', apply_symmetry(boardString, ROT180))
self.assertEqual(' O X ', apply_symmetry(boardString, ROT270))
self.assertEqual(' OX ', apply_symmetry(boardString, VERTICAL))
self.assertEqual(' XO ', apply_symmetry(boardString, HORIZONTAL))
self.assertEqual(' O X', apply_symmetry(boardString, LEFT_DIAGONAL))
self.assertEqual('X O ', apply_symmetry(boardString, RIGHT_DIAGONAL))
def testSymmetricBoards(self):
self.assertEqual([apply_symmetry('XO ', i) for i in range(8)], symmetric_boards('XO '))
def testCanonicalBoard(self):
self.assertEqual((' X', 2), canonical_board('X '))
self.assertEqual((' OX', 2), canonical_board('XO '))
def test_get_symm_index(self):
self.assertEqual(0, get_symm_index(0, 0))
self.assertEqual(6, get_symm_index(0, 1))
self.assertEqual(7, get_symm_index(1, 2))
def test_is_canonical(self):
board, symmetry = canonical_board('X ')
assert is_canonical(board)
if __name__ == '__main__':
unittest.main()
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 2,517
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{"url":"https:\/\/www.usgs.gov\/center-news\/volcano-watch-hawaiian-oral-tradition-describes-formation-k-laueas-caldera","text":"# Volcano Watch \u2014 Hawaiian oral tradition describes formation of K\u012blauea's caldera\n\nRelease Date:\n\nSometimes you rediscover the wheel.\n\n\"Holo Mai Pele\" adapted for the Dance in America series on PBS.\n\n(Public domain.)\n\nGeologic research during the past 10 years shows that K\u012blauea's\u00a0caldera\u00a0formed in about A.D. 1500, immediately after a 60-year-long eruption from a shield near Thurston\u00a0lava tube, and for the next 300 years was the site of sporadic explosive activity. Had we been willing to believe Hawaiian chants about Pele and Hiiaka, and oral tradition related to William Ellis in 1823, we would have known this 100 years ago. Here's the story.\n\nNathaniel Emerson's translations of the chants, published in 1915 in his book \"Pele and Hiiaka: a Myth from Hawaii,\" describe the events, which independently are told in hula by Pualani Kanakaole Kanahele and Nalani Kanakaole in the wonderful \"Holo Mai Pele,\" adapted for the Dance in America series on PBS. The parts of this epic saga relevant to the caldera story follow.\n\nPele's youngest sister, Hiiaka, agrees to travel to Kauai to fetch Lohiau, whom Pele wants as her lover, provided that Pele not destroy the ohia lehua forest in Puna. Pele agrees to protect the forest, provided that Hiiaka returns in 40 days. Many adventures befall Hiiaka and her traveling companion, among them the need to bring Lohiau back to life. All this takes too long for Pele, and Hiiaka, upon climbing to the top of the Waianae Range on her return trip, sees that the Puna forest is aflame. Angry, and tempted by Lohiau but remaining chaste, Hiiaka continues the voyage with Lohiau to Hilo Bay, and they walk to the summit of K\u012blauea. There, in front of her older sister, Hiiaka makes love with Lohiau. Furious, Pele kills Lohiau and throws his body into Kalua o Pele, the pit indenting K\u012blauea's summit shield. Hiiaka digs frantically to recover the body, rocks flying amid warnings not to go too deeply or water will come in and put out Pele's fires. Eventually Hiiaka and Lohiau get together and remain so today.\n\nWhat were the impressive events that destroyed the Puna forest and resulted in the deep hole at K\u012blauea's summit? A reasonable interpretation is that they record the two largest volcanic events to have taken place on the island since human occupation: the 60-year-long eruption of the 'Aila'au\u00a0lava flow\u00a0from the Thurston area and the collapse of K\u012blauea's summit to form the caldera.\n\nThe\u00a0lava\u00a0flow covered most of K\u012blauea north of the east rift zone, reaching to the coast and destroying forest vital to Hawaiian needs. Such a flow is likely recorded in the oral tradition as Pele's revenge for what she thought was a lingering romantic liaison between Hiiaka and Lohiau.\n\nThe collapse of K\u012blauea's summit must have made an equal impression on people living on the volcano. It is memorialized by Hiiaka's digging for Lohiau, an excavation that must have been very deep to elicit the warning about water. The present-day water table is some 515 m (1,700 feet) below the caldera.\n\nTaken at face value, then, the chants tell us that the caldera formed immediately after a huge lava flow, exactly what we scientists have come to recognize only recently.\n\nIn 1823, Ellis was told that K\u012blauea \"had been burning from time immemorial\" and had overflowed some part of the country during the reign of every king that had governed Hawaii: that in earlier ages it used to boil up, overflow its banks, and inundate the adjacent country; but that, for many kings' reigns past, it had kept below the level of the surrounding plain, continually extending its surface and increasing its depth, and occasionally throwing up, with violent explosion, huge rocks or red-hot stones.\"\n\nThis oral tradition says that the caldera had existed \"for many kings' reigns past,\" not just since 1790, as scientists used to believe. If \"many\" means 10-15 kings, that would put the formation of the caldera near A.D. 1500, assuming a generational span of 20-25 years. Though vague, it is consistent with the age of the Ailaau flow and ensuing caldera collapse. The oral tradition also tells of sporadic explosions during the 300 years since the caldera formed.\n\nThe chants and oral traditions confirm what geologists learned only recently about K\u012blauea and demonstrate how important those volcanic events were to island residents. More such chants probably exist, ready to help us understand K\u012blauea's eventful past.\n\n\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\n\n### Volcano Activity Update\n\nThis past week, activity levels at the summit of K\u012blauea Volcano have remained at background levels. The number of\u00a0earthquakes\u00a0located in the summit area has slightly increased (usually less than 10 per day that are large enough to locate) with the largest number located south and west of Halemaumau. Widening of the summit\u00a0caldera, indicating inflation, continues.\n\nEruptive activity at Puu Oo continues. On clear nights, glow is visible from several\u00a0vents\u00a0within the crater.\u00a0Lava\u00a0is flowing through the PKK\u00a0lava tube\u00a0from its source on the southwest flank of Puu Oo to the ocean. About 1 kilometer south of Puu Oo, the Campout flow branches off from the PKK tube. The PKK and Campout tubes feed two widely separated ocean entries, at East Laeapuki and East\u00a0Kailiili, respectively. Both entries are located inside Hawaii Volcanoes National Park.\n\nFrom September 10 through 13, breakouts from the Campout tube provided good viewing-particularly at night--of\u00a0lava\u00a0streams descending Pulama pali. These flows had reached the 400-ft elevation by the 13th, with smaller breakouts extending to the coastal plain along the Campout flow.\n\nAccess to the sea cliff near the ocean entries is closed, due to significant hazards. If you visit the eruption site, check with the rangers for current updates, and remember to carry lots of water when venturing out onto the flow field.\n\nThere were four earthquakes beneath Hawaii Island reported felt within the past week, three of which were located beneath the northwest flank of Mauna Kea. A magnitude-2.8\u00a0earthquake\u00a0occurred at 00:50 a.m. H.s.t. on Thursday, September 7, and was located 11 km (7 miles) southeast of Waimea at a depth of 13 km (8 miles). A magnitude-2.0 earthquake occurred later that same day at 3:09 p.m. and was located 3 km (2 miles) southwest of Puu O`o at a depth of 3 km (2 miles). A magnitude-2.4 earthquake occurred at 5:40 p.m. H.s.t. on Friday, September 8, and a magnitude-3.4 earthquake occurred at 2:48 a.m. on Monday, September 11; both were located 11 km (7 miles) southeast of Waimea at a depth of 14 km (9 miles).\n\nMauna Loa is not erupting. During the past week, earthquake activity remained low beneath the volcano's summit (five earthquakes were located). Extension of distances between locations spanning the summit, indicating inflation, continues at slow rates.","date":"2021-10-19 14:26:01","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.28336334228515625, \"perplexity\": 5374.072218847167}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2021-43\/segments\/1634323585270.40\/warc\/CC-MAIN-20211019140046-20211019170046-00217.warc.gz\"}"}
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Home Tags Posts tagged with "Basel Committee on Banking Supervision (BCBS)"
Islamic banks, which operate according to Shariah principles, are growing rapidly worldwide, claiming billions in assets. IBs appeal to conservative Muslims worldwide because of their adherence to concepts such as profit-and-loss sharing instead of taking interest. But what happens when an Islamic bank fails to fully comply with Shariah rules? One consequence of this risk of loss is that it can limit the bank's ability to meet capital requirements.
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Q: How to use iterate link from tHashInput The schema of "Global_variable_hash" contains "filename" field. The hash itself contains multiple records which are populated earlier in the job. I want to use "filename" field in tFileInputExcel_1 to dynamically set filename of excel for each record. How can I access this variable in tFileInputExcel_1?
I want to execute tFileInputExcel_1 connected flow for each record present in "Global_variable_hash". Hence, I need to access the "filename" variable for each record.
A: You have to use a tFlowToIterate component between tHashInput and tFileInputExcel
Then in tFileInputExcel, you can access your variable which will be listed as a global Variable associated with tFlowToIterate (ctrl+space to get access to component variables).
You can use default parameters in tFlowToIterate. You won't have anything to configure in it.
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Q: Consulta en blanco, Join MYSQL Hola tengo el siguiente problema: cuando quiero realizar una consulta me da en blanco, ¿Cómo puedo resolverlo? así se para futuras consultas, poder resolverlo por mí mismo. ¿Por qué una consulta da en blanco?, ¿no se si tiene algo que ver la sintaxis? ¿Cómo se donde se encuentra el error, si no me aparece error en la consola?
Tengo estas tablas:
CREATE TABLE cliente (
codigo_cliente INTEGER NOT NULL,
nombre_cliente VARCHAR(50) NOT NULL,
nombre_contacto VARCHAR(30) DEFAULT NULL,
apellido_contacto VARCHAR(30) DEFAULT NULL,
telefono VARCHAR(15) NOT NULL,
fax VARCHAR(15) NOT NULL,
linea_direccion1 VARCHAR(50) NOT NULL,
linea_direccion2 VARCHAR(50) DEFAULT NULL,
ciudad VARCHAR(50) NOT NULL,
region VARCHAR(50) DEFAULT NULL,
pais VARCHAR(50) DEFAULT NULL,
codigo_postal VARCHAR(10) DEFAULT NULL,
codigo_empleado_rep_ventas INTEGER DEFAULT NULL,
limite_credito NUMERIC(15,2) DEFAULT NULL,
PRIMARY KEY (codigo_cliente),
FOREIGN KEY (codigo_empleado_rep_ventas) REFERENCES empleado (codigo_empleado)
);
CREATE TABLE pedido (
codigo_pedido INTEGER NOT NULL,
fecha_pedido date NOT NULL,
fecha_esperada date NOT NULL,
fecha_entrega date DEFAULT NULL,
estado VARCHAR(15) NOT NULL,
comentarios TEXT,
codigo_cliente INTEGER NOT NULL,
PRIMARY KEY (codigo_pedido),
FOREIGN KEY (codigo_cliente) REFERENCES cliente (codigo_cliente)
);
CREATE TABLE pago (
codigo_cliente INTEGER NOT NULL,
forma_pago VARCHAR(40) NOT NULL,
id_transaccion VARCHAR(50) NOT NULL,
fecha_pago date NOT NULL,
total NUMERIC(15,2) NOT NULL,
PRIMARY KEY (codigo_cliente, id_transaccion),
FOREIGN KEY (codigo_cliente) REFERENCES cliente (codigo_cliente)
);
/*Estos son mis Inserts*/
INSERT INTO cliente VALUES (1,'GoldFish Garden','Daniel G','GoldFish','5556901745','5556901746','False Street 52 2 A',NULL,'San Francisco',NULL,'USA','24006',19,3000);
INSERT INTO cliente VALUES (3,'Gardening Associates','Anne','Wright','5557410345','5557410346','Wall-e Avenue',NULL,'Miami','Miami','USA','24010',19,6000);
INSERT INTO cliente VALUES (4,'Gerudo Valley','Link','Flaute','5552323129','5552323128','Oaks Avenue nº22',NULL,'New York',NULL,'USA','85495',22,12000);
INSERT INTO cliente VALUES (5,'Tendo Garden','Akane','Tendo','55591233210','55591233211','Null Street nº69',NULL,'Miami',NULL,'USA','696969',22,600000);
INSERT INTO cliente VALUES (6,'Lasas S.A.','Antonio','Lasas','34916540145','34914851312','C/Leganes 15',NULL,'Fuenlabrada','Madrid','Spain','28945',8,154310);
INSERT INTO cliente VALUES (7,'Beragua','Jose','Bermejo','654987321','916549872','C/pintor segundo','Getafe','Madrid','Madrid','Spain','28942',11,20000);
INSERT INTO cliente VALUES (8,'Club Golf Puerta del hierro','Paco','Lopez','62456810','919535678','C/sinesio delgado','Madrid','Madrid','Madrid','Spain','28930',11,40000);
INSERT INTO cliente VALUES (9,'Naturagua','Guillermo','Rengifo','689234750','916428956','C/majadahonda','Boadilla','Madrid','Madrid','Spain','28947',11,32000);
INSERT INTO cliente VALUES (10,'DaraDistribuciones','David','Serrano','675598001','916421756','C/azores','Fuenlabrada','Madrid','Madrid','Spain','28946',11,50000);
INSERT INTO cliente VALUES (11,'Madrileña de riegos','Jose','Tacaño','655983045','916689215','C/Lagañas','Fuenlabrada','Madrid','Madrid','Spain','28943',11,20000);
INSERT INTO cliente VALUES (12,'Lasas S.A.','Antonio','Lasas','34916540145','34914851312','C/Leganes 15',NULL,'Fuenlabrada','Madrid','Spain','28945',8,154310);
INSERT INTO cliente VALUES (13,'Camunas Jardines S.L.','Pedro','Camunas','34914873241','34914871541','C/Virgenes 45','C/Princesas 2 1ºB','San Lorenzo del Escorial','Madrid','Spain','28145',8,16481);
INSERT INTO cliente VALUES (14,'Dardena S.A.','Juan','Rodriguez','34912453217','34912484764','C/Nueva York 74',NULL,'Madrid','Madrid','Spain','28003',8,321000);
INSERT INTO cliente VALUES (15,'Jardin de Flores','Javier','Villar','654865643','914538776','C/ Oña 34',NULL,'Madrid','Madrid','Spain','28950',30,40000);
INSERT INTO cliente VALUES (16,'Flores Marivi','Maria','Rodriguez','666555444','912458657','C/Leganes24',NULL,'Fuenlabrada','Madrid','Spain','28945',5,1500);
INSERT INTO cliente VALUES (17,'Flowers, S.A','Beatriz','Fernandez','698754159','978453216','C/Luis Salquillo4',NULL,'Montornes del valles','Barcelona','Spain','24586',5,3500);
INSERT INTO cliente VALUES (18,'Naturajardin','Victoria','Cruz','612343529','916548735','Plaza Magallón 15',NULL,'Madrid','Madrid','Spain','28011',30,5050);
INSERT INTO cliente VALUES (19,'Golf S.A.','Luis','Martinez','916458762','912354475','C/Estancado',NULL,'Santa cruz de Tenerife','Islas Canarias','Spain','38297',12,30000);
INSERT INTO cliente VALUES (20,'Americh Golf Management SL','Mario','Suarez','964493072','964493063','C/Letardo',NULL,'Barcelona','Cataluña','Spain','12320',12,20000);
INSERT INTO cliente VALUES (21,'Aloha','Cristian','Rodrigez','916485852','914489898','C/Roman 3',NULL,'Canarias','Canarias','Spain','35488',12,50000);
INSERT INTO cliente VALUES (22,'El Prat','Francisco','Camacho','916882323','916493211','Avenida Tibidabo',NULL,'Barcelona','Cataluña','Spain','12320',12,30000);
INSERT INTO cliente VALUES (23,'Sotogrande','Maria','Santillana','915576622','914825645','C/Paseo del Parque',NULL,'Sotogrande','Cadiz','Spain','11310',12,60000);
INSERT INTO cliente VALUES (24,'Vivero Humanes','Federico','Gomez','654987690','916040875','C/Miguel Echegaray 54',NULL,'Humanes','Madrid','Spain','28970',30,7430);
INSERT INTO cliente VALUES (25,'Fuenla City','Tony','Muñoz Mena','675842139','915483754','C/Callo 52',NULL,'Fuenlabrada','Madrid','Spain','28574',5,4500);
INSERT INTO cliente VALUES (26,'Jardines y Mansiones Cactus SL','Eva María','Sánchez','916877445','914477777','Polígono Industrial Maspalomas, Nº52','Móstoles','Madrid','Madrid','Spain','29874',9,76000);
INSERT INTO cliente VALUES (27,'Jardinerías Matías SL','Matías','San Martín','916544147','917897474','C/Francisco Arce, Nº44','Bustarviejo','Madrid','Madrid','Spain','37845',9,100500);
INSERT INTO cliente VALUES (28,'Agrojardin','Benito','Lopez','675432926','916549264','C/Mar Caspio 43',NULL,'Getafe','Madrid','Spain','28904',30,8040);
INSERT INTO cliente VALUES (29,'Top Campo','Joseluis','Sanchez','685746512','974315924','C/Ibiza 32',NULL,'Humanes','Madrid','Spain','28574',5,5500);
INSERT INTO cliente VALUES (30,'Jardineria Sara','Sara','Marquez','675124537','912475843','C/Lima 1',NULL,'Fuenlabrada','Madrid','Spain','27584',5,7500);
INSERT INTO cliente VALUES (31,'Campohermoso','Luis','Jimenez','645925376','916159116','C/Peru 78',NULL,'Fuenlabrada','Madrid','Spain','28945',30,3250);
INSERT INTO cliente VALUES (32,'france telecom','Fraçois','Toulou','(33)5120578961','(33)5120578961','6 place d Alleray 15ème',NULL,'Paris',NULL,'France','75010',16,10000);
INSERT INTO cliente VALUES (33,'Musée du Louvre','Pierre','Delacroux','(33)0140205050','(33)0140205442','Quai du Louvre',NULL,'Paris',NULL,'France','75058',16,30000);
INSERT INTO cliente VALUES (35,'Tutifruti S.A','Jacob','Jones','2 9261-2433','2 9283-1695','level 24, St. Martins Tower.-31 Market St.',NULL,'Sydney','Nueva Gales del Sur','Australia','2000',31,10000);
INSERT INTO cliente VALUES (36,'Flores S.L.','Antonio','Romero','654352981','685249700','Avenida España',NULL,'Madrid','Fuenlabrada','Spain','29643',18,6000);
INSERT INTO cliente VALUES (37,'The Magic Garden','Richard','Mcain','926523468','9364875882','Lihgting Park',NULL,'London','London','United Kingdom','65930',18,10000);
INSERT INTO cliente VALUES (38,'El Jardin Viviente S.L','Justin','Smith','2 8005-7161','2 8005-7162','176 Cumberland Street The rocks',NULL,'Sydney','Nueva Gales del Sur','Australia','2003',31,8000);
INSERT INTO pedido VALUES (1,'2006-01-17','2006-01-19','2006-01-19','Entregado','Pagado a plazos',5);
INSERT INTO pedido VALUES (2,'2007-10-23','2007-10-28','2007-10-26','Entregado','La entrega llego antes de lo esperado',5);
INSERT INTO pedido VALUES (3,'2008-06-20','2008-06-25',NULL,'Rechazado','Limite de credito superado',5);
INSERT INTO pedido VALUES (4,'2009-01-20','2009-01-26',NULL,'Pendiente',NULL,5);
INSERT INTO pedido VALUES (8,'2008-11-09','2008-11-14','2008-11-14','Entregado','El cliente paga la mitad con tarjeta y la otra mitad con efectivo, se le realizan dos facturas',1);
INSERT INTO pedido VALUES (9,'2008-12-22','2008-12-27','2008-12-28','Entregado','El cliente comprueba la integridad del paquete, todo correcto',1);
INSERT INTO pedido VALUES (10,'2009-01-15','2009-01-20',NULL,'Pendiente','El cliente llama para confirmar la fecha - Esperando al proveedor',3);
INSERT INTO pedido VALUES (11,'2009-01-20','2009-01-27',NULL,'Pendiente','El cliente requiere que el pedido se le entregue de 16:00h a 22:00h',1);
INSERT INTO pedido VALUES (12,'2009-01-22','2009-01-27',NULL,'Pendiente','El cliente requiere que el pedido se le entregue de 9:00h a 13:00h',1);
INSERT INTO pedido VALUES (13,'2009-01-12','2009-01-14','2009-01-15','Entregado',NULL,7);
INSERT INTO pedido VALUES (14,'2009-01-02','2009-01-02',null,'Rechazado','mal pago',7);
INSERT INTO pedido VALUES (15,'2009-01-09','2009-01-12','2009-01-11','Entregado',NULL,7);
INSERT INTO pedido VALUES (16,'2009-01-06','2009-01-07','2009-01-15','Entregado',NULL,7);
INSERT INTO pedido VALUES (17,'2009-01-08','2009-01-09','2009-01-11','Entregado','mal estado',7);
INSERT INTO pedido VALUES (18,'2009-01-05','2009-01-06','2009-01-07','Entregado',NULL,9);
INSERT INTO pedido VALUES (19,'2009-01-18','2009-02-12',NULL,'Pendiente','entregar en murcia',9);
INSERT INTO pedido VALUES (20,'2009-01-20','2009-02-15',NULL,'Pendiente',NULL,9);
INSERT INTO pedido VALUES (21,'2009-01-09','2009-01-09','2009-01-09','Rechazado','mal pago',9);
INSERT INTO pedido VALUES (22,'2009-01-11','2009-01-11','2009-01-13','Entregado',NULL,9);
INSERT INTO pedido VALUES (23,'2008-12-30','2009-01-10',NULL,'Rechazado','El pedido fue anulado por el cliente',5);
INSERT INTO pedido VALUES (24,'2008-07-14','2008-07-31','2008-07-25','Entregado',NULL,14);
INSERT INTO pedido VALUES (25,'2009-02-02','2009-02-08',NULL,'Rechazado','El cliente carece de saldo en la cuenta asociada',1);
INSERT INTO pedido VALUES (26,'2009-02-06','2009-02-12',NULL,'Rechazado','El cliente anula la operacion para adquirir mas producto',3);
INSERT INTO pedido VALUES (27,'2009-02-07','2009-02-13',NULL,'Entregado','El pedido aparece como entregado pero no sabemos en que fecha',3);
INSERT INTO pedido VALUES (28,'2009-02-10','2009-02-17','2009-02-20','Entregado','El cliente se queja bastante de la espera asociada al producto',3);
INSERT INTO pedido VALUES (29,'2008-08-01','2008-09-01','2008-09-01','Rechazado','El cliente no está conforme con el pedido',14);
INSERT INTO pedido VALUES (30,'2008-08-03','2008-09-03','2008-08-31','Entregado',NULL,13);
INSERT INTO pedido VALUES (31,'2008-09-04','2008-09-30','2008-10-04','Rechazado','El cliente ha rechazado por llegar 5 dias tarde',13);
INSERT INTO pedido VALUES (32,'2007-01-07','2007-01-19','2007-01-27','Entregado','Entrega tardia, el cliente puso reclamacion',4);
INSERT INTO pedido VALUES (33,'2007-05-20','2007-05-28',NULL,'Rechazado','El pedido fue anulado por el cliente',4);
INSERT INTO pedido VALUES (34,'2007-06-20','2008-06-28','2008-06-28','Entregado','Pagado a plazos',4);
INSERT INTO pedido VALUES (35,'2008-03-10','2009-03-20',NULL,'Rechazado','Limite de credito superado',4);
INSERT INTO pedido VALUES (36,'2008-10-15','2008-12-15','2008-12-10','Entregado',NULL,14);
INSERT INTO pedido VALUES (37,'2008-11-03','2009-11-13',NULL,'Pendiente','El pedido nunca llego a su destino',4);
INSERT INTO pedido VALUES (38,'2009-03-05','2009-03-06','2009-03-07','Entregado',NULL,19);
INSERT INTO pedido VALUES (39,'2009-03-06','2009-03-07','2009-03-09','Pendiente',NULL,19);
INSERT INTO pedido VALUES (40,'2009-03-09','2009-03-10','2009-03-13','Rechazado',NULL,19);
INSERT INTO pedido VALUES (41,'2009-03-12','2009-03-13','2009-03-13','Entregado',NULL,19);
INSERT INTO pedido VALUES (42,'2009-03-22','2009-03-23','2009-03-27','Entregado',NULL,19);
INSERT INTO pedido VALUES (43,'2009-03-25','2009-03-26','2009-03-28','Pendiente',NULL,23);
INSERT INTO pedido VALUES (44,'2009-03-26','2009-03-27','2009-03-30','Pendiente',NULL,23);
INSERT INTO pedido VALUES (45,'2009-04-01','2009-03-04','2009-03-07','Entregado',NULL,23);
INSERT INTO pedido VALUES (46,'2009-04-03','2009-03-04','2009-03-05','Rechazado',NULL,23);
INSERT INTO pedido VALUES (47,'2009-04-15','2009-03-17','2009-03-17','Entregado',NULL,23);
INSERT INTO pedido VALUES (48,'2008-03-17','2008-03-30','2008-03-29','Entregado','Según el Cliente, el pedido llegó defectuoso',26);
INSERT INTO pedido VALUES (49,'2008-07-12','2008-07-22','2008-07-30','Entregado','El pedido llegó 1 día tarde, pero no hubo queja por parte de la empresa compradora',26);
INSERT INTO pedido VALUES (50,'2008-03-17','2008-08-09',NULL,'Pendiente','Al parecer, el pedido se ha extraviado a la altura de Sotalbo (Ávila)',26);
INSERT INTO pedido VALUES (51,'2008-10-01','2008-10-14','2008-10-14','Entregado','Todo se entregó a tiempo y en perfecto estado, a pesar del pésimo estado de las carreteras.',26);
INSERT INTO pedido VALUES (52,'2008-12-07','2008-12-21',NULL,'Pendiente','El transportista ha llamado a Eva María para indicarle que el pedido llegará más tarde de lo esperado.',26);
INSERT INTO pedido VALUES (53,'2008-10-15','2008-11-15','2008-11-09','Entregado','El pedido llega 6 dias antes',13);
INSERT INTO pedido VALUES (54,'2009-01-11','2009-02-11',NULL,'Pendiente',NULL,14);
INSERT INTO pedido VALUES (55,'2008-12-10','2009-01-10','2009-01-11','Entregado','Retrasado 1 dia por problemas de transporte',14);
INSERT INTO pedido VALUES (56,'2008-12-19','2009-01-20',NULL,'Rechazado','El cliente a anulado el pedido el dia 2009-01-10',13);
INSERT INTO pedido VALUES (57,'2009-01-05','2009-02-05',NULL,'Pendiente',NULL,13);
INSERT INTO pedido VALUES (58,'2009-01-24','2009-01-31','2009-01-30','Entregado','Todo correcto',3);
INSERT INTO pedido VALUES (59,'2008-11-09','2008-11-14','2008-11-14','Entregado','El cliente paga la mitad con tarjeta y la otra mitad con efectivo, se le realizan dos facturas',1);
INSERT INTO pedido VALUES (60,'2008-12-22','2008-12-27','2008-12-28','Entregado','El cliente comprueba la integridad del paquete, todo correcto',1);
INSERT INTO pedido VALUES (61,'2009-01-15','2009-01-20',NULL,'Pendiente','El cliente llama para confirmar la fecha - Esperando al proveedor',3);
INSERT INTO pedido VALUES (62,'2009-01-20','2009-01-27',NULL,'Pendiente','El cliente requiere que el pedido se le entregue de 16:00h a 22:00h',1);
INSERT INTO pedido VALUES (63,'2009-01-22','2009-01-27',NULL,'Pendiente','El cliente requiere que el pedido se le entregue de 9:00h a 13:00h',1);
INSERT INTO pedido VALUES (64,'2009-01-24','2009-01-31','2009-01-30','Entregado','Todo correcto',1);
INSERT INTO pedido VALUES (65,'2009-02-02','2009-02-08',NULL,'Rechazado','El cliente carece de saldo en la cuenta asociada',1);
INSERT INTO pedido VALUES (66,'2009-02-06','2009-02-12',NULL,'Rechazado','El cliente anula la operacion para adquirir mas producto',3);
INSERT INTO pedido VALUES (67,'2009-02-07','2009-02-13',NULL,'Entregado','El pedido aparece como entregado pero no sabemos en que fecha',3);
INSERT INTO pedido VALUES (68,'2009-02-10','2009-02-17','2009-02-20','Entregado','El cliente se queja bastante de la espera asociada al producto',3);
INSERT INTO pedido VALUES (74,'2009-01-14','2009-01-22',NULL,'Rechazado','El pedido no llego el dia que queria el cliente por fallo del transporte',15);
INSERT INTO pedido VALUES (75,'2009-01-11','2009-01-13','2009-01-13','Entregado','El pedido llego perfectamente',15);
INSERT INTO pedido VALUES (76,'2008-11-15','2008-11-23','2008-11-23','Entregado',NULL,15);
INSERT INTO pedido VALUES (77,'2009-01-03','2009-01-08',NULL,'Pendiente','El pedido no pudo ser entregado por problemas meteorologicos',15);
INSERT INTO pedido VALUES (78,'2008-12-15','2008-12-17','2008-12-17','Entregado','Fue entregado, pero faltaba mercancia que sera entregada otro dia',15);
INSERT INTO pedido VALUES (79,'2009-01-12','2009-01-13','2009-01-13','Entregado',NULL,28);
INSERT INTO pedido VALUES (80,'2009-01-25','2009-01-26',NULL,'Pendiente','No terminó el pago',28);
INSERT INTO pedido VALUES (81,'2009-01-18','2009-01-24',NULL,'Rechazado','Los producto estaban en mal estado',28);
INSERT INTO pedido VALUES (82,'2009-01-20','2009-01-29','2009-01-29','Entregado','El pedido llego un poco mas tarde de la hora fijada',28);
INSERT INTO pedido VALUES (83,'2009-01-24','2009-01-28',NULL,'Entregado',NULL,28);
INSERT INTO pedido VALUES (89,'2007-10-05','2007-12-13','2007-12-10','Entregado','La entrega se realizo dias antes de la fecha esperada por lo que el cliente quedo satisfecho',35);
INSERT INTO pedido VALUES (90,'2009-02-07','2008-02-17',NULL,'Pendiente','Debido a la nevada caída en la sierra, el pedido no podrá llegar hasta el día ',27);
INSERT INTO pedido VALUES (91,'2009-03-18','2009-03-29','2009-03-27','Entregado','Todo se entregó a su debido tiempo, incluso con un día de antelación',27);
INSERT INTO pedido VALUES (92,'2009-04-19','2009-04-30','2009-05-03','Entregado','El pedido se entregó tarde debido a la festividad celebrada en España durante esas fechas',27);
INSERT INTO pedido VALUES (93,'2009-05-03','2009-05-30','2009-05-17','Entregado','El pedido se entregó antes de lo esperado.',27);
INSERT INTO pedido VALUES (94,'2009-10-18','2009-11-01',NULL,'Pendiente','El pedido está en camino.',27);
INSERT INTO pedido VALUES (95,'2008-01-04','2008-01-19','2008-01-19','Entregado',NULL,35);
INSERT INTO pedido VALUES (96,'2008-03-20','2008-04-12','2008-04-13','Entregado','La entrega se retraso un dia',35);
INSERT INTO pedido VALUES (97,'2008-10-08','2008-11-25','2008-11-25','Entregado',NULL,35);
INSERT INTO pedido VALUES (98,'2009-01-08','2009-02-13',NULL,'Pendiente',NULL,35);
INSERT INTO pedido VALUES (99,'2009-02-15','2009-02-27',NULL,'Pendiente',NULL,16);
INSERT INTO pedido VALUES (100,'2009-01-10','2009-01-15','2009-01-15','Entregado','El pedido llego perfectamente',16);
INSERT INTO pedido VALUES (101,'2009-03-07','2009-03-27',NULL,'Rechazado','El pedido fue rechazado por el cliente',16);
INSERT INTO pedido VALUES (102,'2008-12-28','2009-01-08','2009-01-08','Entregado','Pago pendiente',16);
INSERT INTO pedido VALUES (103,'2009-01-15','2009-01-20','2009-01-24','Pendiente',NULL,30);
INSERT INTO pedido VALUES (104,'2009-03-02','2009-03-06','2009-03-06','Entregado',NULL,30);
INSERT INTO pedido VALUES (105,'2009-02-14','2009-02-20',NULL,'Rechazado','el producto ha sido rechazado por la pesima calidad',30);
INSERT INTO pedido VALUES (106,'2009-05-13','2009-05-15','2009-05-20','Pendiente',NULL,30);
INSERT INTO pedido VALUES (107,'2009-04-06','2009-04-10','2009-04-10','Entregado',NULL,30);
INSERT INTO pedido VALUES (108,'2009-04-09','2009-04-15','2009-04-15','Entregado',NULL,16);
INSERT INTO pedido VALUES (109,'2006-05-25','2006-07-28','2006-07-28','Entregado',NULL,38);
INSERT INTO pedido VALUES (110,'2007-03-19','2007-04-24','2007-04-24','Entregado',NULL,38);
INSERT INTO pedido VALUES (111,'2008-03-05','2008-03-30','2008-03-30','Entregado',NULL,36);
INSERT INTO pedido VALUES (112,'2009-03-05','2009-04-06','2009-05-07','Pendiente',NULL,36);
INSERT INTO pedido VALUES (113,'2008-10-28','2008-11-09','2009-01-09','Rechazado','El producto ha sido rechazado por la tardanza de el envio',36);
INSERT INTO pedido VALUES (114,'2009-01-15','2009-01-29','2009-01-31','Entregado','El envio llego dos dias más tarde debido al mal tiempo',36);
INSERT INTO pedido VALUES (115,'2008-11-29','2009-01-26','2009-02-27','Pendiente',NULL,36);
INSERT INTO pedido VALUES (116,'2008-06-28','2008-08-01','2008-08-01','Entregado',NULL,38);
INSERT INTO pedido VALUES (117,'2008-08-25','2008-10-01',NULL,'Rechazado','El pedido ha sido rechazado por la acumulacion de pago pendientes del cliente',38);
INSERT INTO pedido VALUES (118,'2009-02-15','2009-02-27',NULL,'Pendiente',NULL,16);
INSERT INTO pedido VALUES (119,'2009-01-10','2009-01-15','2009-01-15','Entregado','El pedido llego perfectamente',16);
INSERT INTO pedido VALUES (120,'2009-03-07','2009-03-27',NULL,'Rechazado','El pedido fue rechazado por el cliente',16);
INSERT INTO pedido VALUES (121,'2008-12-28','2009-01-08','2009-01-08','Entregado','Pago pendiente',16);
INSERT INTO pedido VALUES (122,'2009-04-09','2009-04-15','2009-04-15','Entregado',NULL,16);
INSERT INTO pedido VALUES (123,'2009-01-15','2009-01-20','2009-01-24','Pendiente',NULL,30);
INSERT INTO pedido VALUES (124,'2009-03-02','2009-03-06','2009-03-06','Entregado',NULL,30);
INSERT INTO pedido VALUES (125,'2009-02-14','2009-02-20',NULL,'Rechazado','el producto ha sido rechazado por la pesima calidad',30);
INSERT INTO pedido VALUES (126,'2009-05-13','2009-05-15','2009-05-20','Pendiente',NULL,30);
INSERT INTO pedido VALUES (127,'2009-04-06','2009-04-10','2009-04-10','Entregado',NULL,30);
INSERT INTO pedido VALUES (128,'2008-11-10','2008-12-10','2008-12-29','Rechazado','El pedido ha sido rechazado por el cliente por el retraso en la entrega',38);
INSERT INTO pago VALUES (1,'PayPal','ak-std-000001','2008-11-10',2000);
INSERT INTO pago VALUES (1,'PayPal','ak-std-000002','2008-12-10',2000);
INSERT INTO pago VALUES (3,'PayPal','ak-std-000003','2009-01-16',5000);
INSERT INTO pago VALUES (3,'PayPal','ak-std-000004','2009-02-16',5000);
INSERT INTO pago VALUES (3,'PayPal','ak-std-000005','2009-02-19',926);
INSERT INTO pago VALUES (4,'PayPal','ak-std-000006','2007-01-08',20000);
INSERT INTO pago VALUES (4,'PayPal','ak-std-000007','2007-01-08',20000);
INSERT INTO pago VALUES (4,'PayPal','ak-std-000008','2007-01-08',20000);
INSERT INTO pago VALUES (4,'PayPal','ak-std-000009','2007-01-08',20000);
INSERT INTO pago VALUES (4,'PayPal','ak-std-000010','2007-01-08',1849);
INSERT INTO pago VALUES (5,'Transferencia','ak-std-000011','2006-01-18',23794);
INSERT INTO pago VALUES (7,'Cheque','ak-std-000012','2009-01-13',2390);
INSERT INTO pago VALUES (9,'PayPal','ak-std-000013','2009-01-06',929);
INSERT INTO pago VALUES (13,'PayPal','ak-std-000014','2008-08-04',2246);
INSERT INTO pago VALUES (14,'PayPal','ak-std-000015','2008-07-15',4160);
INSERT INTO pago VALUES (15,'PayPal','ak-std-000016','2009-01-15',2081);
INSERT INTO pago VALUES (15,'PayPal','ak-std-000035','2009-02-15',10000);
INSERT INTO pago VALUES (16,'PayPal','ak-std-000017','2009-02-16',4399);
INSERT INTO pago VALUES (19,'PayPal','ak-std-000018','2009-03-06',232);
INSERT INTO pago VALUES (23,'PayPal','ak-std-000019','2009-03-26',272);
INSERT INTO pago VALUES (26,'PayPal','ak-std-000020','2008-03-18',18846);
INSERT INTO pago VALUES (27,'PayPal','ak-std-000021','2009-02-08',10972);
INSERT INTO pago VALUES (28,'PayPal','ak-std-000022','2009-01-13',8489);
INSERT INTO pago VALUES (30,'PayPal','ak-std-000024','2009-01-16',7863);
INSERT INTO pago VALUES (35,'PayPal','ak-std-000025','2007-10-06',3321);
INSERT INTO pago VALUES (38,'PayPal','ak-std-000026','2006-05-26',1171);
Esta es la consulta que deseo hacer:
Esta consula trata de devolver un listado con los clientes que han realizado algún pedido, pero no han realizado ningún pago
Select c.nombre_cliente
from cliente c
Inner Join pedido p on(c.codigo_cliente = p.codigo_pedido)
Inner Join pago pa on(c.codigo_cliente = pa.codigo_cliente)
where pa.codigo_cliente = null;
Y me da en blanco el resultado
A: Al realizar un INNER JOIN por codigo_cliente solo te aparecerán los clientes que tienen pagos.
Para solucionarlo debes hacer un LEFT JOIN
Select c.nombre_cliente
from cliente c
Inner Join pedido p on(c.codigo_cliente = p.codigo_pedido)
LEFTO JOIN pago pa on(c.codigo_cliente = pa.codigo_cliente)
where pa.codigo_cliente = null;
Con esto, traes todos los clientes con pedido, tengan o no pagos, los que no tienen pagos los identificas por el WHERE pa.codigo_cliente = null
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{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 8,712
|
Q: Ggplot (geom_line) with overlaps I would like to have a plot that makes overlaps very clear. More specifically, I would like to plot where a given individual works. Because individuals may work at different workplaces at the same time, I will plot a geom_line for each one of the workplaces. My question is: how do I make it clear when there are overlaps? I tried using some transparency in geom_line() but am looking for something that makes overlaps stand out
You can see below a simple example of 3 individuals and 2 workplaces. Individual A switches from workplace 1 to workplace 2, individual B do the same but is unemployed for some time in-between and individual C works in both places during a short period (this is where I see the overlap).
# individual A
a_id <- c(rep('A',25))
a_period <- c(seq(1, 13), seq(13,24))
a_workplace <-c(rep(1,13), rep(2,12))
# individual B
b_id <- c(rep('B',19))
b_period <- c(seq(2,8), seq(13,24))
b_workplace <-c(rep(1,7), rep(2,12))
# individual C
c_id <- c(rep('C',9))
c_period <- c(seq(1,4), seq(2,6))
c_workplace <-c(rep(1,4), rep(2,5))
# final affiliation data
id <- c(a_id, b_id, c_id)
period <- c(a_period, b_period, c_period)
workplace <- c(a_workplace, b_workplace, c_workplace)
mydata <- data.frame(id, period, workplace)
# affiliation data by workplace
mydata_1 <- mydata %>%
filter(workplace==1) %>%
mutate(workplace=as.factor(workplace))
mydata_2 <- mydata %>%
filter(workplace==2) %>%
mutate(workplace=as.factor(workplace))
I tried the below, but would like still to make the overlaps clearer. Maybe a suggestion of combination of colours that makes overlaps clearer to see?
ggplot(mydata_1, aes(period, id, group=id, col=workplace)) +
geom_line(alpha=0.4) +
geom_line(data=mydata_2, alpha=0.4, aes(period, id, group=id, col=workplace)) +
labs(x="time", y=NULL, title="Work affiliation") +
scale_x_continuous(breaks = seq(0,24, by=2)) +
scale_y_discrete(limits=rev) +
scale_color_manual(values=c("dodgerblue","firebrick1")) +
theme(legend.position = c(.7, .92), legend.direction = "horizontal",
legend.background = element_rect(linetype="solid", colour ="black"),
panel.background = element_rect(fill = "grey97"))
I also don't understand why I can't see the right workplace colours in the legend.
A: I think I would combine the data sets, then have a single geom_line call with a position_dodge. This simplifies your code, shows the overlaps, and displays your legend correctly.
all_data <- rbind(mydata_1, mydata_2)
ggplot(all_data, aes(x = id, y = period, color = workplace)) +
geom_line(position = position_dodge(width = 0.1), size = 2) +
labs(y = "time", title = "Work affiliation") +
scale_y_continuous(breaks = seq(0, 24, by = 2)) +
scale_x_discrete(limits = rev) +
scale_color_manual(values = c("dodgerblue", "firebrick1")) +
coord_flip() +
theme(legend.position = c(.7, .92),
legend.direction = "horizontal",
legend.background = element_rect(linetype = "solid", colour = "black"),
panel.background = element_rect(fill = "grey97"))
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 1,208
|
\section{Introduction}
Quantum Constraint Mechanics (QCM) is a generalized form of Hamiltonian quantum mechanics that enables bound systems of interacting particles to be described in a manifestly covariant manner \cite{AK, RST, CA}. QCM has been applied to problems in nuclear \cite{LC,WC} and high-energy physics \cite{CWA}. The purpose of this paper to show the quantum constraint equations for a relativistic two-particle harmonic oscillator having a total 4-momentum $P_{\mu}$ $(\mu=1,2,3,4)$ and total mass $M_0$ have a concise expression in terms of Lorentz covariant raising $\hat{a}_\mu^{+}$ and lowering $\hat{a}_\mu^{-}$ operators. The forms of these relativistic ladder operators are determined directly from the assumption that they reduce to the form $\hat{a}_\mu^{\pm} = (\hat{a}_i^{\pm}, 0)$ in the rest frame of the oscillator where $\hat{a}_i^{\pm}$ are the non-relativistic ladder operators.
The quantum constraint equations for the relativistic 3-dimensional harmonic oscillator are presented in section 2 of this paper alongside the solution $\Psi$ . Explicit expressions for the Lorentz covariant ladder operators are derived in section 3. It is shown, in particular, that the set of quantum constraints on $\Psi$ can be written in the compact form $\hat{P}_\mu \hat{P}^\mu \Psi= -M_0^2 \Psi$, $\hat{a}_\mu^{+} \hat{a}^{\mu-} \Psi = n \Psi$ and $\hat{P}^\mu \hat{a}_\mu^{\pm} \Psi = 0$ where $(n+\frac{3}{2})\Omega$ is the total (energy)$^2$ of the oscillator and $\Omega$ is the spring constant.
In non-relativistic quantum mechanics there is one component of each of the $\hat{a}_i^{\pm}$ ladder operators for each orthogonal mode of oscillation. By contrast, in the relativistic approach developed here, the $\hat{P}^\mu \hat{a}_\mu^{\pm} \Psi = 0$ constraint condition reduces the number of independent components of $\hat{a}_\mu^{\pm}$ from four to three. The three operators required for raising and lowering the eigenstate of the oscillator are therefore linear combinations of $\hat{a}_\mu^{\pm}$ components. Explicit forms for these linear combination operators are derived in section 4.
The 4-vector convention in this paper will be $x_\mu=(x_1, x_2, x_3, x_4)$ and $x^\mu=(x_1, x_2, x_3, -x_4)$. Natural units, $c=\hbar=1$ will be used throughout.
\section{The Constraint Equations}
Consider a 3-dimensional oscillator consisting of two interacting particles each to be represented using an index $k(=1,2)$. Let $m_{k}$, $x_{k\mu}$ and $p_{k\mu}$ denote the mass, 4-position and 4-momentum of each of the particles respectively. Following Crater and Van Alstine \cite{CA} the center-of-mass and relative coordinates for the system can then be expressed as
\begin{equation} \label{eq: Xdef}
X_{\mu} = M_0^{-1}(\epsilon_1 x_{1\mu} + \epsilon_2 x_{2\mu}), \quad P_{\mu} = p_{1\mu} + p_{2\mu}
\end{equation}
\begin{equation} \label{eq: xdef}
x_{\mu} = x_{1\mu} - x_{2\mu}, \quad p_{\mu} = M_0^{-1}(\epsilon_2 p_{1\mu} - \epsilon_1 p_{2\mu})
\end{equation}
where the $\epsilon_1$ and $\epsilon_2$ parameters take the form
\begin{equation} \label{eq: epsilon1}
\epsilon_1 = (2M_0)^{-1}(M_0^2+m_1^2-m_2^2)
\end{equation}
\begin{equation} \label{eq: epsilon2}
\epsilon_2 = (2M_0)^{-1}(M_0^2+m_2^2-m_1^2)
\end{equation}
The operators for 4-momentum in these two coordinate systems are
\begin{equation} \label{eq: qmreps}
\hat{p}_{k\mu}=\frac{1}{i}\frac{\partial}{\partial x_k^{\mu}}, \quad
\hat{P}_{\mu}=\frac{1}{i}\frac{\partial}{\partial X^{\mu}}, \quad
\hat{p}_{\mu}=\frac{1}{i}\frac{\partial}{\partial x^{\mu}}
\end{equation}
It will be further assumed that the oscillator is in a free state such that the total momentum $P_{\mu}$ satisfies the relationship
\begin{equation} \label{eq: totMom}
P^\mu P_\mu = -M_0^2
\end{equation}
where $M_0$ is the total mass of the oscillator.
It is usual in QCM, to further define the internal constraint space coordinates in both 4-position space
\begin{equation} \label{eq: xperp}
x_{\perp}^\mu = x^\mu + M_0^{-2}P^\mu (P_\nu x^\nu)
\end{equation}
and 4-momentum space
\begin{equation} \label{eq: pperp}
p_{\perp}^\mu = p^\mu + M_0^{-2} P^\mu (P_\nu p^\nu)
\end{equation}
Pre-multiplying these results by $P_\mu$ gives
\begin{equation} \label{eq: xcon}
P_\mu x_{\perp}^\mu = 0
\end{equation}
\begin{equation} \label{eq: pcon}
P_\mu p_{\perp}^\mu = 0
\end{equation}
showing $x_{\perp}^\mu = (x^1,x^2,x^3,0)$ and $p_{\perp}^\mu = (p^1,p^2,p^3,0)$ in the rest frame of the oscillator.
The scalar potential (energy)$^2$ term for two interacting particles in a harmonic oscillator can be written $\Omega^2 x_\perp^2$ where $\Omega$ is the spring constant. The relativistic wave equation constraining the wavefunction $\Psi(x_\mu, X_\mu)$ for two particles interacting through this oscillator potential can be expressed as
\begin{equation}
\hat{K}_T \Psi = (\hat{p}_1^2+\hat{p}_2^2+m_1^2+m_2^2+4\Omega^2 x_\perp^2)\Psi = 0
\end{equation}
This clearly reduces to the sum of two free-particle Klein-Gordon equations in the case $\Omega = 0$. Use of eqs. (\ref{eq: Xdef}) and (\ref{eq: xdef}) enables the $\hat{K}_T$ operator to be transformed into center-of-mass and relative coordinates giving
\begin{equation} \label{eq: TotHamil}
\hat{K}_T \Psi = [\hat{P}^2+m_c^2+4(\hat{p}^2 + \Omega^2 x_\perp^2)]\Psi = 0
\end{equation}
where $m_c=m_1+m_2$ is the combined mass of the two particles. A quantum system of two particles implies the existence of two first-order constraints. For the second condition, Crater and Van Alstine \cite{CA} find
\begin{equation} \label{eq: SubCondition}
\hat{K}_S\Psi = P_{\mu} \hat{p}^{\mu} \Psi = 0
\end{equation}
Here, the operators for $\hat{K}_T$ and $\hat{K}_S$ commute meaning that energy is conserved as the system evolves in a single time parameter.
Eqs. (\ref{eq: TotHamil}) and (\ref{eq: SubCondition}) have a separable solution of the form $\Phi(x_\mu) \exp(iP_\mu X^\mu)$. Use of eq. (\ref{eq: totMom}) to simplify the $K_T \Psi = 0$ constraint condition gives the internal harmonic oscillator equation
\begin{equation} \label{eq: HOE}
(\hat{p}^2+\Omega^2 x_\perp^2) \Psi = 2\sigma \Psi
\end{equation}
where the rest mass of the oscillator can be determined from the condition
\begin{equation} \label{eq: totMass}
M_0^2 = m_1^2+m_2^2+4\sigma + \sqrt{[(m_1^2+m_2^2+4\sigma)^2 - (m_1^2-m_2^2)^2]}
\end{equation}
It can be seen that eq. (\ref{eq: totMass}) gives $M_0=m_c$ for the free-particle case $(\sigma=0)$ and $M_0^2=m_c^2+8\sigma$ for $m_1=m_2$. The non-relativistic limit of this expression is discussed at the end of this section.
Eq. (\ref{eq: HOE}) is readily solved to give the internal oscillator function
\begin{eqnarray} \label{eq: psi}
\Phi(x_\mu) = \frac{1}{\sqrt{2^n}} \left( \frac{\Omega}{\pi} \right)^{3/4} \prod_{i=1}^{i=3} \left[\frac{1}{\sqrt{l_i!}} H_{l_i}(\sqrt{\Omega} x_i^{\prime}) \exp \left(-\frac{\Omega x_{i}^{\prime 2}}{2} \right)\right]
\end{eqnarray}
In this, $H_{l_i}$ are Hermite polynomials and $l_i=0,1,2...$. Inserting eq. (\ref{eq: psi}) into (\ref{eq: HOE}) gives
\begin{equation} \label{eq: sigma}
\sigma = \Omega\left(\frac{3}{2} + n\right)
\end{equation}
where $n=l_1 + l_2 + l_3$.
Eq. (\ref{eq: psi}) preserves its form under the general Lorentz transformation
\begin{equation}
x_i^{\prime} = x_i + \gamma v_i \left(\frac{\gamma v_j x_j }{1+\gamma} - t \right)
\end{equation}
\begin{equation}
t^{\prime} = \gamma(t-v_j x_j)
\end{equation}
(see ref. \cite{CA}) having set $x_\mu=(x_i,t)$. Here, $v_i$ is the velocity of the oscillator and $\gamma = (1-v^2)^{-1/2}$.
The oscillator function (\ref{eq: psi}) has been normalized using the condition
\begin{equation}
\int \Psi^\dag \Psi \delta(M_0^{-1}P_\mu x^\mu)d^4x = 1
\end{equation}
where $\delta(M_0^{-1}P_\mu x^\mu)$ is the Dirac delta function restricting the oscillator to a 3-dimensional constraint space. Here, the choice of constraint space is purely for convenience and simply represents one possible choice of consistent convention of how observers in different inertial reference frames make measurements.
In the non-relativistic limit $(v\ll 1, \sigma \ll m_c^2)$ , the wavefunction $\Psi$ loses its dependence on the relative time t such that eq. (\ref{eq: SubCondition}) reduces to the form $\partial \Psi / \partial t \simeq 0$. Also, the relativistic rest mass $M_0$ given in eq. (\ref{eq: totMass}) can be approximated to give $M_0 \simeq m_c + E_K$ where $E_K = \sigma / m_r$ is the internal kinetic energy of the oscillator and $m_r = m_1m_2 / m_c$ is the reduced mass of the particles. Inserting these results into eq. (\ref{eq: HOE}) leads to the Schr\"{o}dinger equation for the 2-particle harmonic oscillator:
\begin{equation} \label{eq: shrod1}
\frac{1}{2 m_r} \frac{\partial^2 \Psi}{\partial x_i \partial x_i} + \frac{1}{2} m_r \omega^2 x_ix_i\Psi = E_K\Psi
\end{equation}
where $\omega=\Omega/ m_r$.
\section{Ladder Operators}
As is well known \cite{DFL}, the Schr\"{o}dinger equation (\ref{eq: shrod1}) can be simplified in terms of the non-relativistic raising and lowering operators:
\begin{equation} \label{eq: ladder_nr}
\hat{a}_i^{\pm}(\hat{x}_i,\hat{p}_i) = \frac{1}{\sqrt{2 \Omega}} \left( \mp i \hat{p}_i + \Omega \hat{x}_i \right)
\end{equation}
to give
\begin{equation} \label{eq: shrod2}
\left(\hat{a}_i^+ \hat{a}_i^-+\frac{3}{2} \right)\omega \Psi = E_K \Psi
\end{equation}
Eq. (\ref{eq: shrod2}) can also be written in the following equivalent form
\begin{equation} \label{eq: shrod3}
\left(\hat{a}_i^+ \hat{a}_i^-+\frac{3}{2} \right)\Omega \Psi = \sigma \Psi
\end{equation}
or even more concisely as
\begin{equation} \label{eq: shrod4}
\hat{a}_i^+ \hat{a}_i^- \Psi = n \Psi
\end{equation}
Eq. (\ref{eq: xperp}) suggests a Lorentz covariant generalization of eq. (\ref{eq: ladder_nr}) to be
\begin{equation} \label{eq: ladder_lc}
\hat{a}^{\mu \pm}(\hat{x}_{\perp}^\mu,\hat{p}^\mu) = \frac{1}{\sqrt{2 \Omega}} \left( \mp i \hat{p}^\mu + \Omega \hat{x}_{\perp}^{\mu} \right)
\end{equation}
In comparing, eqs. (\ref{eq: ladder_nr}) and (\ref{eq: ladder_lc}) it can be seen $\hat{x}_{\perp}^\mu$ replaces $\hat{x}^\mu$ but that $\hat{p}_{\perp}^\mu$ does not need to replace $\hat{p}^\mu$ since eqs. (\ref{eq: pperp}) and (\ref{eq: SubCondition}) give $\hat{p}_{\perp}^\mu=\hat{p}^\mu$. It follows therefore that eq. (\ref{eq: ladder_lc}) reduces exactly to eq. (\ref{eq: ladder_nr}) in the rest frame of the oscillator.
Evaluating the product $\hat{a}_\mu^{+}\hat{a}^{\mu-}$ using eq. (\ref{eq: ladder_lc}) gives
\begin{equation}\label{eq: aprop1}
\hat{a}_\mu^{+}\hat{a}^{\mu-} = (2 \Omega)^{-1}(\hat{p}^2+\Omega^2 x_\perp^2 - 3 \Omega)
\end{equation}
This expression can be rewritten as
\begin{equation}\label{eq: aprop2}
\left(\hat{a}_{\mu}^+ \hat{a}^{\mu-}+\frac{3}{2}\right)\Omega \Psi = \sigma \Psi
\end{equation}
having used eqs. (\ref{eq: HOE}) and (\ref{eq: sigma}). Here, it can be seen eqs. (\ref{eq: shrod3}) and (\ref{eq: aprop2}) are identical in form except in passing from the non-relativistic to the relativistic forms that $\mu$ replaces i as the summation index.
Hence, using eqs. (\ref{eq: xcon}), (\ref{eq: ladder_lc}) and (\ref{eq: aprop2}) to simplify the constraint eqs. (\ref{eq: TotHamil}) and (\ref{eq: SubCondition}) leads to
\begin{equation} \label{eq: KG}
\hat{P}_\mu \hat{P}^\mu \Psi= -M_0^2 \Psi
\end{equation}
\begin{equation} \label{eq: lo1}
\hat{a}_\mu^{+} \hat{a}^{\mu-} \Psi = n \Psi
\end{equation}
\begin{equation} \label{eq: lo2}
\hat{P}^\mu \hat{a}_\mu^{\pm} \Psi = 0
\end{equation}
Eqs. (\ref{eq: KG}) through (\ref{eq: lo2}) constitute a complete set of quantum constraint equations for the relativistic 3-dimensional harmonic oscillator expressed in terms of the Lorentz covariant ladder operators (\ref{eq: ladder_lc}). The first of these results is the Klein-Gordon equation describing the oscillator in center-of-mass coordinates. The second is clearly a Lorentz covariant generalization of the non-relativistic oscillator eq. (\ref{eq: shrod2}) and the third is the constraint on the $\hat{a}_\mu^{\pm}$ operators reducing the number of independent components from four to three.
\section{Raising and Lowering Operations}
It is clear that each of the ladder operators $\hat{a}_\mu^{\pm}$ has four components but the three-dimensional harmonic oscillator only has three independent modes of oscillation. In the rest frame of the oscillator, this is straightforward to interpret since eq. (\ref{eq: lo2}) gives $\hat{a}_4 \Psi = 0$ meaning there is one component of $\hat{a}_i^{\pm}$ for each spatial mode of oscillation. The complication for a moving oscillator is that $\hat{a}_4 \Psi$ does not vanish. The $\hat{P}^\mu \hat{a}_\mu^{\pm} \Psi = 0$ condition must therefore be interpreted as defining three linearly independent combinations of $\hat{a}_\mu^{\pm}$ components for the purpose of raising and lowering each of the three modes of oscillation. The task ahead is to determine the explicit form of these linear combinations.
A good starting point for the present task is to consider of the general Lorentz transformation equations:
\begin{equation} \label{eq: alt}
\hat{a}_i^{\pm \prime} = \hat{a}_i^{\pm} + \gamma v_i \left( \frac{\gamma v_j \hat{a}_j^{\pm}}{\gamma+1} + \hat{a}_4^\pm \right)
\end{equation}
\begin{equation}
\hat{a}_4^{\pm \prime} = \gamma (\hat{a}_4^{\pm} + v_i \hat{a}_i^{\pm}) = 0
\end{equation}
that rotates the 4-vector $\hat{a}_\mu^{\pm \prime}$ from the rest frame of the oscillator to a moving frame where its components are denoted $\hat{a}_\mu^{\pm}$. Notice from eq. (\ref{eq: ladder_lc}) that eq. (\ref{eq: alt}) enables each of the components of $\hat{a}_i^{\pm \prime}$ defined in the rest frame of the oscillator to be expressed in terms of $\hat{x}_{\perp}^\mu$ and $\hat{p}^\mu$ operators in the moving frame. It is also helpful to spot that eq. (\ref{eq: alt}) can be simplified using eq. (\ref{eq: lo2}) to give
\begin{equation}
\hat{a}_i^{\pm \prime} = \hat{a}_i^{\pm} - \frac{P_i \hat{a}_4^{\pm}}{(E+M_0)}
\end{equation}
having set $P_\mu = (P_i, E)$. This result can also be expressed in the form
\begin{equation} \label{eq: explicitladders}
\hat{a}_i^{\pm \prime} = \frac{1}{\sqrt{2 \Omega}}\left[ \mp \left( \frac{\partial}{\partial x_i} + \frac{P_i}{E+M_0} \frac{\partial}{\partial t} \right) + \Omega x_i + \Omega\frac{P_i}{M_0} \left( \frac{P_jx_j}{M_0+E}-t\right) \right]
\end{equation}
where the dependence on the $\hat{x}_{\perp}^\mu$ and $\hat{p}^\mu$ operators has been made explicit.
The explicit form of the oscillator function (\ref{eq: psi}) can be written as
\begin{equation} \label{eq: psi2}
\Phi=\frac{1}{\sqrt{2^n}} \left( \frac{\Omega}{\pi} \right)^{3/4} \Phi_1\Phi_2\Phi_3
\end{equation}
where
\begin{eqnarray}
\Phi_i =\frac{1}{\sqrt{l_i!}} H_{l_i}\left[\sqrt{\Omega} x_i + \sqrt{\Omega}\frac{P_i}{M_0} \left( \frac{P_jx_j}{M_0+E}-t\right) \right]
\nonumber \\
\exp \left\{-\frac{\Omega}{2} \left[x_i + \frac{P_i}{M_0} \left( \frac{P_jx_j}{M_0+E}-t\right) \right]^2 \right\}
\end{eqnarray}
Clearly, it can be seen
\begin{equation} \label{eq: simple1}
\left( \frac{\partial}{\partial x_i} + \frac{P_i}{E+M_0} \frac{\partial}{\partial t} \right) \left[x_j + \frac{P_j}{M_0} \left( \frac{P_kx_k}{M_0+E}-t\right) \right] = \delta_{ij}
\end{equation}
where $\delta_{ij}$ is the Kronecker delta. It follows from this result that
\begin{equation} \label{eq: simple2}
\frac{1}{\Phi}\left( \frac{\partial \Phi}{\partial x_i} + \frac{P_i}{E+M_0} \frac{\partial \Phi}{\partial t} \right) = \frac{1}{\Phi_i}\left( \frac{\partial \Phi_i}{\partial x_i} + \frac{P_i}{E+M_0} \frac{\partial \Phi_i}{\partial t} \right)
\end{equation}
Thus, applying eq. (\ref{eq: explicitladders}) to the oscillator function (\ref{eq: psi2}) it can be shown with the help of eqs. (\ref{eq: simple1}) and (\ref{eq: simple2}) that the relativistic ladder operators have the following set of properties.
\begin{equation} \label{eq: l1}
\hat{a}_1^{-\prime} \Phi(x_\mu,P_\mu,l_1, l_2, l_3) = \sqrt{l_1} \Phi(x_\mu,P_\mu,l_1-1, l_2, l_3)
\end{equation}
\begin{equation} \label{eq: l2}
\hat{a}_2^{-\prime} \Phi(x_\mu,P_\mu,l_1, l_2, l_3) = \sqrt{l_2} \Phi(x_\mu,P_\mu,l_1, l_2-1, l_3)
\end{equation}
\begin{equation} \label{eq: l3}
\hat{a}_3^{-\prime} \Phi(x_\mu,P_\mu,l_1, l_2, l_3) = \sqrt{l_3} \Phi(x_\mu,P_\mu,l_1, l_2, l_3-1)
\end{equation}
for lowering the quantum state of the oscillator, alongside
\begin{equation} \label{eq: r1}
\hat{a}_1^{+\prime} \Phi(x_\mu,P_\mu,l_1, l_2, l_3) = \sqrt{l_1+1} \Phi(x_\mu,P_\mu,l_1+1, l_2, l_3)
\end{equation}
\begin{equation} \label{eq: r2}
\hat{a}_2^{+\prime} \Phi(x_\mu,P_\mu,l_1, l_2, l_3) = \sqrt{l_2+1} \Phi(x_\mu,P_\mu,l_1, l_2+1, l_3)
\end{equation}
\begin{equation} \label{eq: r3}
\hat{a}_3^{+\prime} \Phi(x_\mu,P_\mu,l_1, l_2, l_3) = \sqrt{l_3+1} \Phi(x_\mu,P_\mu,l_1, l_2, l_3+1)
\end{equation}
for raising it. These fully relativistic expressions hold true in all inertial frames of reference.
Eqs. (\ref{eq: l1}) through (\ref{eq: r1}) can be used to show
\begin{equation} \label{eq: lo_prime}
\hat{a}_\mu^{+ \prime} \hat{a}^{\mu- \prime} \Phi = n \Phi
\end{equation}
Comparing eqs. (\ref{eq: lo1}) and (\ref{eq: lo_prime}) gives $\hat{a}_\mu^{+ } \hat{a}^{\mu-} = \hat{a}_\mu^{+ \prime} \hat{a}^{\mu- \prime}$ as is to be expected.
\section{Concluding Remarks}
It has been shown that the non-relativistic ladder operators $\hat{a}^{\pm}_i$, for raising and lowering the eigenstates of the harmonic oscillator, have a straightforward Lorentz covariant generalization $\hat{a}^{\pm}_\mu$ that reduces to the form $(\hat{a}^{\pm}_i,0)$ in the rest frame of the oscillator. Two significant results follow. Firstly, the $\hat{a}^{\pm}_\mu$ operators enable the quantum constraint equations for the relativistic oscillator to be expressed in a particularly concise form analogous to the simplification of the Schr\"{o}dinger equations for the harmonic oscillator in terms of $\hat{a}^{\pm}_i$ operators. Secondly, the constraint to three dimensions is shown to generate three independent linear combinations of $\hat{a}^{\pm}_\mu$ components for raising and lowering the eigenstates of the relativistic harmonic oscillator. The explicit forms of these linear combinations have been identified.
\newpage
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 4,828
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Q: Every entered username and password works in PHP login I have a problem in my php code. I want to make login system which takes username and password from database. I almost made everything work. But there is one problem.. When you enter name and password/ doesn't matter what, even random/ it logs me in and redirects me to the place i want. How to fix that and make it use only right username and password from database ? I will import my login code file here. Thanks in advance, sorry for my English.
<?php
include 'dbh.php';
$uid = $_POST['uid'];
$pwd = $_POST['uid'];
$query = "SELECT * FROM user WHERE uid='$uid' AND pwd='$pwd'";
$result = mysqli_query($conn, $query);
if ($result = mysqli_query($conn, $query))
{
while ($row = mysqli_fetch_assoc($result))
{
printf("Login success\n");
}
// If the while loop fails, password/username combo was incorrect
printf("Login failed - Invalid username or password.");
} else {
printf("Login failed, could not query the database.\n");
}
header("Location: panel.php");
?>
A: Use mysqli_num_rows
$sql="SELECT * FROM user WHERE uid='$uid' AND pwd='$pwd'";
if ($result=mysqli_query($con,$sql))
{
if (mysqli_num_rows($result)!=0) {
printf("Login success\n");
}else{
printf("Login failed - Invalid username or password.");
}
mysqli_free_result($result);
}
A: First of all, you are WIDE OPEN to SQL Injection, you will want to update that. Its covered in tons of other places, look it up.
But to fix your issue, You are redirecting regardless of your checks. Move this to your while loop:
while ($row = mysqli_fetch_assoc($result))
{
printf("Login success\n");
header("Location: panel.php");
}
Having that at the bottom means it gets fired no matter what.
A: Try this
<?php
function Db(){
$host = "localhost"; // your db settings
$username = "yourusername";
$password = "yourpass";
$db = "users";
$conn = new mysqli($host, $username, $password, $db);
// use mysqli instead mysql_connect, it is outdated I guess
if(!$conn){
die("Could not connect");
}
}
if(isset($_POST['login'])){
$uid = trim($_POST['username']);
$pwd = trim($_POST['password']);
if($uid == ""){
$err[] = "Username is missing.";
}elseif($pwd == ""){
$err[] = "Password is missing.";
}else{ // When validation succeed then make query.
$db = Db();
$uid = $db->real_escape_string($uid); // escape strings from mysql injection
$pwd = $db->real_escape_string($pwd);
$sql = "SELECT * FROM users
WHERE username = '$uid'
AND password = '$pwd'";
$result = $db->query($sql);
if($result->num_rows == 1){
header("location:panel.php"); // login succeed
}else{
$err[] = "Username or password are incorrect";
header("location:login.php"); // login failed
}
}
}
?>
<?php
if(isset($err)):
foreach($err as $loginErr):
echo $loginErr; // Print login errors.
endforeach;
endif;
?>
<!-- HTML login form goes here -->
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 245
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Hereditas Historiae
Website hosted by Irène Diependaal to foster some historical knowledge necessary to understand our present times
Andrew Marr - Ruling Britannia (1995)
Elizabeth II - Cecil Beaton, 2 June 1953 - National Portrait Gallery, London
'The British state is a pretty odd beast. First, what is the state? It is the government of the country, the historical form of the nation, the accepted focus of political authority. It is not us, the people, but something which claims somehow to be over us and around us and to be in some legal way (though this is clearly nonsense) prior to us. It associates itself strongly with the Crown. We don't mean the headwear itself, of course: the days when we got worked up about fetish-objects such as the sceptre or the Great Seal are long gone. But we still associate the state with the person who occasionally wears and holds the fetishobjects, a shrewd and by all accounts sardonic woman in her sixties, of immigrant stock, and, by extension, with her rather curious family. More loosely still, the "crown" refers to her less curious but also less amusing secretaries of state and ministers of state; her army, navy, air force, marines, judges, courts, police folk, tax-gatherers, lawyers, civil servants, incivil servants and so on and so forth - all the law-makers, law-enforcers, war-makers, peacekeepers and others whose jobs and titles descend from the heyday of the nation-state. They are the servants of the state which, alongside the Crown, appears to consist of a few lorryloads of case law, various Archbishops of advanced views and the Bank of England.
Because of the Civil War, the Commonwealth, the Restoration and the Glorious Revolution of 1688, no constitutionalist would stop there, but would immediately go on to recite "TheQueen-in-Parliament" as being the deep sovereign core of the British state, by which of course the constitutionalist would really mean the Queen-not-in-Parliament, except-on-the-veryrare-occasions-when-she-is-asked-along-to-read-somebody-else'sspeech-like-a-very-grand-TV-newscaster. (….) Are ministers, then, the true fountainhead of authority, the living expression of sovereignty? The trouble with that is that fewer and fewer British people would accept it. We have become true democrats and, in our hearts, most of us now assume that it is "we" collectively, the people, who are the truest and deepest source of legitimate national authority, a sovereignty we loan to our parliamentary and state institutions, and through them to ministers and the constitutional monarchy itself. (….)'
'Let us start by looking again, because everybody always does look again, at the monarchy, symbol of the continuity and centralism of the British political system. In the previous chapter, I discussed the function of the monarchy as a theoretical fountainhead of legitimacy and authority; here I want to look at it as a functioning part of the state. And even today, no one has written more engagingly about this survival of archaism in modem times than Walter Bagehot - yes, him again, that thickly-whiskered Victorian super-pundit whose flashes of insight some 130 years ago have stayed scorched on the country's retina ever since. Most students of British politics have heard of his phrase about the Victorian Monarchy, at the beginning of the period of mass polities, when he warned of the danger of letting "daylight in upon magic". He meant that the mob needed its suspension of belief in the charade. But even then the mob wasn't quite so sure. It is less often remembered that Bagehot was writing at a time when there was in fact a lively and vociferous republican movement in British politics: in the 1860s, Queen Victoria was not popular. The sentences he dashed out remain vividly relevant to our times, when the monarchy is again on a descending curve: "Above all things, our royalty is to be reverenced, and if you begin to poke about it you cannot reverence it. When there is a select committee on the Queen, the charm of royalty will be gone. Its mystery is its life. We must not let daylight in upon magic."
To get his message aright, you need to read those words with a faint, worldly-wise sneer in your voice. Bagehot was a robustly cynical writer, who did not revere the monarchy himself. He had begun his account of the institution by suggesting that, without the Queen, the government of his day would fail and pass away. But he quickly went on to admit that the attention paid to Victoria at Windsor, or the Prince of Wales going to the Derby, was faintly silly: 'it is nice to trace how the actions of a retired widow and an unemployed youth become of such importance." This is hardly the hallowed BBC Richard Dimbleby tone. Yet after Bagehot wrote, the monarchy became more popular, reverenced and un-thought-about, so that his dictum about secrecy and magic carne quickly to seem like an approving description of the British monarchy's dignity, rather than a cynical one-liner. (…)'
'We live in a different world: here is not the place to recount in full or even full summary the sordid and self-destructive exhibitionism of the younger air-headed Windsors, the sexual secrets spilled out, the marital misery publicized, the open acknowledgement of betrayal and bed-hopping. But it is worth noting that this has not been a simple tale of a great institution assaulted by journalists and eventually surrendering, but of the willing involvement of silly people with famous names in a circulation-boosting newspaper game which could only end in their personal and constitutional humiliation. The Waleses fought out their incompatibilities through biographers and journalists, heedless of the pain it would cause to their children or the damage it would do to their special status. The toe-curling stuff that came out ensured that no one could ever pretend, as they once had done, that these were in any sense special people. It wasn't just daylight that was let in upon the magic, and destroyed it, but volleys of revolutionary flashlight. It hasn't been Kalashnikovs or Mausers which accomplished the assassination of monarchy here, but Leicas and Nikons. (….) The result has been exactly as Bagehot predicted. If we do not yet have a select committee on the Queen, we do have the beginnings of parliamentary auditing, and a generally sceptical, businesslike tone when it comes to the Civil List and royal wealth generally. (….)
The possibility of a further move to a disguised republic suggests, of course, that the monarchy retains some genuine role in the real British constitution today, that it is something voters should bother to think about. This is so, but the practical aspects of Royal power have become tightly circumscribed. The Queen's powers to make war or peace, conclude treaties, appoint officials and achieve numerous other things, have largely been passed to the Prime Minister, who combines the title of the Queen's First Minister with many of the practical powers of a republican president. From there is suspended a giant mobile of committees and quangos, appointments for professional busybodies and snobbish bureaucracies which depend ultimately upon the authority of monarchy. For the Prime Minister, the monarchy acts as a kind of grand PR agency. The famous (and inevitably Bagehotian) dictum about the Queen's right to advise, encourage and warn is not substantially different from what such an agency would do for a client: the monarch can be a kind of candid friend to, the Prime Minister, but the daily struggle of government makes this friendship of limited practical importance. She is less, much less, than the Chief Whip. The real muscle of the monarch only comes into play in the highly unusual circumstances of there being no president-mimicking figure resident at Downing Street when illness, parliamentary putsch or an indecisive election result give Buckingham Palace an umpiring role. The historian Peter Hennessy, giving a lecture in 1994, found only five "real or near real contingencies" since 1949 where the Queen's reserve powers were relevant.'
Postscript by Irène Diependaal written for Hereditas Historiae
At the time of writing Ruling Britannia: The failure and future of British democracy (1995), Andrew Marr was the chief political commentator for The Independent, a quality newspaper in Great Britain. In an earlier stage of his journalist career he was political editor of The Economist and The Scotsman.
Ruling Brittannia was more or less a political pamphlet by Andrew Marr on the eve of general elections in Great Britain. Marr advocated constitutional and political reform in his book. He didn't revise the book.
Andrew Marr afterwards changed his views on the monarchy and especially Queen Elizabeth II in writing Diamond Queen. Quotations from this book are also to be found in this section of Hereditas Historiae.
Since 1995 the views on Walter Bagehot, one of the founders of The Economist, had received some more academic scrutiny. Andrew Marr didn't take part of that development. He wrote the "Bagehot column" in The Economist for some time, but had already left The Economist to go the Independent by the time he wrote this particular book.
Irène Diependaal
Essay reviews
On monarchy and royalty
Walter Bagehot - The English Constituion (1867, 1873)
The Economist - The death of Queen Victoria (1901)
The Economist - An idea whose time has passed (1994)
The Economist - The people's monarchy (1997)
Andrew Morton - Diana in her own words (1997)
The Guardian - The irrelevant monarchy (2000)
The Act of Settlement (1701)
Vernon Bogdanor - The Guardian has got it wrong (2000)
Jonathan Freedland - The people versus the Crown (2000)
Andrew Marr - What the Queen does (2011)
Andrew Marr - The future (2011)
The Economist - Letting daylight upon the magic (2015)
The Guardian view on the black spider' memos (2015)
The Guardian - Prince Charles's letters
Stephen Bates - Royalty Inc. (2015)
Craig Brown - The never-ending (but ever-changing) saga of the royal (2017)
Jonathan Freedland - Diana's life shaped Britain (2017)
Andrew Morton - Sex, lies & audiotape
Jenni Russell - Diana saved the Queen (2017)
The Guardian View on Diana. 20 years on (2017)
Hilary Mantel - The princess myth (2017)
Allison Pearson - Diana: a legacy of love (2017)
Charles Moore - The worst news (2017)
Patrick Jephson - The end of a fairy tale (2017)
Guy Kelly - Wildlife (2017)
Bryan Appleyard - Princess Diana: a rustling that rocked the crown (2017)
The Times - Match Point (2017)
The Daily Telegraph - A modern romance to celebrate as a nation (2017)
The New York Times - Breaking News! A Prince Is Born! (2018)
The Economist/Bagehot - Something old, something new (2018)
The Guardian view on the royal wedding: have a lovely day (2018)
New York Times - A new era dawns (2018)
The Sunday Times - Meghan and Harry have cheered us all up (2018)
The Mail on Sunday - A family that embraces the whole nation (2018)
The Times - Charles at 70 (2018)
Guardian View - A crisis in the making (2019)
The Times View - Silent Monarchy (2019)
The Economist - Archie, first royal Instagram baby (2019)
Sunday Times - Archie: a very American royal baby (2019)
On aristocracy and nobility
At the turn of a new era
A post-truth world?
In pursuit of truthful history stories
History & Historiography
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 6,436
|
This Beautiful Town Home will not last long. Inside has been freshly painted. See through gas log fireplace in the living rm./dining rm. Office/study could be a 3rd Bdrm. Step outside on the back patio and relax with a beautiful pond with fountain and walking trail only yards away. What a gorgeous view! This community offers all sorts of daily, weekly and monthly activities. Community is located close to shopping, I-540, Churches, Schools, Restaurants etc. Two car attached garage.
Just listed in 55+ Heritage Pines. Welcome to this beautiful, spacious home filled w/ updates - 2 BR + Bonus/flex room + sunroom. Extensive HW & tile flooring, SS appliances, granite counter tops. 2nd floor bonus/flex room has adjacent 1/2 bath. Recent renovations include new custom roll in tile shower handicapped ramp, refinished cabinets, new paint. Refrigerator, washer/dryer all convey. A true gem! Heritage Pines amenities include clubhouse, pool, tennis. Convenient location. See agent notes.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 5,484
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Telethon (també coneguts amb el nom TeLeTHon) és una banda de pop-rock i punk rock de Milwaukee, Wisconsin (EUA) formada el desembre de l'any 2014, anteriorment coneguda com Fitness abans del novembre de 2015. Es feu coneguda per escriure una òpera rock sobre estar en línia extremadament i apocalípticament, i per publicar un vídeo amb lletra mitjançant una pantalla compartida de Gmail.
Discografia
Àlbums d'estudi
2015: Witness (sota el nom de Fitness)
2016: Citrosis
2019: Hard Pop
2021: Swim Out Past The Breakers
Àlbums en directe
2017: The Grand Spontanean
2018: The Grand Spontanean (Commentary)
EPs
2018: Modern Abrasive
Singles
2018: It Shits!!! (Bomb the Music Industry! Cover)
2021: Selfstarter A.E.
Demos
2020: Nerve-Wracked & Overfeeling: Telethon Demos, Voice Memos, and Oddities 2014-2019
Membres
Kevin Tully -Veu/Guitarra
Jack Sibilski – Guitarra/Cors
Alex Meylink – Baix/Cors
Nate Johnson: Orgue/Piano/Sintetitzadors
Erik Atwell – Bateria/Percussió
Referències
Músics de Wisconsin
Milwaukee
Punk rock
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 799
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Az utolsó skót király (The Last King of Scotland) egy 2006-os díjnyertes brit filmdráma Giles Foden azonos című regénye alapján. A film Dr. Nicholas Garrigan kitalált történetét meséli el. A fiatal doktor Ugandába utazik, ahol Idi Amin Dada, a véreskezű diktátor személyes orvosa lesz. A főszerepben Forest Whitaker látható, aki alakításáért 2007-ben számos díjat nyert, köztük Oscart, Arany Glóbuszt és BAFTA-t.
A filmet korlátozott számú mozi mutatta be az Amerikai Egyesült Államokban 2006. szeptember végén, míg hazájában a következő év elején került a mozikba. Magyarország egyik utolsó állomása volt Az utolsó skót királynak, 2007. április 5-én.
Szereplők
Történet
1970-ben, Nicholas Garrigan frissen szerzett orvosi diplomát. Azonban nincs ínyére az apjával való munka, így a skót fiatalember Ugandába utazik, hogy a helyi lakosok segítségére legyen. Éppen akkor érkezik, mikor Idi Amin Dada katonai puccsal, a nép támogatását élvezve átveszi a hatalmat a kommunista Obotétől. Garrigan munkatársával, Sarah-val ellátogat Amin beszédére a faluban, ahol a kívülálló férfit megnyeri az új elnök kiállása és szavai. Nem sokkal később Nicholas ellátja Amin sérülését, és egy hirtelen cselekedetével – és skót származása révén – elnyeri a diktátor szimpátiáját, aki rövidesen állást ajánl neki a fővárosban, Kampalában, mint az ő személyes orvosa és az egészségügyi minisztérium segítője. Nicholas egyre bizalmasabb kapcsolatba kerül Aminnal, ám ezen hűség súlyos következményekkel jár. Szeretete és csodálata iránta szép lassan félelemmé és bizonytalansággá válik. Nagy-Britannia helyi képviselői is nyomást gyakorolnak rá, mert Amint népirtással vádolják, ráadásul Garrigan viszonyba kezd Amin egyik feleségével, Kayjel, aminek nem várt hozadéka lesz. Nicholas számára bezárul a kör: a kiút érdekében olyan döntéseket kell meghoznia, melyek ha a elnök tudtára jutnak, halált hozhatnak rá.
A film és a történelem
Garrigan fiktív szereplő, ám története hasonlóságokat mutat az angol születésű Bob Astles életével. Akárcsak a regény, a film is a kitalációt vegyíti Uganda valós történelmével, hogy így nyújtson bepillantást Amin totalitárius uralmára. Míg Amin életének több alapvető történése megjelenik a vásznon, a film gyakran eltér bizonyos eseményektől részleteiben. Emellett az idővel is szabadosan él. Például, az ázsiaiak kitoloncolása 1972-ben történt, míg a repülőgépeltérítésre 1976-ban került sor, azonban az adaptálás ezeket rövid egymásutánban prezentálja.
Számos, a filmben látható ugandai földrajzi tényező nem létezett az 1970-es években.
Érdekességek
A pornófilm, amit Amin bedrogozva néz, a Mély torok.
Díjak és jelentősebb jelölések
Oscar-díj
díj: legjobb férfi főszereplő – (Forest Whitaker)
Golden Globe-díj
díj: legjobb férfi főszereplő – dráma – (Forest Whitaker)
BAFTA-díj
díj: Alexander Korda-díj a legjobb brit filmnek – (Andrea Calderwood, Lisa Bryer, Charles Steel, Kevin Macdonald, Peter Morgan és Jeremy Brock)
díj: legjobb férfi főszereplő – (Forest Whitaker)
díj: legjobb adaptált forgatókönyv – (Peter Morgan, Jeremy Brock)
jelölés: legjobb film – (Andrea Calderwood, Lisa Bryer, Charles Steel)
jelölés: legjobb férfi mellékszereplő – (James McAvoy)
Bostoni Filmkritikusok Egyesülete
díj: legjobb színész (Forest Whitaker)
Brit Bátorság Film díj
díj: legjobb rendező (Kevin Macdonald)
díj: legjobb technikai teljesítmény (Anthony Dod Mantle – fényképezés)
Broadcast Filmkritikusok Egyesülete
díj: legjobb színész (Forest Whitaker)
Chicagoi Filmkritikusok Egyesülete
díj: legjobb színész (Forest Whitaker)
Dallasi Filmkritikusok Egyesülete
díj: legjobb színész (Forest Whitaker)
Evening Standard Brit Film díj
díj: legjobb forgatókönyv
díj: legjobb technikai teljesítmény (Anthony Dod Mantle – fényképezés)
Floridai Filmkritikusok Egyesülete
díj: legjobb színész (Forest Whitaker)
Image-díj
díj: legjobb színész (Forest Whitaker)
Las Vegasi Filmkritikusok Egyesülete
díj: legjobb színész (Forest Whitaker)
London Filmkritikusok díja
díj: az év színésze (Forest Whitaker)
Los Angelesi Filmkritikusok Egyesülete
díj: legjobb színész (Forest Whitaker)
Nemzeti Filmszemle, USA
díj: legjobb színész (Forest Whitaker)
Nemzeti Filmkritikusok Egyesülete, USA
díj: legjobb színész (Forest Whitaker)
New York-i Filmkritikusok Egyesülete
díj: legjobb színész (Forest Whitaker)
Online Filmkritikusok Egyesülete
díj: legjobb színész (Forest Whitaker)
Santa Barbara Nemzetközi Filmfestivál
díj (Forest Whitaker)
Satellite-díj
díj: legjobb színész, dráma (Forest Whitaker)
Film Színészek Egyesülete
díj: legjobb színész (Forest Whitaker)
Southeasterni Filmfritikusok Egyesülete
díj: legjobb színész (Forest Whitaker)
Stockholm Filmfestivál
díj: legjobb fényképezés (Anthony Dod Mantle)
Washington DC Area Filmkritikusok Egyesülete
díj: legjobb színész (Forest Whitaker)
További információk
2006 filmjei
Könyvadaptációk
Brit életrajzi filmek
Brit filmdrámák
InterCom-filmek
20th Century Fox-filmek
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{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 6,689
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package bapspatil.silverscreener.adapters;
import android.content.Context;
import android.view.LayoutInflater;
import android.view.View;
import android.view.ViewGroup;
import android.widget.ImageView;
import androidx.recyclerview.widget.RecyclerView;
import com.bumptech.glide.load.resource.drawable.DrawableTransitionOptions;
import java.util.ArrayList;
import bapspatil.silverscreener.R;
import bapspatil.silverscreener.model.Movie;
import bapspatil.silverscreener.network.RetrofitAPI;
import bapspatil.silverscreener.utils.GlideApp;
import butterknife.BindView;
import butterknife.ButterKnife;
public class MovieRecyclerViewAdapter extends RecyclerView.Adapter<MovieRecyclerViewAdapter.MovieViewHolder> {
private ArrayList<Movie> mMoviesArrayList;
private Context mContext;
private ItemClickListener mClickListener;
public MovieRecyclerViewAdapter(Context context, ArrayList<Movie> movieArrayList, ItemClickListener itemClickListener) {
this.mContext = context;
this.mMoviesArrayList = movieArrayList;
this.mClickListener = itemClickListener;
}
@Override
public MovieViewHolder onCreateViewHolder(ViewGroup viewGroup, int viewType) {
View view = LayoutInflater.from(mContext).inflate(R.layout.rv_movie_item, viewGroup, false);
return new MovieViewHolder(view);
}
@Override
public void onBindViewHolder(MovieViewHolder holder, int position) {
Movie theMovie = mMoviesArrayList.get(position);
if (theMovie.getPosterBytes() != null) {
GlideApp.with(mContext)
.load(theMovie.getPosterBytes())
.centerCrop()
.error(R.drawable.tmdb_placeholder)
.fallback(R.drawable.tmdb_placeholder)
.transition(new DrawableTransitionOptions().crossFade())
.into(holder.mPosterImageView);
} else {
GlideApp.with(mContext)
.load(RetrofitAPI.POSTER_BASE_URL + theMovie.getPosterPath())
.centerCrop()
.error(R.drawable.tmdb_placeholder)
.fallback(R.drawable.tmdb_placeholder)
.transition(new DrawableTransitionOptions().crossFade())
.into(holder.mPosterImageView);
}
}
@Override
public int getItemCount() {
if (mMoviesArrayList == null) return 0;
else return mMoviesArrayList.size();
}
public interface ItemClickListener {
void onItemClick(int position, ImageView posterImageView);
}
public class MovieViewHolder extends RecyclerView.ViewHolder implements View.OnClickListener {
@BindView(R.id.poster_image_view)
ImageView mPosterImageView;
MovieViewHolder(View itemView) {
super(itemView);
ButterKnife.bind(this, itemView);
itemView.setOnClickListener(this);
}
@Override
public void onClick(View v) {
if (mClickListener != null)
mClickListener.onItemClick(getAdapterPosition(), mPosterImageView);
}
}
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 5,484
|
Player Ratings: West Brom 2 – 2 Arsenal
Well, the game did play out to some of my expectations. I expected that the match wouldn't be a walk in the park but I never expected a draw or drop of points. I expected a bad performance from Denison but not a freak goal and mistake from Almunia and Squillaci. I expected any one of Arshavin, Van Persie and Nasri to produce a big moment but I never expected four goals to be scored. As it stands, we are now five points behind Manchester united with a game in hand.
As far as the performance is concerned, it was below par for like an hour and only when Arshavin scored the first goal out of nowhere, we became alive. The more alarming thing is that it took two goals for our players to wake. But that can be taken as an improvement because when we played them last time at the Emirates, it took three goals for us to realize that we were losing, and eventually we did lose that game.
The defense today was in shambles as everyone made mistakes after mistakes. No communication, no coordination, no positioning, everything was erratic to say the least. In the middle also we failed to create much. Our movement and passing wasn't sharp enough. Upfront, we had very limited chances to score from.
And as for learning from our mistakes, that we will never do. We again had plenty of possession but we created very little opportunities. We again conceded by giving away an unnecessary corner, by a mistake of the keeper and defender and by not closing down the opposition or attacking the aerial balls.
West Brom on the other hand scored two goals with their two shots on goal and looked threatening every time they were in our half.
However, I am disgusted the most with Denilson's performance and Almunia and Squillaci's mix up which sums up our failings of the season very nicely. Denilson for me shall never start for Arsenal again. He has been given chance after chance and everytime he disappoints. It's becoming unbearable to watch him trot at a snail's pace and then give away the ball when under no pressure. Simply not acceptable if we want to win something.
Same goes for Almunia. He may produce a couple of good games but mistakes such as the one committed today are a telling us quite clearly that he never will be a good keeper and will always cost points. Squillaci too needs to step up exponentially or he will be joining them soon enough. He is just a step behind.
The only positive if it can be taken as a positive is the way we came back. We could have even won it in the end. However, if we had started playing from the first minute it would never have come to that and I see this as two points dropped and not one point gained.
Almunia (1): I don't know what he was thinking when he came out of goal like that. Horrible piece of keeping that spoilt the game. It is mistakes like these that he will never be a good keeper as I said before.
Sagna (5): He made a lot of uncharacteristic errors as his positioning was not good and left his side exposed a lot. The corner which led to West brom's first goal should never have been conceded had Sagna not lost his man.
Koscielny (5): He also made plenty of uncharacteristic mistakes. Needs to improve his partnership with Squillaci or else we will be seeing more performances like these.
Squillaci (3): Horrible mistake for the second goal. Did produce a great block late in the game to deny West Brom a win. Needs lots of improvement.
Clichy (5.5): Upfront delivered in a few good crosses, one of which should have been a goal, had Ramsey done better. However, he did give away the ball on more than a few occasions which led to nervous moments at the back.
Wilshere (6): Nothing much from the youngster as he did well in the second half alongside Nasri in the middle of the park.
Denilson (2): My temper with him has crossed the boiling point. He was in the lineup today as we have no other defensive midfielder. Showed again that he doesn't want to play.
Nasri (6): Again nothing much from Nasri but similarly to Wilshere did well in the midfield in the second half.
Arshavin (7): Anonymous for like 75 percent of the game. However, produced a magical moment for the first goal and then crossed the ball which led to the second goal.
Van Persie (6.5): Tried his best even without support. Scored the vital second goal.
Ramsey (5.5): He isn't ready to start games. Lost his man for the first goal and missed a simple tap in the first half. Not going to judge him much as he hasn't played football at this level for a year.
Chamakh (6) and Bendtner (6) provide good support to van Persie and increased our presence in the box. Bendtner provided the assist for the second goal.
3 Comments | Uncategorized | Tagged: Andrei Arshavin, Arsenal FC, Manuel Almunia, Nicklas Bendtner, Robin van Persie, Samir Nasri, Sébastien Squillaci, West Bromwich Albion F.C. | Permalink
You are currently browsing the redgunners blog archives for the day Sunday, March 20th, 2011.
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 1,783
|
Q: Knockout: Add items into nested json hierarchy I would like to know how to add items within a nested hierarchy. I was able to do it when I was not using the mapping plugin, but only in the top level.
Here's the Fiddle: https://jsfiddle.net/kyr6w2x3/3/
<input type="text"
data-bind="value: newSlideTitle" placeholder="Awesome slide name">
<button type="button"
data-bind="click: $root.addSlide.bind($parent, $data)">Add slide</button>
self.removeSlide = function(slide) { this.slides.remove(slide) };
self.addSlide = function(slide) {
this.slides.push(new Slide({
slideTitle: this.newSlideTitle(),
slideImage: this.newSlideImage()
}));
self.newSlideTitle("");
self.newSlideImage("");
};
I would like to know how to make the form (line 20 of html) working so it adds a slide. Thanks!
A: What I would do, I'd create a separate View Model for each Array and try to keep them in a way so you would be able to add a new instance of that VM easily and also you are able to access to each observableArray in order to add or any manipulations.
In your code you don't have an access to this.slides to push new Slide which I could not find it in your code.
Example : https://jsfiddle.net/kyr6w2x3/6/
function PageItemViewModel(data){
var self = this;
self.pageName = ko.observable(data.pageName);
self.pageRows = ko.observableArray([]);
// create a new instance of PageRowItemViewModel for each data.pageRows
self.pageRows($.map(data.pageRows, function (item) {
return new PageRowItemViewModel(item);
}));
}
function PageRowItemViewModel(data){
var self = this;
self.rowType = ko.observable(data.rowType);
self.slides = ko.observableArray([]);
self.rowBackgroundColor = ko.observable(data.rowBackgroundColor);
// create a new instance of SlideItemViewModel for each data.slides
self.slides($.map(data.slides, function (item) {
return new SlideItemViewModel(item);
}));
}
function SlideItemViewModel(data){
var self = this;
self.slideTitle = ko.observable(data.slideTitle);
self.slideImage = ko.observable(data.slideImage);
}
function ViewModel(data){
var self = this;
// Define an observableArray
self.pages = ko.observableArray([]);
self.OutputJson = function(){
console.log(ko.toJSON(self));
}
self.newSlideTitle = ko.observable();
self.newSlideImage = ko.observable();
// create a new instance of PageItemViewModel for each website
self.pages($.map(website, function (item) {
return new PageItemViewModel(item);
}));
self.removePage = function(pageName) { self.pages.remove(pageName) };
self.removeRow = function(rowType) { this.pageRows.remove(rowType) };
self.addRow = function(rowType) {
//
}
self.removeSlide = function(slide) { this.slides.remove(slide) };
self.removeSlide = function(slide) { this.slides.remove(slide) };
self.addSlide = function(item) {
//here you have an access to your item which is an instance of your PageRowItemViewModel
item.slides.push( new SlideItemViewModel({slideTitle :self.newSlideTitle() ?self.newSlideTitle() : "NEW" ,slideImage :self.newSlideImage() ? self.newSlideImage() : "NEW IMAGE" }));
};
}
// rowImages:" 'image1.jpg','image2.jpg','image3.jpg' "
var website = [
{pageName: "Home", pageType:"home", pageRows: [
{rowType: "slideshow", rowBackgroundColor: "#ddddef", slides: [
{ slideTitle:"Fabulous", slideImage:"img1.png"},
{ slideTitle:"Amazing", slideImage:"img2.png"},
{ slideTitle:"Elegant", slideImage:"img3.png"}
] },
{rowType: "slideshow", rowBackgroundColor: "#ffddcc", slides: [
{ slideTitle:"Wonderful", slideImage:"img1.png"},
{ slideTitle:"Compelling", slideImage:"img2.png"},
{ slideTitle:"Magestic", slideImage:"img3.png"}
] }
]
},
{pageName: "about", pageRows: []},
{pageName: "contact", pageRows: []}
];
_vm = new ViewModel(website);
ko.applyBindings(_vm );
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 7,465
|
HealthRight International, formerly known as Doctors of the World-USA, is a global health organization, based in New York City. HealthRight was founded in 1990 by physician and human rights advocate Dr. Jonathan
Mann.
They work to guarantee that marginalized communities have equitable access to healthcare, in the intersection of public health and human rights. By ensuring marginalized populations have access to social, health, and mental services, introducing cutting-edge social technologies, expanding the field of health and social services, and enhancing the capabilities of civil society organizations, they aim to improve life quality and enable marginalized populations to exercise basic rights.
Headquartered in New York, HealthRight has worked in over 30 countries, with current projects in Kenya, Ukraine, Uganda, the United States, and Vietnam.
History and Organization
Founding
HealthRight International was founded in 1990 by Jonathan Mann as he perceived a void in the health and human rights organizations within the United States. He set out to form a special organization to develop long-term initiatives to advance and defend health and human rights both domestically and overseas.
During the Haitian Refugees Crisis in Guantanamo Bay in 1993, HealthRight International, then still known as Doctors of the World-USA, was present in the camp. The witnessing of the atrocities led Doctors of the World-USA to be very outspoken about condemning and criticizing the camp.
Subsidiaries
Ukrainian Foundation for Public Health (UFPA)
The Ukrainian Foundation for Public Health was founded in 2008 as a country specific subsidiary to HealthRight International. They have focused on expanding HealthRight International's mission throughout Ukraine. Specifically focusing on young women and girls, their partners and children in difficult living circumstances, as well as Pregnant women and young mothers at risk of abandoning their newborn infants or deprivation of parental rights. As well as at-risk adolescents and HIV-positive teenagers and their family members and adolescents, youth, and women in conflict with the law.
Merger
Peter C. Alderman Foundation (PCAF)
The Peter C. Alderman Foundation (PCAF) is a foundation dedicated to providing medical professionals and other indigenous caregivers with the resources to treat mental anguish utilizing Western medical techniques mixed with regional healing traditions in order to lessen the suffering of victims of terrorism and mass violence in post-conflict nations.
On April 23, 2018 HealthRight and PCAF announced their merger in order to better serve the mental health requirements of the underserved communities they work with globally. The merger allowed PCAF to incorporate its vast knowledge and expertise in global mental health across HealthRight's current and future programs. Since 2018, PCAF has been operating as the Peter C. Alderman Program for Global Mental Health.
For the past several years HealthRight International has hosted the HEALTH + HUMAN RIGHTS AWARDS. PCAF supports HealthRight's work leveraging global resources to address local health challenges, creating sustainable solutions and lasting change for communities around the world.
Current project areas
HIV
Launched in 2019, the innovative SACCO Health and Wellness project aims to increase testing among men by partnering with the Transportation Savings Credit and Cooperative Organization (SACCO) for boda boda, local motorbike transportation, drivers. This is done by integrating mental health intervention alongside HIV education and testing models to address the mental health consequences of COVID-19 and enhance HIV outcomes. The program was piloted in Kitale, Kenya, in 2018-2019, where it successfully tested 5,000 men and their partners for HIV. Recently, HealthRight International joined the Gilead Zeroing In conference discussing the SACCO project.
Response to the 2022 Russian invasion of Ukraine
HealthRight/UFPH is one of a select group of NGOs that continued to assist vulnerable communities and war survivors within Ukraine. HealthRight has doubled its personnel in Ukraine over the first five months following the beginning of the war.
They have placed a specific focus on Reproductive, Maternal, Newborn, Child, and Adolescent Health of the displaced populations, specifically reproductive health. Additionally, the Ukrainian Foundation for Public Health, with support from UNICEF, has put on 50 mobile response teams consisting of social workers, lawyers, physicians, and psychologists, to help displaced Ukrainians at reception points across the country, offering specialist expertise and advice to the thousands who need it.
Legal Status and Size
HealthRight is a 501(c)(3) organization, with recent annual revenue of about US$4.8 million.
See also
Jonathan Mann
Universal Declaration of Human Rights
International Covenant on Economic, Social, and Cultural Rights
References
External links
HealthRight International Homepage
HealthRight International blog
Health charities in the United States
Medical and health organizations based in New York City
International medical and health organizations
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 4,049
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De tunnel van rue du Peuple is een spoortunnel in de gemeente Soumagne. De tunnel heeft een lengte van 221 meter. De dubbelsporige HSL 3 gaat door de tunnel.
De tunnel werd aangelegd volgens het cut & cover-principe om de hogesnelheidslijn maximaal te integreren in het landschap en de hoogteverschillen op de lijn beperkt te houden.
Rue Peuple
Rue P
Soumagne
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 6,593
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Philip James Alexander (born 4 September 1962) is an English former association footballer and American footballer who is the CEO of Bristol City.
Association football
Alexander's English football career began at Reading. Alexander then joined amateur Wokingham Town, before signing for Norwich City for £2,000 in 1981.
American football
Alexander played for Farnham Knights and London Monarchs as a kicker. In the Monarchs first year he was "Operation Discovery Player of the year", was voted to the All World League team and was the first Brit to get his hands on the World Bowl trophy.
Executive career
Alexander was appointed chief executive of Crystal Palace in 1996, In December 2022 he was appointed CEO at Bristol City.
References
External links
Former Chief Executive Phil Alexander joins Bristol City F.C.
Phil Alexander appointed new CEO
1962 births
Living people
English footballers
American football placekickers
Crystal Palace F.C. directors and chairmen
Association football defenders
English players of American football
Footballers who switched code
English Football League players
Wokingham Town F.C. players
Norwich City F.C. players
Miramar Rangers AFC players
London Monarchs players
Bracknell Town F.C. players
English football managers
Bracknell Town F.C. managers
English expatriate footballers
English expatriate sportspeople in New Zealand
Expatriate association footballers in New Zealand
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 5,931
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SoftBank is in talks with investors to pump an additional $15bn (£11bn) into its $100bn Vision Fund as the firm looks to find new ways of raising money for its investment engine.
The Japanese technology conglomerate has already ploughed more than $70bn into some of the world's most prolific start-ups and is reportedly weighing up new means of adding more cash to the Saudi-backed fund.
Masayoshi Son, the billionaire founder of SoftBank Group, has previously declared his intention for the company to raise further capital, indicating that he plans to launch a new $100bn fund in order to keep up SoftBank's dealmaking.
The company has considered a range of options to raise new money, including persuading current investor Saudi Arabia to waive rights on debt repayments, sources told Bloomberg.
Saudi Arabia's Public Investment Fund, led by crown prince Mohammed bin Salman, made a five-year $45bn pledge to SoftBank upon the launch of the Vision Fund in 2016.
SoftBank is also keen to keep enough in reserve to buy shares in the companies it has backed while raising new capital, but a deal is far from certain, the sources said.
Some of the Vision Fund's biggest investments have included WeWork, Grab and a $31bn buyout of Cambridge-based chipmaker ARM Holdings.
Uber and Slack, two key investments for SoftBank, are looking to go public later this year and the company could plan to use profits generated from those flotations as extra cash for its fund.
In recent months, SoftBank has made it clear that it intends to invest further in markets such as China and India, after announcing that it would be opening a permanent office in Mumbai and hiring an investment team for the Vision Fund in Shanghai.
Rajeev Misra, chief executive of SoftBank Investment Advisers UK, which manages the fund, has said "India represents an enormous addressable market comprising a young, tech-enabled population". It currently has offices in London, California and Tokyo.
SoftBank could not be reached for comment.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 8,960
|
{"url":"https:\/\/stats.stackexchange.com\/questions\/141362\/how-can-i-get-slope-and-standard-error-at-several-levels-of-a-continuous-by-cont","text":"# How can I get slope and standard error at several levels of a continuous by continuous interaction in R?\n\nI'm comparing the slopes of several different response variables (DVs; representing different populations) to a set of predictors (IVs). For some DVs a 2-way interaction (continuous by continuous) is supported. To facilitate my comparison of IV coefficients I'd like to plot the slope estimates and 95% CI on a single graph (separate graph for each IV), and for the DV's with an interaction I'd like to plot the slope at ~3 values of the continuous moderator variable (e.g., \"DV 1\" in figure below).\n\nI'm sure there is a variety of ways to get these values, but I'm hoping someone can point me to a simple bit of code or a package that can help automate this process for me. I should also note my models are from lme4.\n\nThe 'effects' package handily calculates predicted values at user-specified levels of the moderator variable, but doesn't provide slopes or SE to my knowledge (although I could figure these out from the predicted values, I'm hoping for a more stream-lined method).\n\nHere is some toy data, although it doesn't produce an interaction like I show in the figure;\n\nset.seed(50)\nx1 <- rnorm(100,2,10)\nx2 <- rnorm(100,2,10)\ny1 <- x1+x2+x1*x2+rnorm(100,0,100)\n\nmodel1<-lm(y1 ~ x1*x2)\n\n\nAnd here is the predicted values plotted from 'effects', but I want the slopes and SE of these lines...\n\nlibrary(effects)\nmodel1.eff<-effect(\"x1*x2\",model1,xlevels=3)\nplot(model1.eff,multiline=T,ci.style=\"bands\")\nas.data.frame(model1.eff)\n\n\nIn order to examine simple slopes at different levels of one of the continuous variables, you can simply center the other continuous variable to focus on the slope of interest. In a model with a continuous by continuous interaction, like so: $$y = \\beta_0 + \\beta_1x_1 + \\beta_2x_2 + \\beta_3x_1*x_2$$ the two single predictor coefficients ($\\beta_1$ and $\\beta_2$) are simple slopes for the predictor when the other predictor (however it is centered) is equal to 0.\n\nSo, if I run your practice code above, I get the following output:\n\nCall:\nlm(formula = y1 ~ x1 * x2)\n\nResiduals:\nMin 1Q Median 3Q Max\n-281.996 -70.148 -3.702 70.190 209.182\n\nCoefficients:\nEstimate Std. Error t value Pr(>|t|)\n(Intercept) 17.7519 10.8121 1.642 0.104\nx1 1.4175 1.0151 1.397 0.166\nx2 0.8222 1.0614 0.775 0.440\nx1:x2 0.8911 0.1295 6.882 6.04e-10 ***\n---\nSignif. codes: 0 \u2018***\u2019 0.001 \u2018**\u2019 0.01 \u2018*\u2019 0.05 \u2018.\u2019 0.1 \u2018 \u2019 1\n\nResidual standard error: 100.6 on 96 degrees of freedom\nMultiple R-squared: 0.4283, Adjusted R-squared: 0.4105\nF-statistic: 23.98 on 3 and 96 DF, p-value: 1.15e-11\n\n\nThe x1 output gives us the test of the x1 slope at x2 = 0. Thus we get a slope, standard error, and (as a bonus) the test of that parameter estimate compared to 0. If we wanted to get the simple slope of x1 (and standard error and sig. test) when x2 = 6, we simply use a linear transformation to make a value of 6 on x2 the 0 point:\n\nx2.6<- x2-6\n\n\nBy viewing summary stats, we can see that this is the exact same variable as before, but it has been shifted down on the number line by 6 units:\n\nsummary(x2)\nsummary(x2.6)\n\n> summary(x2)\nMin. 1st Qu. Median Mean 3rd Qu. Max.\n-31.0400 -5.9520 1.3430 0.8396 8.0090 22.3800\n\n> summary(x2.6)\nMin. 1st Qu. Median Mean 3rd Qu. Max.\n-37.040 -11.950 -4.657 -5.160 2.009 16.380\n\n\nNow, if we re-run the same model but substitute x2 for our newly centered variable x2.6, we get this:\n\nmodel1.6<- lm(y1~x1*x2.6)\nsummary(model1.6)\n\nCall:\nlm(formula = y1 ~ x1 * x2.6)\n\nResiduals:\nMin 1Q Median 3Q Max\n-281.996 -70.148 -3.702 70.190 209.182\n\nCoefficients:\nEstimate Std. Error t value Pr(>|t|)\n(Intercept) 22.6853 12.6384 1.795 0.0758 .\nx1 6.7639 1.2346 5.479 3.44e-07 ***\nx2.6 0.8222 1.0614 0.775 0.4404\nx1:x2.6 0.8911 0.1295 6.882 6.04e-10 ***\n---\nSignif. codes: 0 \u2018***\u2019 0.001 \u2018**\u2019 0.01 \u2018*\u2019 0.05 \u2018.\u2019 0.1 \u2018 \u2019 1\n\nResidual standard error: 100.6 on 96 degrees of freedom\nMultiple R-squared: 0.4283, Adjusted R-squared: 0.4105\nF-statistic: 23.98 on 3 and 96 DF, p-value: 1.15e-11\n\n\nIf we compare this output to the old output we can see that the omnibus F is still 23.98, the interaction t is still 6.882 and the slope for x2.6 is still .822 (and nonsignificant). However, our coefficient for x1 is now much larger and significant. This slope is now the simple slope of x1 when x2 is equal to 6 (or when x2.6 = 0). By centering by several different variables, we can test several different simple effects (and obtain slopes and standard errors) without that much work. By using a (dreaded in the R community) for loop to iterate through the list, we can test several different simple effects quite efficiently:\n\ncenteringValues<- c(1,2,3,4,5,6) # Creating a vector of values to center around\n\nfor(i in 1:length(centeringValues)){ #Making a for loop that iterates through the list\nx<- x2-i # Creating a predictor that is the newly centered variable\nprint(paste0('x.',centeringValues[i])) # printing x.centering value so you can keep track of output\nprint(summary(lm(y1~x1*x))[4]) # printing coefficients for the model with the center variable\n\n}\n\n\nThis code first creates a vector of values you want to become the 0 point for the variable you do not want the slope for (in this example, x2). Next, create a for loop that iterates through the positions in this list (i.e. if the list has 3 items, the for loop will iterate through the values 1 to 3). Next, create a new variable that is the centered version of the variable for which you do not want centered slopes (in this case we are interested in simple slopes for x1, so we center x2). Finally, print the coefficients from the model that includes your newly centered variable in place of the raw variable. This results in the following output:\n\n[1] \"x.1\"\n$coefficients Estimate Std. Error t value Pr(>|t|) (Intercept) 18.5741364 10.8815154 1.7069439 9.106513e-02 x1 2.3085985 1.0143100 2.2760286 2.506664e-02 x 0.8222252 1.0613590 0.7746909 4.404262e-01 x1:x 0.8910530 0.1294695 6.8823366 6.041102e-10 [1] \"x.2\"$coefficients\nEstimate Std. Error t value Pr(>|t|)\n(Intercept) 19.3963616 11.0528627 1.7548722 8.247158e-02\nx1 3.1996515 1.0299723 3.1065415 2.489385e-03\nx 0.8222252 1.0613590 0.7746909 4.404262e-01\nx1:x 0.8910530 0.1294695 6.8823366 6.041102e-10\n\n[1] \"x.3\"\n$coefficients Estimate Std. Error t value Pr(>|t|) (Intercept) 20.2185867 11.3215341 1.7858522 7.728065e-02 x1 4.0907045 1.0613132 3.8543802 2.096928e-04 x 0.8222252 1.0613590 0.7746909 4.404262e-01 x1:x 0.8910530 0.1294695 6.8823366 6.041102e-10 [1] \"x.4\"$coefficients\nEstimate Std. Error t value Pr(>|t|)\n(Intercept) 21.0408119 11.6808159 1.8013135 7.479290e-02\nx1 4.9817575 1.1070019 4.5002249 1.905339e-05\nx 0.8222252 1.0613590 0.7746909 4.404262e-01\nx1:x 0.8910530 0.1294695 6.8823366 6.041102e-10\n\n[1] \"x.5\"\n$coefficients Estimate Std. Error t value Pr(>|t|) (Intercept) 21.8630371 12.1226545 1.8034859 7.444873e-02 x1 5.8728105 1.1653521 5.0395160 2.193149e-06 x 0.8222252 1.0613590 0.7746909 4.404262e-01 x1:x 0.8910530 0.1294695 6.8823366 6.041102e-10 [1] \"x.6\"$coefficients\nEstimate Std. Error t value Pr(>|t|)\n(Intercept) 22.6852623 12.6383944 1.7949481 7.580894e-02\nx1 6.7638636 1.2345698 5.4787212 3.439867e-07\nx 0.8222252 1.0613590 0.7746909 4.404262e-01\nx1:x 0.8910530 0.1294695 6.8823366 6.041102e-10\n\n\nHere you can see the output provides the coefficients for several tests, but the only thing that changes each time is the slope for x1. The slope for x1 in each output represents the slope for x1 when x2 is equal to whatever centering value we have assigned for that iteration. Hope this helps!\n\n\u2022 Thanks @wool, your answer provides the output I was after, but I think I found a more stream-lined way to attain it once I realized what I was after is called \"marginal effects\" (see my answer) \u2013\u00a0Dave M Apr 1 '15 at 16:06\n\nWhile @wools answer appears more than adequate, here is another alternative that allows the calculation of marginal effect of x1 given x2, from a single model output without centering the x variables;\n\nAccording to http:\/\/statistics.ats.ucla.edu\/stat\/r\/faq\/concon.htm ; where the model is\n\ny ~ \u03b20 + \u03b21x1 + \u03b22x2+ \u03b23x1\u2217x2\n\nthen slope for x1 at a given value of x2 is \u03b21 + \u03b23 * x2\n\nSo I can choose a few values of x2 as;\n\nat.x2<-c(-6, 1, 6)\n\nslopes <- coef(model1)[\"x1\"] + coef(model1)[\"x1:x2\"] * at.x2\n\n\nAccording to How to calculate the standard error of the marginal effects in interactions (robust regression)? Standard error for slopes = sqrt(var(b1) + var(b3) x2^2 + 2 x2 * cov(b1,b3) )\n\nestvar<-vcov(model1); model1.vcov<-as.data.frame(as.matrix(estvar))\nvar.b1<-model1.vcov[\"x1\",\"x1\"]\nvar.b3<-model1.vcov[\"x1:x2\",\"x1:x2\"]\ncov.b1.b3<-model1.vcov[\"x1\",\"x1:x2\"]\n\nSEs <- rep(NA, length(at.x2))\nfor (i in 1:length(at.x2)){\nj <- at.x2[i]\nSEs[i] <- sqrt(var.b1 + var.b3 * j^2 + 2*j* cov.b1.b3)\n}\n\ncbind(SEs, slopes)","date":"2020-03-30 11:12:58","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.5896065831184387, \"perplexity\": 1313.2402551377577}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 20, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2020-16\/segments\/1585370496901.28\/warc\/CC-MAIN-20200330085157-20200330115157-00349.warc.gz\"}"}
| null | null |
double lap;
int currentParty;
const char* mySide() {
if (currentParty == 1) return "Generator";
else return "Evaluator";
}
int main(int argc, char *argv[]) {
printf("Linear Regression\n");
printf("=================\n\n");
// Check args
if (argc == 4) {
// Initialize protocols and obtain connection information
const char *remote_host = strtok(argv[1], ":");
const char *port = strtok(NULL, ":");
ProtocolDesc pd;
protocolIO io;
// Make connection between two shells
// Modified ocTestUtilTcpOrDie() function from ~/obliv-c/test/oblivc/common/util.c
log_info("Connecting to %s on port %s ...\n", remote_host, port);
if(argv[2][0] == '1') {
if(protocolAcceptTcp2P(&pd,port)!=0) {
log_err("TCP accept from %s failed\n", remote_host);
exit(1);
}
}
else {
if(protocolConnectTcp2P(&pd,remote_host,port)!=0) {
log_err("TCP connect to %s failed\n", remote_host);
exit(1);
}
}
// Final initializations before entering Yao protocol
currentParty = (argv[2][0]=='1'?1:2);
setCurrentParty(&pd, currentParty); // only checks for a '1'
io.src = argv[3]; // filename
lap = wallClock();
// Execute Yao protocol and cleanup
execYaoProtocol(&pd, linReg, &io); // starts 'linReg()'
cleanupProtocol(&pd);
double runtime = wallClock() - lap; // stop clock here
// Print results and store runtime data
log_info("%s total time: %lf seconds\n", mySide(), runtime);
log_info("Yao Gate Count: %u\n", yaoGateCount());
write_runtime(io.n, runtime, currentParty, "runtime.dat");
printf("\n");
log_info("Slope \tm = %15.6e\n", (double) DESCALE(io.m)); // print slope
log_info("y-intercept\tb = %15.6e\n", (double) DESCALE(io.b)); // print y-intercept
log_info("Correlation\tr = %15.6e\n", sqrt((double) DESCALE(io.rsqr))); // print correlation
} else {
log_info("Usage: %s <hostname:port> <1|2> <filename>\n"
"\tHostname usage:\n"
"\tlocal -> 'localhost' remote -> IP address or DNS name\n", argv[0]);
}
return 0;
}
void load_data(protocolIO *io, int** x, int** y, int party) {
FILE *inputFile = fopen(io->src, "r");
if (inputFile == NULL) {
log_err("File '%s' not found\n", io->src);
clean_errno();
exit(1); // causes TCP error for non-null party
}
io->n = 0;
int memsize = ALLOC;
double a;
while (!feof(inputFile)) {
int dataPoints = fscanf(inputFile, "%lf", &a);
if (dataPoints != 1) {
if (dataPoints < 0 && feof(inputFile)) {
break;
} else {
log_err("Input from '%s' does not match file format. Check input file.\n\t"
"File format exception found at Line %d or %d in file.\n",
io->src, io->n, io->n + 1); // prints to both parties if filename is same
clean_errno();
exit(1);
}
}
io->n += 1;
if (io->n > memsize) {
memsize *= 2;
*x = realloc(*x, sizeof(int) * memsize);
*y = realloc(*y, sizeof(int) * memsize);
check_mem(*x, *y, party);
}
int aint = a * SCALE;
assert(APPROX((double) DESCALE(aint), a));
if (party == 1) {
*(*x + io->n - 1) = aint; // messy, but needed for dereferencing
} else if (party == 2) {
*(*y + io->n - 1) = aint;
}
}
log_info("Loading %d data points ...\n", io->n);
fclose(inputFile);
}
void write_runtime(int n, double time, int party, const char* dest) {
FILE *file = fopen(dest, "a");
if (file == NULL) {
log_err("File '%s' not found\n", dest);
clean_errno();
exit(1);
}
fprintf(file, "[party %d] %d points, %lf seconds\n", party, n, time);
log_info("Runtime data stored in file '%s'\n", dest);
}
void check_mem(int* x, int* y, int party) {
if((party == 1 && x == NULL) || (party == 2 && y == NULL)) {
log_err("Memory allocation failed\n");
clean_errno();
exit(1);
}
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 8,448
|
\section{\label{sec:level1} Introduction}
Electron transport via inelastic hops between localized states in
disordered conductors has been studied for many years, with the main
focus on the average transport characteristics (e.g., dc current
dependence on temperature and applied electric field) and to a
lesser extent on the $1/f$ noise - see
Refs.~\cite{MottBook,ShklovskiiBook,EfrosPollackCollection,KoganBook}
for comprehensive reviews of this work. The relatively recent
observation \cite{AverinLikharev1991, MatsuokaLikharev1998,
Review2002} that hopping transport may provide quasi-continuous
(``sub-electron") charge transfer gave a motivation for the
extension of this work to the statistics of the electric charge $Q$
carried over by the hopping current.
The idea of the quasi-continuous charge transfer is quite simple:
due to the electrostatic polarization, each electron hop between two
localized sites inside the conductor leads to a step-like increase
of the ``external charge" $Q(t)$, which may be defined as the time
integral of current $I(t)$ flowing through the wires connecting the
conductor's electrodes to the electric field source. If an electron
is transferred through the whole sample in one hop (as happens in
the usual tunnel junctions), the charge step $\vert \Delta Q \vert$
is equal to the fundamental charge $e$. However, if an electron in
an extended conductor hops between two sites which are separated by
a distance $\Delta r$ much less than the conductor length $L$, then
the step $\vert \Delta Q \vert$ is of the order of $e \times (\vert
\Delta r \vert /L) \ll e$. (The exact expression depends on the
sample and electrode geometry.) This means that the charge transport
becomes nearly continuous, just as in long diffusive conductors
\cite{Review2002,NavehAverinLikharev1998}. This phenomenon may have
several useful applications in single-electronics, especially since
the hopping conductors (in contrast to their diffusive counterparts)
may provide the necessary high values of resistance $R \gg \hbar
/e^2$ \cite{Likharev1999} without adding too much stray capacitance
to that of single-electron islands.
One of the manifestations of the quasi-continuous charge transport
is the suppression of the shot noise \cite{KoganBook,
JongBeenakker1997, BlanterButtiker2000}. Namely, for sufficiently
small values of the observation frequency $f$ (with a possible
exception for the $1/f$ noise at very low frequencies) the current
noise spectral density $S_{I} \left( f \right)$ becomes
approximately $L_c/L \ll 1$ times the Schottky value $2eI$, where
$L_c$ is some characteristic length scale. This prediction
\cite{AverinLikharev1991} has been confirmed in several recent
experimental \cite{Kuznetsovetal2000,Roshkoetal2002} and theoretical
\cite{1DKorotkovLikharev2000, 2DSverdlovKorotkovLikharev2001,
2DCLP-KinkhabwalaSverdlovKorotkovLikharev2004,
2DCIP-KinkhabwalaSverdlovKorotkovLikharev2004} studies of hopping.
The goal of this work has been to study another manifestation of the
quasi-continuous charge transfer at hopping, which is more closely
related to its most important potential application: the ability to
``ground" sub-electron amounts of electric charge
\cite{Likharev1999}. For this, we have analyzed the simple system
shown in Fig.~\ref{fig:deviceschematic}: a hopping conductor shunts
an external capacitance $C$ with an initial charge $Q_i$. The
capacitance charge $Q$ leads to a nonvanishing electric field
$E=V/L=Q/CL$ applied to the conductor, which causes electrons to hop
through the conductor. These hops result in the gradual reduction of
the charge $Q$ and hence the field $E$. At the perfectly continuous
(``Ohmic") conduction the process would continue until $Q$ and $E$
vanished completely (at $T \rightarrow 0$); however, for hopping
conductors of a finite size $L \times W$ the charge relaxation stops
at a certain finite residual charge which generally depends not only
on the macroscopic parameters of the system, but also on the
particular distribution of the localized sites over space and energy
and on the initial charge $Q_i$.
Though qualitative experimental evidence of sub-electron charge
relaxation has been obtained long ago \cite{Lambe,Kuzmin}, to the
best of our knowledge this phenomenon has never been studied in
detail. The objective of this work has been to study the dynamics of
this charge relaxation process, and the statistics of the residual
charge theoretically. The problem is essentially classical, but
multi-particle, highly nonlinear, and statistical, so that most
results have to be obtained by numerical (Monte Carlo) simulation
using modern supercomputer facilities (see the Acknowledgments
section below).
\begin{figure}
\begin{center}
\includegraphics[height=2.6in]{fig01.eps}
\end{center}
\caption{The system under analysis (schematically).}
\label{fig:deviceschematic}
\end{figure}
\section{\label{sec:level1} Model}
For the hopping conductor, we have used the same model whose average
transport characteristics and current noise had been extensively
explored recently for the case of fixed, constant applied field $E$
\cite{2DCLP-KinkhabwalaSverdlovKorotkovLikharev2004,
2DCIP-KinkhabwalaSverdlovKorotkovLikharev2004}. Briefly, the
conductor is ``fully frustrated" in the sense that the localized
sites are randomly and uniformly distributed, with a constant
``seed" density of states $\nu_0$, over both the rectangular 2D
sample of area $L \times W$ and a broad interval of ``seed" energies
$\varepsilon^{\left( 0 \right)}$. The full energy $U$ of the system
is the sum of the ``seed" energies of all occupied sites and the
electrostatic energy of the Coulomb interaction of the hopping
electrons with each other and the external capacitance:
\begin{equation}
U = \sum_{j} n_j\varepsilon^{\left( 0 \right)}_j + \frac{e^2}{2
\kappa} \sum_{j, k\neq j}\left(n_j-\frac{1}{2}\right)
\left(n_{k}-\frac{1}{2}\right) G\left( {\bf r}_j, {\bf r}_{k}
\right) + \frac{Q^2}{2C}. \label{eq:totalsystemenergy}
\end{equation}
Here $n_j$ (equal to either 0 or 1) is the occupation number of the
$j^{\textrm{th}}$ localized site, while $\kappa$ is the dielectric
constant of the insulating environment \cite{neutrality}. For the
simplest geometry of a 2D conductor connecting two semi-space-shaped
electrodes, the Green's function $G$ in
Eq.~(\ref{eq:totalsystemenergy}) may be simply expressed as a sum
over the infinite set of image charges in the electrodes:
\begin{eqnarray}
&G\left( {\bf r}_j, {\bf r}_k\right)& = \sum_{n=
-\infty}^{\infty}\left[ \frac{1}{\sqrt{\left( 2nL+x_k-x_j\right)^2 +
\left(
y_k-y_j\right)^2}} \right.\nonumber \\
&& \left. \,\,\,\,\,\,\,\,\,\, \,\,\,\,\,\,\,\,\,\,
\,\,\,\,\,\,\,\,\,\, \,\,\,\,\,\,\,\,\,\, -\frac{1}{\sqrt{\left(
2nL+x_k+x_j\right)^2 + \left( y_k-y_j\right)^2}} \right].
\label{eq:greenfunction}
\end{eqnarray}
For this geometrical model, the total charge $Q$ of the capacitor
(including the polarization component) is
\begin{equation}
Q = Q_i - \left[ N_e e + \sum_{j} e \left(n_j-\frac{1}{2}\right)
\frac{x_{j}}{L} \right], \label{eq:charge}
\end{equation}
where $Q_i$ is the initial charge and $x_j$ is the $j^{\textrm{th}}$
site position along the sample length $L$, while $N_e$ is the total
number of electrons that have passed through the conductor from the
start of the relaxation process until the given moment. In the limit
of large charge ($\left\vert Q \right\vert \gg Q_{R}$) the effect of
capacitance on hopping transport is equivalent to that of the
electric field $E=Q/CL$.
Electron hops are permitted from any occupied site $j$ to any
unoccupied site $k$ with the rate
\begin{equation}
\gamma_{jk}=\Gamma_{jk}\exp \left(-\frac{r_{jk}}{a}\right),
\label{eq:distancerateequation}
\end{equation}
where $a$ is the localization length, and
\begin{equation}
\hbar \Gamma_{jk}\left( \Delta U_{jk} \right)=g\frac{\Delta
U_{jk}}{1-\exp\left( -\Delta U_{jk}/k_{B}T\right) }.
\label{eq:energyrateequation}
\end{equation}
Here $\Delta U_{jk}$ is the difference of the total system energy
$U$ before and after the hop, and $g$ is a small dimensionless
parameter which affects only the scale of hopping conductivity
$\sigma_0\equiv g e^2/\hbar$. The numerical study has been carried
out using the classical Monte Carlo technique by Bortz, Kalos and
Leibowitz \cite{BKL} in the form suggested by Bakhvalov $\it
{et~al.}$ \cite{Bakhvalovetal1989}, which has become the de facto
standard for simulations of single-electron tunneling
\cite{Wasshuber}. An important feature of this algorithm is that it
is not slowed down by the gradual reduction of hopping rates at
charge relaxation.
\section{\label{sec:level1} Charge Relaxation Dynamics}
Figure~\ref{fig:zerotemperatureQRestimedependence} shows, by thin
lines, typical results of our Monte Carlo simulations for two values
of the dimensionless parameter of the Coulomb interaction strength,
$\chi \equiv e^{2} \nu_{0} a/ \kappa$. Note the logarithmic time
scale and the linear scale of $Q$; in such coordinates the
exponential relaxation of average charge in an $RC$ circuit with a
linear Ohmic resistor looks like a sharp step down at $t \approx
RC$. We indeed observe such behavior at hopping when the initial
electric field is low, i.e. in the high temperature limit. However,
motivated by prospects of practical applications
\cite{Likharev1999}, our main focus is on the opposite,
``high-field" (low-temperature) limit.
Figure~\ref{fig:zerotemperatureQRestimedependence} shows that in
this case the dynamics of discharge through the hopping conductor is
rather different: it slows down dramatically at $Q \rightarrow 0$.
This is exactly what should be expected from the previous studies of
variable-range hopping at constant applied field, which show that
the hopping conductance drops exponentially as the field decreases
\cite{MottBook, ShklovskiiBook, EfrosPollackCollection,
2DSverdlovKorotkovLikharev2001,
2DCLP-KinkhabwalaSverdlovKorotkovLikharev2004,
2DCIP-KinkhabwalaSverdlovKorotkovLikharev2004}. A qualitatively
similar dynamics is also typical for the qualitatively close (but
quantitatively different) problem of intrinsic relaxation in
electron glasses - see, e.g., recent publications~\cite{glass1,
glass2, glass3} and prior work cited therein.
\begin{figure}
\begin{center}
\includegraphics[height=6.0in]{fig02ab.eps}
\end{center}
\caption{Capacitance charge $Q$ relaxation (at $T=0$) for the cases
of (a) negligible ($\chi=0$) and (b) substantial ($\chi=0.5$)
Coulomb interaction of hopping electrons. Thin lines show Monte
Carlo results (for 6 realizations of each case) for several values
of external capacitance $C$, with fixed conductor size $L \times W =
80 \times 40 a^2$. The thick gray curves correspond to the results
of the solution of Eq.~(\ref{eq:timederivativeofQres}) with
Eq.~(\ref{eq:zerocoulombhighelectricfieldconductivity}) for panel
(a) and Eq.~(\ref{eq:nonzerocoulombhighelectricfieldconductivity})
for panel (b) for $C/C_0 = 100$, with the central curve
corresponding to the best-fit parameters $A$ and $B$ and the outer
curves corresponding to the uncertainty in these parameters. (See
the text.) Time is measured in units of $t_0 \equiv \hbar \nu_{0}
a^2/g$, while capacitance is expressed in units of $C_{0} \equiv
e^{2}\nu_{0}a^2$.} \label{fig:zerotemperatureQRestimedependence}
\end{figure}
It has turned out that most of the relaxation process, while the
charge is sufficiently large ($\left\vert Q \right\vert \gg Q_R$),
may be well described by the mean-field equation
\begin{equation}
\frac{dQ}{dt} = -I\left( T, E, \chi \right) = -\sigma\left(T, E,
\chi \right) E W, \label{eq:timederivativeofQres}
\end{equation}
where $\sigma\left(T, E, \chi \right)$ is the nonlinear conductance
in the constant applied field $E$. In the low-temperature limit
($k_{B}T \ll e E r$, where $r$ is the average length of the hops
contributing substantially into the current), we can use the
following analytical expressions obtained by fitting the results of
our numerical simulations of constant-field hopping within the same
model \cite{2DCLP-KinkhabwalaSverdlovKorotkovLikharev2004,
2DCIP-KinkhabwalaSverdlovKorotkovLikharev2004}:
(i) If Coulomb interaction is negligible, $\chi^3 \ll E/E_0$,
\begin{equation}
\frac{\sigma}{\sigma_0} \approx A \left( E, 0 \right) \exp
\left[-\left( B \left( E, 0 \right) \frac{E_0}{E} \right)^{1/3}
\right], \label{eq:zerocoulombhighelectricfieldconductivity}
\end{equation}
where $eE_{0}a \equiv 1/\nu_{0}a^2$, while $A \left( E, \chi
\right)$ and $B\left( E, \chi \right)$ are dimensionless, weak
functions of the applied field $E$ and Coulomb interaction strength
$\chi$. In a prior study
\cite{2DCLP-KinkhabwalaSverdlovKorotkovLikharev2004}, we have found
the best fit for the pre-exponential (model-specific) function to be
$A\left(E, 0\right) = \left(9.2 \pm 0.6
\right)\left(E/E_0\right)^{\left( 0.80 \pm 0.02\right)}$, with $B$
treated as a constant: $B\left( E, 0 \right) = 0.65\pm 0.02$.
(ii) If Coulomb effects are substantial, then
\begin{equation}
\frac{\sigma}{\sigma_0} \approx A \left( E, \chi \right) \exp
\left[-\left( B \left( E, \chi \right) \frac{\chi E_0}{E}
\right)^{1/2} \right].
\label{eq:nonzerocoulombhighelectricfieldconductivity}
\end{equation}
For the particular value of $\chi = 0.5$, a similar approach to
fitting gives \cite{2DCIP-KinkhabwalaSverdlovKorotkovLikharev2004}
$A \left( E , 0.5 \right) = \left(3.0 \pm 0.4
\right)\left(E/E_0\right)^{\left( 0.72 \pm 0.07\right)}$ with
$B\left( E, 0.5 \right) = 1.68\pm 0.07$.
For relatively low fields, $E \ll E_0$, these formulas describe the
so-called ``high-field" variable range hopping \cite{Shklovskii1973,
ApsleyHughes19741975, PollackRiess1976, RentzschShlimakBerger1979,
vanderMeerSchuchardtKeiper1982}.
Broad gray curves in
Fig.~\ref{fig:zerotemperatureQRestimedependence} show the results of
integration of the mean field equation using these formulas for one
value of capacitance $C/C_0 = 100$. (The middle curves correspond to
the best fit values, while the outer curves reflect the fitting
uncertainties specified above.) One can see that at $\left\vert Q
\right\vert \gg Q_{R}$ the relaxation results may be well described
by the mean-field approach. However, this approach does not work at
$Q \rightarrow 0$ where it predicts the complete relaxation of
charge, while in reality (and numerical experiment) the process
stalls at a certain ``residual" charge.
\section{\label{sec:level1} Residual Charge Statistics}
Figure~\ref{fig:QrmsVSlength} shows some of our results for the
r.m.s$.$ value $Q_R$ of the residual charge, obtained for a broad
range of ``macroscopic" parameters of the system, including external
capacitance $C$ and normalized Coulomb interaction strength $\chi$,
as a function of the conductor area $L \times W$. (These results do
not change noticeably if the systems are annealed after the
relaxation.)
\begin{figure}
\begin{center}
\includegraphics[height=3.6in]{fig03.eps}
\end{center}
\caption{The r.m.s$.$ value $Q_R$ of the residual charge at $T=0$
for negligible ($\chi=0$) and finite ($\chi$ = 0.1 and 0.5) Coulomb
interaction, as a function of the conductor area ($L \times W$) for
different external capacitances $C$, and two different aspect ratios
($L:W$ = 2:1 and 1:1). Each point represents data averaged over a
large number ($10^3$) of conductor samples with vertical error bars
corresponding to the uncertainty of such averaging. (Error bars are
shown on figure, unless smaller than the symbol size). Thin lines
are only guides for the eye. The bold horizontal line corresponds to
Eq.~(\ref{eq:QrmsUniformDistribution}), while the bold tilted lines
are the best power-law fits for large-sample data.}
\label{fig:QrmsVSlength}
\end{figure}
For sufficiently small samples, the number of localized sites is so
low that no internal hopping events may occur within the energy
interval of interest, and the initial charge can only relax by
direct tunneling between the electrodes, giving changes of $Q$ in
multiples of $e$. The Coulomb blockade theory (see, e.g.,
Ref$.$~\cite{AverinLikharev1991}) shows that at low temperatures
such tunneling is blocked at $\left\vert Q \right\vert < e/2$. If
the initial charge $Q_i$ is random (as has been accepted in our
calculations), then the residual charge is uniformly distributed
within the range from $-e/2$ to $+e/2$, and the r.m.s$.$ residual
charge is
\begin{equation}
\frac{Q_{R}}{e} = \frac{1}{e} \left[ \int_{-e/2}^{e/2} Q^2
\frac{dQ}{e}\right]^{1/2} = \frac{1}{\sqrt{12}},
\label{eq:QrmsUniformDistribution}
\end{equation}
in a good accordance with the simulation results
(Fig.~\ref{fig:QrmsVSlength}).
On the other hand, if the conductor area is increased, $Q_{R}$
decreases, since there are more and more internal localized sites
available for further charge relaxation. Our results
(Fig.~\ref{fig:QrmsVSlength}) show also that $Q_{R}$ always
increases with capacitance $C$ and, at substantial Coulomb
interaction, with its strength $\chi$.
\begin{figure}
\begin{center}
\includegraphics[height=3.6in]{fig04.eps}
\end{center}
\caption{The same results for $Q_{R}$ as in
Fig.~\ref{fig:QrmsVSlength}, re-plotted to emphasize their universal
scaling with system parameters. Solid lines show the best fits to
the asymptotic behavior of $Q_{R}$ for large samples.}
\label{fig:QrmsScaling}
\end{figure}
Rather unexpectedly, we have found that for a broad range of system
parameters, all these dependencies may be very well approximated by
``universal" laws, different for the cases when Coulomb interaction
is negligible ($\chi^3 \ll Q_R/CLE_0)$ or substantial - see
Fig.~\ref{fig:QrmsScaling}. In the former case, $Q_{R}/e =
F_{0}(X_0)$, where
\begin{equation}
X_{0} = \frac{L W}{a^2} \frac{C_0}{C} = L W \nu_{0} \frac {e^2}{C},
\label{eq:xxxhighelectricfieldQresoftime}
\end{equation}
while in the latter case $Q_{R}/e = F_{\chi}(X_\chi)$, where
\begin{equation}
X_{\chi} = \frac{L W}{a^2} \frac{C_0^2}{ \chi^2 C^2 } = \frac {L W
\kappa^{2}}{C^2}. \label{eq:xxxhighelectricfieldQresoftime}
\end{equation}
At small values of their arguments, both functions $F$ tend to
$1/\sqrt{12}$, in agreement with
Eq.~(\ref{eq:QrmsUniformDistribution}). Their asymptotic behavior is
also functionally similar, $F(X) \rightarrow DX^{-\beta}$ at $X
\rightarrow \infty$, but with different best-fit values of the
coefficients: for $\chi = 0$, $D = 0.64 \pm 0.01$ and $\beta = 0.41
\pm 0.01$, while for $\chi \sim 1$, $D = 1.1 \pm 0.1$ and $\beta =
0.28$, with the error bar about $0.03$ for the dependence on $C$ and
of the order of 0.01 for other variables contributing to $X_{\chi}$.
\section{\label{sec:level1} Discussion}
For the case of negligible Coulomb interaction, the asymptotic power
law for function $F_0(X_0)$ may be readily explained , using the
basic ideas of the Coulomb blockade \cite{AverinLikharev1991}.
Charge relaxation continues with the reduction of the system energy
(on the average, dominated by the capacitor energy $U$) until the
number $N$ of localized sites available for hopping becomes less
than one. If the capacitance charge before a hop is $Q$, the range
of capacitive energy of available initial sites is $\Delta U \sim
Q^{2}/2C$, so that the average number of such sites per unit area is
$n_i \sim \nu_{0} \Delta U \sim \nu_{0} Q^{2} /2C $, and their total
number in the sample of area $L \times W$ is $N_i \sim L W n_i \sim
L W \nu_0 Q^2/2C$. In order to estimate $N$, we need to multiply
$N_i$ by the average number $N_f$ of available final sites for each
initial site. For small changes of charge, $\vert \Delta Q \vert \ll
e$, the area $\vert \Delta x \vert \times W$ where such states can
reside is much smaller than the sample area $L \times W$, because
such charge change corresponds to a hop by distance $\vert \Delta x
\vert = L \times \vert \Delta Q \vert /e \ll L$. Hence $N_f \sim LW
\nu_0 (\vert \Delta Q\ \vert /e) (Q - \Delta Q)^2/2C$ and we get the
following estimate
\begin{equation}
N \sim N_i N_f \sim \left ( \frac {L W \nu_{0}}{2C} \right )^2 \frac
{Q^2 \vert \Delta Q \vert (Q - \Delta Q)^2}{e}.
\label{eq:N0}
\end{equation}
Now, from the natural requirement that $N$ drops below 1 as soon as
$\vert Q \vert$, $\vert \Delta Q \vert$, and $\vert Q-\Delta Q
\vert$ all become, on the average, of the order of $Q_R$, we get
\begin{equation}
\frac {Q_{R}}{e} \sim \left( \frac{L W \nu_{0} e^2}{C}
\right)^{-2/5} = {X_0}^{-2/5}, \label{eq:scaling0}
\end{equation}
which when compared to the power law $F(X)$ discussed above gives
$\beta = 2/5 = 0.40$, i.e$.$ inside the narrow interval $0.41 \pm
0.01$ given by the numerical experiment.
For the case of substantial Coulomb interaction of hopping
electrons, the situation is more complex - see, e.g$.$, the
discussion on pp$.$ 435-443 of Ref.~\cite{EfrosPollackCollection}.
It is well documented that ``external" transport (bringing electrons
into and out of the hopping conductor) may be well understood in
terms of the simple quasiparticles introduced by Efros and
Shklovskii \cite{ShklovskiiBook}, with energy
\begin{equation}
\varepsilon_j \equiv \varepsilon^{(0)}_j + \frac{e^2}{\kappa}
\sum_{l\neq j} \left( n_l-\frac{1}{2}\right) G\left( {\bf r}_j, {\bf
r}_l\right). \label{eq:singleparticleenergy}
\end{equation}
In 2D systems, their density of states at low energies $\epsilon$ is
given by the famous Coulomb-gap expression \cite{ShklovskiiBook}
\begin{equation}
\nu\left(\varepsilon \right) \approx \frac{2 \kappa^2}{\pi e^4}
\vert \varepsilon \vert. \label{eq:singleparticleDoS}
\end{equation}
If we naively repeat the above calculation of $Q_R$, just replacing
$\nu_0$ with $\nu (\epsilon)$ from the last expression, we get
\begin{equation}
\frac {Q_{R}}{e} \sim \left( \frac{LW \kappa^2}{C^2} \right)^{-2/9}
= {X_{\chi}}^{-2/9},\label{eq:scalingchi}
\end{equation}
i.e$.$ the experimentally observed universality $(X_{\chi} = LW
\kappa^2 /C^2)$, but with an exponent $\beta = 2/9 \approx 0.22$
which is significantly outside of the experimental interval $0.28
\pm 0.01$.
Actually, for intra-sample transport, more adequate quasiparticles
may be the so-called ``dipole excitations" (essentially,
electron-hole pairs with correlated energies) whose density
$F(\Omega,r)$ depends on both the pair energy $\Omega$ and the
distance $r$ between the pair components (see
\cite{EfrosPollackCollection} p.435). In contrast to constant-field
transport, the residual charge statistics are dominated by
large-size pairs (hops), with $x-$component of the order of $L(\vert
\Delta Q \vert/e)$ and $y-$component of the order of $W$. If we
neglect, for such hops, the interaction of the pair components in
comparison with $\Omega$, then $F$ depends only on energy:
\begin{equation}
F(\Omega)=\int_{0}^{A} d\varepsilon_1 \int_{-A}^{0} d\varepsilon_2
\nu(\varepsilon_1) \nu(\varepsilon_2)
\delta(\varepsilon_1-\varepsilon_2-\Omega).
\end{equation}
For energies $\Omega$ much less than both the cutoff energy $A$ and
the Coulomb gap width, this integral yields
\begin{equation}
F=\left ( \frac{2 \kappa^2}{\pi e^4}\right )^2 \frac{\Omega^3}{6}.
\end{equation}
Now, following the arguments used above, we can accept $\Omega \sim
Q^2/2C$, and take $LW$ for the possible area of the pair centers,
and $L(\vert \Delta Q \vert/e)W$ for the pair area. After the
integration of $F$ from 0 to $\Omega$, for the possible number of
pairs within our energy range we get
\begin{equation}
N \sim \frac {1}{24} \left ( \frac{2 \kappa^2}{\pi e^4}\right )^2
\left (\frac {Q^2}{2C} \right )^4 L^2W^2 \frac {\vert \Delta Q
\vert}{e}.
\end{equation}
Again, requiring that $N \sim 1$ at $Q, \vert \Delta Q \vert \sim
Q_R$, we get back to the estimate given by Eq.
(\ref{eq:scalingchi}).
It is not quite clear presently whether the discrepancy between
these analytical arguments and the results of our numerical
experiments may be overcome by an account of electron-hole pairs of
smaller size, with strongly interacting pair components.
\section{\label{sec:level1} Offset Charge Grounding}
The results of this work allow one to estimate the prospects of
applying hopping conductors as ``grounding" devices for the random
background charge in single-electron devices. Figure
\ref{fig:Ground} shows this idea on the example of a single-electron
transistor \cite{AverinLikharev1991,Likharev1999}. Charged
impurities, randomly located in the vicinity of the transistor's
single-electron island, induce on it a net polarization charge. The
``integer" ($e$-multiple) part of this ``background" charge is
automatically compensated by tunneling through the transistor's
tunnel junctions, but its fractional part $-e/2 < Q_0 < +e/2$ cannot
be compensated in this way. This random charge is equivalent to a
random shift $\Delta V_g = Q_0 /C_g$ of the gate voltage; such
shifts are one of the main obstacles on the way toward integrated
circuits using single-electron devices, because for most of them the
tolerable background charge range is as narrow as $\sim 0.1e$
\cite{Likharev1999}. The problem may be solved by connecting the
single-electron island to ``ground" through a hopping conductor
which would provide a slow relaxation of the background charge
\cite{Likharev1999}. (For digital applications, the characteristic
relaxation time has to be much longer than at least the circuit
clock cycle, and more preferably the full time of the calculation
performed by the circuit.)
\begin{figure}
\begin{center}
\includegraphics[height=2.8in]{fig05.eps}
\end{center}
\caption{Background charge ``grounding" using a hopping conductor
(schematically).} \label{fig:Ground}
\end{figure}
For typical hopping conductors technologically compatible with
silicon technology (e.g., amorphous semiconductors and metal
oxides), the dielectric constant $\kappa$ is of the order of 10,
while the electron effective mass $m \sim 0.2 m_0$. This gives the
localization radius $a \sim \hbar^2 \kappa /m e^2 \sim 3$ nm and the
level splitting scale $e^2/\kappa a \approx m e^4/\kappa^2 \hbar^2
\sim 30$ meV. In order to stay on the dielectric side of the
metal-insulator transition, the average distance between the
localized sites should be above $\sim 4a$ \cite{MottBook}; for the
3D density of states $\nu_3$ this gives the condition $\nu_3
\lesssim 10^{19}$ eV$^{-1}$cm$^{-3}$. This condition is well
satisfied, e.g., for most species of amorphous silicon, where
$\nu_3$ at mid-bandgap is of the order of 10$^{16}$
eV$^{-1}$cm$^{-3}$ (see, e.g., Ref$.$~\cite{a-Si}). For thin films
of such material with thickness $t \sim a \sim 3$ nm, the 2D density
of states $\nu_0 \sim 3 \times 10^{9}$ eV$^{-1}$cm$^{-2}$. For these
parameters, the Coulomb interaction parameter $\chi$ is much smaller
than 1, and we can use Eq.~(\ref{eq:scaling0}) for estimates. Even
for the least demanding applications of single-electron devices, the
electron addition energy $e^2/C$ should be at least 30 $k_BT$
\cite{Likharev1999}, so that according to Eq.~(\ref{eq:scaling0}),
$X_0$ has to be above $\sim 300$.
Let us accept $L=W$ in order to minimize the conductors' self-
(``stray") capacitance $C_s$ (which, as we will show shortly, may
present a major problem) at fixed area $L \times W$. For the usual
conditions of low-temperature experiments with single-electron
devices, $T \sim 0.1$ K, $C$ may be of the order of $10^{-14}$ F, so
that with our parameters $L$ should be above $\sim$ 30 nm. This is
less than the typical length ($\sim$ 1 $\mu$m) of the
single-electron island in such experiments, so that the grounding
idea may actually work \cite{PriorObserv}.
On the other hand, for the most important case of room-temperature
single-electron devices ($ T \approx 300$ K), the island capacitance
should be much less, $C < 10^{-18}$ F, so that the quasi-continuous
conduction is only possible at $L \gtrsim$ 15 $\mu$m. Stray
capacitance $C_s$ of such a conductor would be larger than $\sim
10^{-15}$ F, i.e. much larger than $C$, thus increasing the total
effective capacitance of the island well above the acceptable value.
To summarize, our calculations indicate that the fractional charge
grounding is possible, but practicable only for low-temperature
experiments rather than for room-temperature single-electron
devices. Fortunately, by now an alternative way to solve (or rather
circumvent) the random background charge problem in digital
nanoelectronics has been suggested. This approach is based on
reconfigurable hybrid CMOS-nanodevice digital circuits which may be
re-routed around ``bad" devices - see, e.g.,
Ref$.$~\cite{Springer2005}. Recent calculations have shown that this
approach may provide defect tolerance up to $\sim$ 10\% in memory
circuits and $> 20$\% in logic circuits. This is much higher than
the estimated lower bound on the fraction
($\sim$0.1\%~\cite{Likharev1999}) of single-electron devices whose
threshold is substantially shifted by random background charges.
\ack{The authors would like to thank B. I. Shklovskii for numerous
illuminating discussions. Useful comments by A. Efros, T. Grenet, A.
N. Korotkov, A. M{\"o}bius, M. Pollak and V. A. Sverdlov are also
gratefully acknowledged. The work was supported in part by the
Engineering Physics Program of the Office of Basic Energy Sciences
at the U.S. Department of Energy, and by the Semiconductor Research
Corporation. We also acknowledge the use of the following
supercomputer resources: our group's cluster $Njal$ (purchase and
installation funded by U.S. DoD's DURINT program via AFOSR), Oak
Ridge National Laboratory's IBM SP computer $Eagle $ (funded by the
Department of Energy's Office of Science and Energy Efficiency
program), and also IBM SP system $Tempest$ at Maui High Performance
Computing Center and IBM SP system $Habu$ at NAVO Shared Resource
Center (computer time granted by DOD's High Performance Computing
Modernization Program).}
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\bibitem{RentzschShlimakBerger1979} R. Rentzsch, I. S. Shlimak and H. Berger, Phys. Status Solidi A \textbf{54}, 487 (1979).
\bibitem{vanderMeerSchuchardtKeiper1982} M. van der Meer, R. Schuchardt and R. Keiper, Phys. Status Solidi B \textbf{110}, 571 (1982).
\bibitem{a-Si} T. Sameshita and S. Usui, J. Appl. Phys. \textbf{70}, 1281 (1991).
\bibitem{PriorObserv} Actually, the first qualitative observations of relaxation of sub-electron background
charge to $Q_R \ll e$ in early experiments \cite{Lambe,Kuzmin} may
be considered as the first, albeit unintentional implementations of
this idea.
\bibitem{Springer2005} K. K. Likharev and D. V. Strukov, ``CMOL: Devices, Circuits, and Architectures",
in \emph{Introducing Molecular Electronics}, edited by G. Cuniberti \textit{et al.} (Springer, Berlin, 2005), pp. 447-477.
\endbib
\end{document}
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If you have questions, comments, or would like to set up a studio visit, please send me an Email. If you'd like to be notified of upcoming exhibitions and other news, subscribe to the mailing list.
I am interested in the delusion of memory and its arbitrary relationship with present awareness.
I digitally composite monochromatic, photographic images, project the collage onto a physical substrate and render it in paint. Throughout this reductive/regenerative process, the original images lose distinction and are reinterpreted to befit their present circumstances, with little regard for the particulars of their origin.
Mair, Moray. "Jon Reischl's Paintings Are Surreal And Expressionistic Explorations of Memory."
Art Hounds: Dances Made to Order, Jon Reischl and Common Room tours.
The Artist Within Interviews Jon Reischl.
The A List: An Evening of the Odds.
An Evening of the Odds: New Work by Jon Reischl showing at Nicademus Art.
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{"url":"http:\/\/openstudy.com\/updates\/4ff2c2ace4b03c0c488b2d42","text":"## angela210793 4 years ago Y=x*arctanx when does y'=0???\n\n1. anonymous\n\ni believe the first step would be to differentiate =_= this sounds complicated...\n\n2. anonymous\n\nis it y' =0 when x=0\n\n3. anonymous\n\n$\\frac{d(x*\\tan^{-1}x)}{dx} = \\frac{x}{1 + x^2} + \\tan^{-1}x$\n\n4. anonymous\n\ni wonder how we can solve for x $\\large \\frac{x}{1+ x^2} + \\tan^{-1} x = 0$\n\n5. anonymous\n\nyup it is when x = 0 and no other solution\n\n6. anonymous\n\nwe all know that..but *how* do we prove it..\n\n7. anonymous\n\nthis is hard to prove i think..\n\n8. anonymous\n\ntake tan(inverse)x on other side and draw graphs of both arctan(x) and -x\/(1+x^2) you will find their graphs cutting each other at x = 0 only\n\n9. anonymous\n\nhmm i wonder if it's possible algebraically\n\n10. angela210793\n\ni have to study the monotony ,asimptotes and then graph it-_- and i haven't found the roots yet :(\n\n11. anonymous\n\nno not possible that way @igbasallote\n\n12. anonymous\n\nyes @angela210793 u have to study that to solve these type of questions.\n\n13. angela210793\n\ni know...but i can't find the roots :'(\n\n14. anonymous\n\nso better study these topics first then find the roots\n\n15. angela210793\n\noh wait...(atctg)'=1\/1+x^2 no?\n\n16. anonymous\n\nYes you are doing wrong earlier..\n\n17. angela210793\n\nwhen y'=o?\n\n18. anonymous\n\n$x + \\tan^{-1}x^2 + \\tan^{-1}x = 0$ $x^2.\\tan^{-1}x + x + \\tan^{-1}x = 0$ $D = b^2 - 4ac$ $D = 1 - 4\\tan^{-2}x$ $x = \\frac{-1 \\pm \\sqrt{1-4\\tan^{-2}x}}{2\\tan^{-1}x}$\n\n19. anonymous\n\nWell, I am just trying.. Ha ha ha..\n\n20. angela210793\n\n:O i dont understand anyway can u check if this is right...two different methods gave me two different answers :(\n\n21. angela210793\n\n|dw:1341311440181:dw|\n\n22. anonymous\n\n|dw:1341311735216:dw| only when x tends to 0 when when there is 1\/x instead of x it tends to infinity\n\n23. anonymous\n\n24. anonymous\n\nYour handwriting is fine @mayank_mak , gj :-D\n\n25. angela210793\n\n@mayank_mak thanks a lot :D and ur handwriting is very nice :D\n\n26. anonymous\n\nwe can prove it if you like\n\n27. angela210793\n\n28. anonymous\n\nsorry i was writing too much you have the derivative right? it is $\\frac{x}{x^2+1}+\\tan^{-1}(x)$ and this is clearly zero if $$x=0$$ by inspection\n\n29. anonymous\n\nnot much to that. now to show that this is the only solution, note that the derivative of this is $\\frac{2}{(x^2+1)^2}$ and this is always positive, which means your function is strictly increasing so there is only on solution\n\n30. angela210793\n\nderivative of wht is 2\/(x^2+1)^2???\n\n31. anonymous\n\nderivative of $\\frac{x}{x^2+1}+\\tan^{-1}(x)$\n\n32. angela210793\n\ny did u find derivative of tht??\n\n33. anonymous\n\nto prove that it was strictly increasing\n\n34. angela210793\n\nohh..i got tht...\n\n35. angela210793\n\ni thought u were still explaining monotony\n\n36. anonymous\n\nit is clear that for all $$x$$ the function $$\\frac{2}{(x+1)^2}>0$$ and so it is increasing for all $$x$$ if you have one zero, there cannot be another one\n\n37. anonymous\n\ni mean \"and so your derivative is increasing for all $$x$$\"\n\n38. angela210793\n\ni got it..thnx :D\n\n39. anonymous\n\nyw","date":"2016-10-22 16:24:51","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.767132043838501, \"perplexity\": 3934.7497731953654}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 20, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2016-44\/segments\/1476988719027.25\/warc\/CC-MAIN-20161020183839-00218-ip-10-171-6-4.ec2.internal.warc.gz\"}"}
| null | null |
LAMB, VOLUME 2***
E-text prepared by Keren Vergon, William Flis, and the Project Gutenberg
Online Distributed Proofreading Team
THE WORKS OF CHARLES AND MARY LAMB, VOLUME 2
ELIA; and THE LAST ESSAYS OF ELIA
BY
CHARLES LAMB
EDITED BY
E.V. LUCAS
[Illustration]
WITH A FRONTISPIECE
INTRODUCTION
This volume contains the work by which Charles Lamb is best known and
upon which his fame will rest--_Elia_ and _The Last Essays of Elia_.
Although one essay is as early as 1811, and one is perhaps as late as
1832, the book represents the period between 1820 and 1826, when Lamb
was between forty-five and fifty-one. This was the richest period of
his literary life.
The text of the present volume is that of the first edition of each
book--_Elia_, 1823, and _The Last Essays of Elia_, 1833. The principal
differences between the essays as they were printed in the _London
Magazine_ and elsewhere, and as they were revised for book form by
their author, are shown in the Notes, which, it should be pointed out,
are much fuller in my large edition. The three-part essay on "The Old
Actors" (_London Magazine_, February, April, and October, 1822), from
which Lamb prepared the three essays; "On Some of the Old Actors,"
"The Artificial Comedy of the Last Century," and "The Acting of
Munden," is printed in the Appendix as it first appeared. The absence
of the "Confessions of a Drunkard" from this volume is due to the fact
that Lamb did not include it in the first edition of _The Last Essays
of Elia_. It was inserted later, in place of "A Death-Bed," on account
of objections that were raised to that essay by the family of
Randal Norris. The story is told in the notes to "A Death-Bed." The
"Confessions of a Drunkard" will be found in Vol. I.
In Mr. Bedford's design for the cover of this edition certain Elian
symbolism will be found. The upper coat of arms is that of Christ's
Hospital, where Lamb was at school; the lower is that of the Inner
Temple, where he was born and spent many years. The figures at the
bells are those which once stood out from the facade of St. Dunstan's
Church in Fleet Street, and are now in Lord Londesborough's garden in
Regent's Park. Lamb shed tears when they were removed. The tricksy
sprite and the candles (brought by Betty) need no explanatory words of
mine.
E.V.L.
CONTENTS
APPENDIX
TEXT NOTE
PAGE PAGE
The South-Sea House 1 342
Oxford in the Vacation 8 345
Christ's Hospital Five and Thirty Years Ago 14 350
The Two Races of Men 26 355
New Year's Eve 31 358
Mrs. Battle's Opinions on Whist 37 361
A Chapter on Ears 43 363
All Fools' Day 48 367
A Quaker's Meeting 51 367
The Old and the New Schoolmaster 56 369
Valentine's Day 63 370
Imperfect Sympathies 66 370
Witches, and other Night-Fears 74 372
My Relations 80 373
Mackery End, in Hertfordshire 86 375
Modern Gallantry 90 377
The Old Benchers of the Inner Temple 94 379
Grace Before Meat 104 384
My First Play 110 385
Dream-Children; A Reverie 115 388
Distant Correspondents 118 389
The Praise of Chimney-Sweepers 124 390
A Complaint of the Decay of Beggars in the Metropolis 130 392
A Dissertation upon Roast Pig 137 395
A Bachelor's Complaint of the Behaviour of Married
People 144 397
On Some Old Actors 150 397
On the Artificial Comedy of the Last Century 161 399
On the Acting of Munden 168 400
THE LAST ESSAYS OF ELIA
TEXT NOTE
PAGE PAGE
Preface, by a Friend of the late Elia 171 402
Blakesmoor in H----shire 174 405
Poor Relations 178 408
Stage Illusion 185 408
To the Shade of Elliston 188 409
Ellistoniana 190 410
Detached Thoughts on Books and Reading 195 411
The Old Margate Hoy 201 415
The Convalescent 208 416
Sanity of True Genius 212 416
Captain Jackson 215 416
The Superannuated Man 219 417
The Genteel Style in Writing 226 420
Barbara S---- 230 421
The Tombs in the Abbey 235 423
Amicus Redivivus 237 424
Some Sonnets of Sir Philip Sydney 242 426
Newspapers Thirty-five Years Ago 249 428
Barrenness of the Imaginative Faculty in the
Productions of Modern Art 256 433
Rejoicings upon the New Year's Coming of Age 266 436
The Wedding 271 436
The Child Angel: a Dream 276 437
A Death-Bed 279 437
Old China 281 438
Popular Fallacies--
I. That a Bully is always a Coward 286 440
II. That Ill-gotten Gain never Prospers 287 440
III. That a Man must not Laugh at his own Jest 287 440
IV. That such a One shows his Breeding.--That
it is Easy to Perceive he is no Gentleman 288 440
V. That the Poor Copy the Vices of the Rich 288 440
VI. That Enough is as Good as a Feast 290 440
VII. Of Two Disputants, the Warmest is Generally
in the Wrong 291 440
VIII. That Verbal Allusions are not Wit, because
they will not Bear a Translation 292 440
IX. That the Worst Puns are the Best 292 440
X. That Handsome is that Handsome does 294 441
XI. That We must not look a Gift-horse in the
Mouth 296 441
XII. That Home is Home though it is never so
Homely 298 442
XIII. That You must Love Me, and Love my Dog 302 442
XIV. That We should Rise with the Lark 305 443
XV. That We should Lie Down with the Lamb 308 443
XVI. That a Sulky Temper is a Misfortune 309 443
APPENDIX
TEXT NOTE
PAGE PAGE
On Some of the Old Actors (_London Magazine_, Feb., 1822) 315 444
The Old Actors (_London Magazine_, April, 1822) 322 444
The Old Actors (_London Magazine_, October, 1822) 331 444
NOTES 337
INDEX 447
FRONTISPIECE
ELIA
From a Drawing by Daniel Maclise, now preserved in the Victoria and
Albert Museum.
ELIA
(_From the 1st Edition, 1823_)
THE SOUTH-SEA HOUSE
Reader, in thy passage from the Bank--where thou hast been receiving
thy half-yearly dividends (supposing thou art a lean annuitant
like myself)--to the Flower Pot, to secure a place for Dalston, or
Shacklewell, or some other thy suburban retreat northerly,--didst thou
never observe a melancholy looking, handsome, brick and stone edifice,
to the left--where Threadneedle-street abuts upon Bishopsgate? I dare
say thou hast often admired its magnificent portals ever gaping wide,
and disclosing to view a grave court, with cloisters and pillars, with
few or no traces of goers-in or comers-out--a desolation something
like Balclutha's.[1]
This was once a house of trade,--a centre of busy interests. The
throng of merchants was here--the quick pulse of gain--and here some
forms of business are still kept up, though the soul be long since
fled. Here are still to be seen stately porticos; imposing staircases;
offices roomy as the state apartments in palaces--deserted, or thinly
peopled with a few straggling clerks; the still more sacred interiors
of court and committee rooms, with venerable faces of beadles,
door-keepers--directors seated in form on solemn days (to proclaim a
dead dividend,) at long worm-eaten tables, that have been mahogany,
with tarnished gilt-leather coverings, supporting massy silver
inkstands long since dry;--the oaken wainscots hung with pictures
of deceased governors and sub-governors, of queen Anne, and the
two first monarchs of the Brunswick dynasty;--huge charts, which
subsequent discoveries have antiquated;--dusty maps of Mexico, dim as
dreams,--and soundings of the Bay of Panama!--The long passages hung
with buckets, appended, in idle row, to walls, whose substance might
defy any, short of the last, conflagration;--with vast ranges of
cellarage under all, where dollars and pieces of eight once lay,
an "unsunned heap," for Mammon to have solaced his solitary heart
withal,--long since dissipated, or scattered into air at the blast of
the breaking of that famous BUBBLE.--
Such is the SOUTH-SEA HOUSE. At least, such it was forty years ago,
when I knew it,--a magnificent relic! What alterations may have been
made in it since, I have had no opportunities of verifying. Time, I
take for granted, has not freshened it. No wind has resuscitated the
face of the sleeping waters. A thicker crust by this time stagnates
upon it. The moths, that were then battening upon its obsolete ledgers
and day-books, have rested from their depredations, but other light
generations have succeeded, making fine fretwork among their single
and double entries. Layers of dust have accumulated (a superfoetation
of dirt!) upon the old layers, that seldom used to be disturbed, save
by some curious finger, now and then, inquisitive to explore the
mode of book-keeping in Queen Anne's reign; or, with less hallowed
curiosity, seeking to unveil some of the mysteries of that tremendous
HOAX, whose extent the petty peculators of our day look back upon with
the same expression of incredulous admiration, and hopeless ambition
of rivalry, as would become the puny face of modern conspiracy
contemplating the Titan size of Vaux's superhuman plot.
Peace to the manes of the BUBBLE! Silence and destitution are upon thy
walls, proud house, for a memorial!
Situated as thou art, in the very heart of stirring and living
commerce,--amid the fret and fever of speculation--with the Bank,
and the 'Change, and the India-house about thee, in the hey-day of
present prosperity, with their important faces, as it were, insulting
thee, their _poor neighbour out of business_--to the idle and merely
contemplative,--to such as me, old house! there is a charm in thy
quiet:--a cessation--a coolness from business--an indolence almost
cloistral--which is delightful! With what reverence have I paced thy
great bare rooms and courts at eventide! They spoke of the past:--the
shade of some dead accountant, with visionary pen in ear, would flit
by me, stiff as in life. Living accounts and accountants puzzle
me. I have no skill in figuring. But thy great dead tomes, which
scarce three degenerate clerks of the present day could lift from
their enshrining shelves--with their old fantastic flourishes, and
decorative rubric interlacings--their sums in triple columniations,
set down with formal superfluity of cyphers--with pious sentences at
the beginning, without which our religious ancestors never ventured to
open a book of business, or bill of lading--the costly vellum covers
of some of them almost persuading us that we are got into some _better
library_,--are very agreeable and edifying spectacles. I can look
upon these defunct dragons with complacency. Thy heavy odd-shaped
ivory-handled penknives (our ancestors had every thing on a larger
scale than we have hearts for) are as good as any thing from
Herculaneum. The pounce-boxes of our days have gone retrograde.
The very clerks which I remember in the South-Sea House--I speak of
forty years back--had an air very different from those in the public
offices that I have had to do with since. They partook of the genius
of the place!
They were mostly (for the establishment did not admit of superfluous
salaries) bachelors. Generally (for they had not much to do) persons
of a curious and speculative turn of mind. Old-fashioned, for a reason
mentioned before. Humorists, for they were of all descriptions; and,
not having been brought together in early life (which has a tendency
to assimilate the members of corporate bodies to each other), but,
for the most part, placed in this house in ripe or middle age, they
necessarily carried into it their separate habits and oddities,
unqualified, if I may so speak, as into a common stock. Hence they
formed a sort of Noah's ark. Odd fishes. A lay-monastery. Domestic
retainers in a great house, kept more for show than use. Yet pleasant
fellows, full of chat--and not a few among them had arrived at
considerable proficiency on the German flute.
The cashier at that time was one Evans, a Cambro-Briton. He had
something of the choleric complexion of his countrymen stamped on his
visage, but was a worthy sensible man at bottom. He wore his hair, to
the last, powdered and frizzed out, in the fashion which I remember
to have seen in caricatures of what were termed, in my young days,
_Maccaronies_. He was the last of that race of beaux. Melancholy
as a gib-cat over his counter all the forenoon, I think I see him,
making up his cash (as they call it) with tremulous fingers, as if
he feared every one about him was a defaulter; in his hypochondry
ready to imagine himself one; haunted, at least, with the idea of
the possibility of his becoming one: his tristful visage clearing
up a little over his roast neck of veal at Anderton's at two (where
his picture still hangs, taken a little before his death by desire
of the master of the coffee-house, which he had frequented for the
last five-and-twenty years), but not attaining the meridian of its
animation till evening brought on the hour of tea and visiting. The
simultaneous sound of his well-known rap at the door with the stroke
of the clock announcing six, was a topic of never-failing mirth in the
families which this dear old bachelor gladdened with his presence.
Then was his _forte_, his glorified hour! How would he chirp, and
expand, over a muffin! How would he dilate into secret history! His
countryman, Pennant himself, in particular, could not be more eloquent
than he in relation to old and new London--the site of old theatres,
churches, streets gone to decay--where Rosamond's pond stood--the
Mulberry-gardens--and the Conduit in Cheap--with many a pleasant
anecdote, derived from paternal tradition, of those grotesque figures
which Hogarth has immortalized in his picture of _Noon_,--the worthy
descendants of those heroic confessors, who, flying to this country,
from the wrath of Louis the Fourteenth and his dragoons, kept alive
the flame of pure religion in the sheltering obscurities of Hog-lane,
and the vicinity of the Seven Dials!
Deputy, under Evans, was Thomas Tame. He had the air and stoop of a
nobleman. You would have taken him for one, had you met him in one of
the passages leading to Westminster-hall. By stoop, I mean that gentle
bending of the body forwards, which, in great men, must be supposed
to be the effect of an habitual condescending attention to the
applications of their inferiors. While he held you in converse, you
felt strained to the height in the colloquy. The conference over,
you were at leisure to smile at the comparative insignificance of
the pretensions which had just awed you. His intellect was of the
shallowest order. It did not reach to a saw or a proverb. His mind was
in its original state of white paper. A sucking babe might have posed
him. What was it then? Was he rich? Alas, no! Thomas Tame was very
poor. Both he and his wife looked outwardly gentlefolks, when I fear
all was not well at all times within. She had a neat meagre person,
which it was evident she had not sinned in over-pampering; but in
its veins was noble blood. She traced her descent, by some labyrinth
of relationship, which I never thoroughly understood,--much less can
explain with any heraldic certainty at this time of day,--to the
illustrious, but unfortunate house of Derwentwater. This was the
secret of Thomas's stoop. This was the thought--the sentiment--the
bright solitary star of your lives,--ye mild and happy pair,--which
cheered you in the night of intellect, and in the obscurity of your
station! This was to you instead of riches, instead of rank, instead
of glittering attainments: and it was worth them altogether. You
insulted none with it; but, while you wore it as a piece of defensive
armour only, no insult likewise could reach you through it. _Decus et
solamen._
Of quite another stamp was the then accountant, John Tipp. He neither
pretended to high blood, nor in good truth cared one fig about the
matter. He "thought an accountant the greatest character in the world,
and himself the greatest accountant in it." Yet John was not without
his hobby. The fiddle relieved his vacant hours. He sang, certainly,
with other notes than to the Orphean lyre. He did, indeed, scream
and scrape most abominably. His fine suite of official rooms in
Threadneedle-street, which, without any thing very substantial
appended to them, were enough to enlarge a man's notions of himself
that lived in them, (I know not who is the occupier of them now)
resounded fortnightly to the notes of a concert of "sweet breasts,"
as our ancestors would have called them, culled from club-rooms and
orchestras--chorus singers--first and second violoncellos--double
basses--and clarionets--who ate his cold mutton, and drank his punch,
and praised his ear. He sate like Lord Midas among them. But at the
desk Tipp was quite another sort of creature. Thence all ideas, that
were purely ornamental, were banished. You could not speak of any
thing romantic without rebuke. Politics were excluded. A newspaper was
thought too refined and abstracted. The whole duty of man consisted in
writing off dividend warrants. The striking of the annual balance in
the company's books (which, perhaps, differed from the balance of last
year in the sum of 25_l._ 1_s._ 6_d._) occupied his days and nights
for a month previous. Not that Tipp was blind to the deadness of
_things_ (as they call them in the city) in his beloved house, or did
not sigh for a return of the old stirring days when South Sea hopes
were young--(he was indeed equal to the wielding of any the most
intricate accounts of the most flourishing company in these or those
days):--but to a genuine accountant the difference of proceeds is
as nothing. The fractional farthing is as dear to his heart as the
thousands which stand before it. He is the true actor, who, whether
his part be a prince or a peasant, must act it with like intensity.
With Tipp form was every thing. His life was formal. His actions
seemed ruled with a ruler. His pen was not less erring than his heart.
He made the best executor in the world: he was plagued with incessant
executorships accordingly, which excited his spleen and soothed his
vanity in equal ratios. He would swear (for Tipp swore) at the little
orphans, whose rights he would guard with a tenacity like the grasp of
the dying hand, that commended their interests to his protection. With
all this there was about him a sort of timidity--(his few enemies used
to give it a worse name)--a something which, in reverence to the dead,
we will place, if you please, a little on this side of the heroic.
Nature certainly had been pleased to endow John Tipp with a sufficient
measure of the principle of self-preservation. There is a cowardice
which we do not despise, because it has nothing base or treacherous in
its elements; it betrays itself, not you: it is mere temperament; the
absence of the romantic and the enterprising; it sees a lion in the
way, and will not, with Fortinbras, "greatly find quarrel in a straw,"
when some supposed honour is at stake. Tipp never mounted the box of a
stage-coach in his life; or leaned against the rails of a balcony; or
walked upon the ridge of a parapet; or looked down a precipice; or let
off a gun; or went upon a water-party; or would willingly let you go
if he could have helped it: neither was it recorded of him, that for
lucre, or for intimidation, he ever forsook friend or principle.
Whom next shall we summon from the dusty dead, in whom common
qualities become uncommon? Can I forget thee, Henry Man, the wit,
the polished man of letters, the _author_, of the South-Sea House?
who never enteredst thy office in a morning, or quittedst it in
mid-day--(what didst _thou_ in an office?)--without some quirk that
left a sting! Thy gibes and thy jokes are now extinct, or survive
but in two forgotten volumes, which I had the good fortune to rescue
from a stall in Barbican, not three days ago, and found thee terse,
fresh, epigrammatic, as alive. Thy wit is a little gone by in these
fastidious days--thy topics are staled by the "new-born gauds" of the
time:--but great thou used to be in Public Ledgers, and in Chronicles,
upon Chatham, and Shelburne, and Rockingham, and Howe, and Burgoyne,
and Clinton, and the war which ended in the tearing from Great Britain
her rebellious colonies,--and Keppel, and Wilkes, and Sawbridge,
and Bull, and Dunning, and Pratt, and Richmond,--and such small
politics.--
A little less facetious, and a great deal more obstreperous, was fine
rattling, rattleheaded Plumer. He was descended,--not in a right line,
reader, (for his lineal pretensions, like his personal, favoured a
little of the sinister bend) from the Plumers of Hertfordshire. So
tradition gave him out; and certain family features not a little
sanctioned the opinion. Certainly old Walter Plumer (his reputed
author) had been a rake in his days, and visited much in Italy, and
had seen the world. He was uncle, bachelor-uncle, to the fine old whig
still living, who has represented the county in so many successive
parliaments, and has a fine old mansion near Ware. Walter flourished
in George the Second's days, and was the same who was summoned before
the House of Commons about a business of franks, with the old Duchess
of Marlborough. You may read of it in Johnson's Life of Cave. Cave
came off cleverly in that business. It is certain our Plumer did
nothing to discountenance the rumour. He rather seemed pleased
whenever it was, with all gentleness, insinuated. But, besides
his family pretensions, Plumer was an engaging fellow, and sang
gloriously.--
Not so sweetly sang Plumer as thou sangest, mild, child-like, pastoral
M----; a flute's breathing less divinely whispering than thy Arcadian
melodies, when, in tones worthy of Arden, thou didst chant that song
sung by Amiens to the banished Duke, which proclaims the winter wind
more lenient than for a man to be ungrateful. Thy sire was old surly
M----, the unapproachable church-warden of Bishopsgate. He knew not
what he did, when he begat thee, like spring, gentle offspring of
blustering winter:--only unfortunate in thy ending, which should have
been mild, conciliatory, swan-like.--
Much remains to sing. Many fantastic shapes rise up, but they must
be mine in private:--already I have fooled the reader to the top of
his bent;--else could I omit that strange creature Woollett, who
existed in trying the question, and _bought litigations_?--and still
stranger, inimitable, solemn Hepworth, from whose gravity Newton might
have deduced the law of gravitation. How profoundly would he nib a
pen--with what deliberation would he wet a wafer!--
But it is time to close--night's wheels are rattling fast over me--it
is proper to have done with this solemn mockery.
Reader, what if I have been playing with thee all this
while--peradventure the very _names_, which I have summoned up before
thee, are fantastic--insubstantial--like Henry Pimpernel, and old John
Naps of Greece:--
Be satisfied that something answering to them has had a being. Their
importance is from the past.
[Footnote 1: I passed by the walls of Balclutha, and they were
desolate.--Ossian.]
OXFORD IN THE VACATION
Casting a preparatory glance at the bottom of this article--as the
wary connoisseur in prints, with cursory eye (which, while it reads,
seems as though it read not,) never fails to consult the _quis
sculpsit_ in the corner, before he pronounces some rare piece to be a
Vivares, or a Woollet--methinks I hear you exclaim, Reader, _Who is
Elia?_
Because in my last I tried to divert thee with some half-forgotten
humours of some old clerks defunct, in an old house of business, long
since gone to decay, doubtless you have already set me down in your
mind as one of the self-same college--a votary of the desk--a notched
and cropt scrivener--one that sucks his sustenance, as certain sick
people are said to do, through a quill.
Well, I do agnize something of the sort. I confess that it is my
humour, my fancy--in the forepart of the day, when the mind of your
man of letters requires some relaxation--(and none better than such
as at first sight seems most abhorrent from his beloved studies)--to
while away some good hours of my time in the contemplation of indigos,
cottons, raw silks, piece-goods, flowered or otherwise. In the first
place ******* and then it sends you home with such increased appetite
to your books ***** not to say, that your outside sheets, and waste
wrappers of foolscap, do receive into them, most kindly and naturally,
the impression of sonnets, epigrams, _essays_--so that the very
parings of a counting-house are, in some sort, the settings up of an
author. The enfranchised quill, that has plodded all the morning among
the cart-rucks of figures and cyphers, frisks and curvets so at its
ease over the flowery carpet-ground of a midnight dissertation.--It
feels its promotion. ***** So that you see, upon the whole, the
literary dignity of _Elia_ is very little, if at all, compromised in
the condescension.
Not that, in my anxious detail of the many commodities incidental
to the life of a public office, I would be thought blind to certain
flaws, which a cunning carper might be able to pick in this Joseph's
vest. And here I must have leave, in the fulness of my soul, to regret
the abolition, and doing-away-with altogether, of those consolatory
interstices, and sprinklings of freedom, through the four
seasons,--the _red-letter days_, now become, to all intents and
purposes, _dead-letter days_. There was Paul, and Stephen, and
Barnabas--
Andrew and John, men famous in old times
--we were used to keep all their days holy, as long back as I was at
school at Christ's. I remember their effigies, by the same token,
in the old _Baskett_ Prayer Book. There hung Peter in his uneasy
posture--holy Bartlemy in the troublesome act of flaying, after the
famous Marsyas by Spagnoletti.--I honoured them all, and could almost
have wept the defalcation of Iscariot--so much did we love to keep
holy memories sacred:--only methought I a little grudged at the
coalition of the _better Jude_ with Simon-clubbing (as it were) their
sanctities together, to make up one poor gaudy-day between them--as an
economy unworthy of the dispensation.
These were bright visitations in a scholar's and a clerk's life--"far
off their coming shone."--I was as good as an almanac in those days.
I could have told you such a saint's-day falls out next week, or the
week after. Peradventure the Epiphany, by some periodical infelicity,
would, once in six years, merge in a Sabbath. Now am I little better
than one of the profane. Let me not be thought to arraign the wisdom
of my civil superiors, who have judged the further observation of
these holy tides to be papistical, superstitious.
Only in a custom of such long standing, methinks, if their Holinesses
the Bishops had, in decency, been first sounded--but I am wading out
of my depths. I am not the man to decide the limits of civil and
ecclesiastical authority--I am plain Elia--no Selden, nor Archbishop
Usher--though at present in the thick of their books, here in the
heart of learning, under the shadow of the mighty Bodley.
I can here play the gentleman, enact the student. To such a one as
myself, who has been defrauded in his young years of the sweet food of
academic institution, nowhere is so pleasant, to while away a few idle
weeks at, as one or other of the Universities. Their vacation, too, at
this time of the year, falls in so pat with _ours_. Here I can take
my walks unmolested, and fancy myself of what degree or standing I
please. I seem admitted _ad eundem_. I fetch up past opportunities.
I can rise at the chapel-bell, and dream that it rings for _me_. In
moods of humility I can be a Sizar, or a Servitor. When the peacock
vein rises, I strut a Gentleman Commoner. In graver moments, I
proceed Master of Arts. Indeed I do not think I am much unlike
that respectable character. I have seen your dim-eyed vergers, and
bed-makers in spectacles, drop a bow or curtsy, as I pass, wisely
mistaking me for something of the sort. I go about in black, which
favours the notion. Only in Christ Church reverend quadrangle, I can
be content to pass for nothing short of a Seraphic Doctor.
The walks at these times are so much one's own,--the tall trees of
Christ's, the groves of Magdalen! The halls deserted, and with open
doors, inviting one to slip in unperceived, and pay a devoir to some
Founder, or noble or royal Benefactress (that should have been ours)
whose portrait seems to smile upon their over-looked beadsman, and
to adopt me for their own. Then, to take a peep in by the way at
the butteries, and sculleries, redolent of antique hospitality: the
immense caves of kitchens, kitchen fire-places, cordial recesses;
ovens whose first pies were baked four centuries ago; and spits which
have cooked for Chaucer! Not the meanest minister among the dishes but
is hallowed to me through his imagination, and the Cook goes forth a
Manciple.
Antiquity! thou wondrous charm, what art thou? that, being nothing,
art every thing! When thou _wert_, thou wert not antiquity--then thou
wert nothing, but hadst a remoter _antiquity_, as thou called'st it,
to look back to with blind veneration; thou thyself being to thyself
flat, _jejune, modern_! What mystery lurks in this retroversion? or
what half Januses[1] are we, that cannot look forward with the same
idolatry with which we for ever revert! The mighty future is as
nothing, being every thing! the past is every thing, being nothing!
What were thy _dark ages_? Surely the sun rose as brightly then as
now, and man got him to his work in the morning. Why is it that we can
never hear mention of them without an accompanying feeling, as though
a palpable obscure had dimmed the face of things, and that our
ancestors wandered to and fro groping!
Above all thy rarities, old Oxenford, what do most arride and solace
me, are thy repositories of mouldering learning, thy shelves--
What a place to be in is an old library! It seems as though all the
souls of all the writers, that have bequeathed their labours to these
Bodleians, were reposing here, as in some dormitory, or middle state.
I do not want to handle, to profane the leaves, their winding-sheets.
I could as soon dislodge a shade. I seem to inhale learning, walking
amid their foliage; and the odour of their old moth-scented coverings
is fragrant as the first bloom of those sciential apples which grew
amid the happy orchard.
Still less have I curiosity to disturb the elder repose of MSS.
Those _variae lectiones_, so tempting to the more erudite palates, do
but disturb and unsettle my faith. I am no Herculanean raker. The
credit of the three witnesses might have slept unimpeached for me. I
leave these curiosities to Porson, and to G.D.--whom, by the way, I
found busy as a moth over some rotten archive, rummaged out of some
seldom-explored press, in a nook at Oriel. With long poring, he is
grown almost into a book. He stood as passive as one by the side of
the old shelves. I longed to new-coat him in Russia, and assign him
his place. He might have mustered for a tall Scapula.
D. is assiduous in his visits to these seats of learning. No
inconsiderable portion of his moderate fortune, I apprehend, is
consumed in journeys between them and Clifford's-inn--where, like a
dove on the asp's nest, he has long taken up his unconscious abode,
amid an incongruous assembly of attorneys, attorneys' clerks,
apparitors, promoters, vermin of the law, among whom he sits, "in calm
and sinless peace." The fangs of the law pierce him not--the winds of
litigation blow over his humble chambers--the hard sheriffs officer
moves his hat as he passes--legal nor illegal discourtesy touches
him--none thinks of offering violence or injustice to him--you would
as soon "strike an abstract idea."
D. has been engaged, he tells me, through a course of laborious years,
in an investigation into all curious matter connected with the two
Universities; and has lately lit upon a MS. collection of charters,
relative to C----, by which he hopes to settle some disputed
points--particularly that long controversy between them as to
priority of foundation. The ardor with which he engages in
these liberal pursuits, I am afraid, has not met with all the
encouragement it deserved, either here, or at C----. Your caputs,
and heads of colleges, care less than any body else about these
questions.--Contented to suck the milky fountains of their Alma
Maters, without inquiring into the venerable gentlewomen's years, they
rather hold such curiosities to be impertinent--unreverend. They have
their good glebe lands _in manu_, and care not much to rake into the
title-deeds. I gather at least so much from other sources, for D. is
not a man to complain.
D. started like an unbroke heifer, when I interrupted him. _A priori_
it was not very probable that we should have met in Oriel. But D.
would have done the same, had I accosted him on the sudden in his own
walks in Clifford's-inn, or in the Temple. In addition to a provoking
short-sightedness (the effect of late studies and watchings at the
midnight oil) D. is the most absent of men. He made a call the other
morning at our friend _M.'s_ in Bedford-square; and, finding nobody at
home, was ushered into the hall, where, asking for pen and ink, with
great exactitude of purpose he enters me his name in the book--which
ordinarily lies about in such places, to record the failures of
the untimely or unfortunate visitor--and takes his leave with many
ceremonies, and professions of regret. Some two or three hours after,
his walking destinies returned him into the same neighbourhood again,
and again the quiet image of the fire-side circle at _M.'s_--Mrs.
_M._ presiding at it like a Queen Lar, with pretty _A.S._ at her
side--striking irresistibly on his fancy, he makes another call
(forgetting that they were "certainly not to return from the country
before that day week") and disappointed a second time, inquires
for pen and paper as before: again the book is brought, and in the
line just above that in which he is about to print his second name
(his re-script)--his first name (scarce dry) looks out upon him
like another Sosia, or as if a man should suddenly encounter his
own duplicate!--The effect may be conceived. D. made many a good
resolution against any such lapses in future. I hope he will not keep
them too rigorously.
For with G.D.--to be absent from the body, is sometimes (not to speak
it profanely) to be present with the Lord. At the very time when,
personally encountering thee, he passes on with no recognition--or,
being stopped, starts like a thing surprised--at that moment, reader,
he is on Mount Tabor--or Parnassus--or co-sphered with Plato--or, with
Harrington, framing "immortal commonwealths"--devising some plan of
amelioration to thy country, or thy species--peradventure meditating
some individual kindness or courtesy, to be done to _thee thyself_,
the returning consciousness of which made him to start so guiltily at
thy obtruded personal presence.
D. is delightful any where, but he is at the best in such places as
these. He cares not much for Bath. He is out of his element at Buxton,
at Scarborough, or Harrowgate. The Cam and the Isis are to him "better
than all the waters of Damascus." On the Muses' hill he is happy, and
good, as one of the Shepherds on the Delectable Mountains; and when he
goes about with you to show you the halls and colleges, you think you
have with you the Interpreter at the House Beautiful.
[Footnote 1: Januses of one face.--SIR THOMAS BROWNE.]
CHRIST'S HOSPITAL FIVE AND THIRTY YEARS AGO
In Mr. Lamb's "Works," published a year or two since, I find a
magnificent eulogy on my old school,[1] such as it was, or now appears
to him to have been, between the years 1782 and 1789. It happens,
very oddly, that my own standing at Christ's was nearly corresponding
with his; and, with all gratitude to him for his enthusiasm for the
cloisters, I think he has contrived to bring together whatever can be
said in praise of them, dropping all the other side of the argument
most ingeniously.
I remember L. at school; and can well recollect that he had some
peculiar advantages, which I and others of his schoolfellows had not.
His friends lived in town, and were near at hand; and he had the
privilege of going to see them, almost as often as he wished, through
some invidious distinction, which was denied to us. The present worthy
sub-treasurer to the Inner Temple can explain how that happened. He
had his tea and hot rolls in a morning, while we were battening upon
our quarter of a penny loaf--our _crug_--moistened with attenuated
small beer, in wooden piggins, smacking of the pitched leathern jack
it was poured from. Our Monday's milk porritch, blue and tasteless,
and the pease soup of Saturday, coarse and choking, were enriched
for him with a slice of "extraordinary bread and butter," from the
hot-loaf of the Temple. The Wednesday's mess of millet, somewhat less
repugnant--(we had three banyan to four meat days in the week)--was
endeared to his palate with a lump of double-refined, and a smack of
ginger (to make it go down the more glibly) or the fragrant cinnamon.
In lieu of our _half-pickled_ Sundays, or _quite fresh_ boiled beef
on Thursdays (strong as _caro equina_), with detestable marigolds
floating in the pail to poison the broth--our scanty mutton crags on
Fridays--and rather more savoury, but grudging, portions of the same
flesh, rotten-roasted or rare, on the Tuesdays (the only dish which
excited our appetites, and disappointed our stomachs, in almost equal
proportion)--he had his hot plate of roast veal, or the more tempting
griskin (exotics unknown to our palates), cooked in the paternal
kitchen (a great thing), and brought him daily by his maid or aunt! I
remember the good old relative (in whom love forbade pride) squatting
down upon some odd stone in a by-nook of the cloisters, disclosing the
viands (of higher regale than those cates which the ravens ministered
to the Tishbite); and the contending passions of L. at the unfolding.
There was love for the bringer; shame for the thing brought, and the
manner of its bringing; sympathy for those who were too many to share
in it; and, at top of all, hunger (eldest, strongest of the passions!)
predominant, breaking down the stony fences of shame, and awkwardness,
and a troubling over-consciousness.
I was a poor friendless boy. My parents, and those who should care for
me, were far away. Those few acquaintances of theirs, which they could
reckon upon being kind to me in the great city, after a little forced
notice, which they had the grace to take of me on my first arrival
in town, soon grew tired of my holiday visits. They seemed to them
to recur too often, though I thought them few enough; and, one after
another, they all failed me, and I felt myself alone among six hundred
playmates.
O the cruelty of separating a poor lad from his early homestead! The
yearnings which I used to have towards it in those unfledged years!
How, in my dreams, would my native town (far in the west) come back,
with its church, and trees, and faces! How I would wake weeping, and
in the anguish of my heart exclaim upon sweet Calne in Wiltshire!
To this late hour of my life, I trace impressions left by the
recollection of those friendless holidays. The long warm days of
summer never return but they bring with them a gloom from the haunting
memory of those _whole-day-leaves_, when, by some strange arrangement,
we were turned out, for the live-long day, upon our own hands, whether
we had friends to go to, or none. I remember those bathing-excursions
to the New-River, which L. recalls with such relish, better, I think,
than he can--for he was a home-seeking lad, and did not much care
for such water-pastimes:--How merrily we would sally forth into the
fields; and strip under the first warmth of the sun; and wanton like
young dace in the streams; getting us appetites for noon, which
those of us that were pennyless (our scanty morning crust long since
exhausted) had not the means of allaying--while the cattle, and the
birds, and the fishes, were at feed about us, and we had nothing to
satisfy our cravings--the very beauty of the day, and the exercise
of the pastime, and the sense of liberty, setting a keener edge upon
them!--How faint and languid, finally, we would return, towards
nightfall, to our desired morsel, half-rejoicing, half-reluctant, that
the hours of our uneasy liberty had expired!
It was worse in the days of winter, to go prowling about the streets
objectless--shivering at cold windows of printshops, to extract a
little amusement; or haply, as a last resort, in the hope of a little
novelty, to pay a fifty-times repeated visit (where our individual
faces should be as well known to the warden as those of his own
charges) to the Lions in the Tower--to whose levee, by courtesy
immemorial, we had a prescriptive title to admission.
L.'s governor (so we called the patron who presented us to the
foundation) lived in a manner under his paternal roof. Any complaint
which he had to make was sure of being attended to. This was
understood at Christ's, and was an effectual screen to him against the
severity of masters, or worse tyranny of the monitors. The oppressions
of these young brutes are heart-sickening to call to recollection. I
have been called out of my bed, and _waked for the purpose_, in the
coldest winter nights--and this not once, but night after night--in
my shirt, to receive the discipline of a leathern thong, with eleven
other sufferers, because it pleased my callow overseer, when there has
been any talking heard after we were gone to bed, to make the six
last beds in the dormitory, where the youngest children of us slept,
answerable for an offence they neither dared to commit, nor had the
power to hinder.--The same execrable tyranny drove the younger part of
us from the fires, when our feet were perishing with snow; and, under
the cruelest penalties, forbad the indulgence of a drink of water,
when we lay in sleepless summer nights, fevered with the season, and
the day's sports.
There was one H----, who, I learned, in after days, was seen expiating
some maturer offence in the hulks. (Do I flatter myself in fancying
that this might be the planter of that name, who suffered--at Nevis,
I think, or St. Kits,--some few years since? My friend Tobin was the
benevolent instrument of bringing him to the gallows.) This petty Nero
actually branded a boy, who had offended him, with a red hot iron; and
nearly starved forty of us, with exacting contributions, to the one
half of our bread, to pamper a young ass, which, incredible as it may
seem, with the connivance of the nurse's daughter (a young flame of
his) he had contrived to smuggle in, and keep upon the leads of the
_ward_, as they called our dormitories. This game went on for better
than a week, till the foolish beast, not able to fare well but he must
cry roast meat--happier than Caligula's minion, could he have kept
his own counsel--but, foolisher, alas! than any of his species in the
fables--waxing fat, and kicking, in the fulness of bread, one unlucky
minute would needs proclaim his good fortune to the world below;
and, laying out his simple throat, blew such a ram's horn blast, as
(toppling down the walls of his own Jericho) set concealment any
longer at defiance. The client was dismissed, with certain attentions,
to Smithfield; but I never understood that the patron underwent any
censure on the occasion. This was in the stewardship of L.'s admired
Perry.
Under the same _facile_ administration, can L. have forgotten the cool
impunity with which the nurses used to carry away openly, in open
platters, for their own tables, one out of two of every hot joint,
which the careful matron had been seeing scrupulously weighed out for
our dinners? These things were daily practised in that magnificent
apartment, which L. (grown connoisseur since, we presume) praises so
highly for the grand paintings "by Verrio, and others," with which it
is "hung round and adorned." But the sight of sleek well-fed blue-coat
boys in pictures was, at that time, I believe, little consolatory to
him, or us, the living ones, who saw the better part of our provisions
carried away before our faces by harpies; and ourselves reduced (with
the Trojan in the hall of Dido)
To feed our mind with idle portraiture.
L. has recorded the repugnance of the school to _gags_, or the fat
of fresh beef boiled; and sets it down to some superstition. But
these unctuous morsels are never grateful to young palates (children
are universally fat-haters) and in strong, coarse, boiled meats,
_unsalted_, are detestable. A _gag-eater_ in our time was equivalent
to a _goul_, and held in equal detestation.--suffered under the
imputation.
--'Twas said
He ate strange flesh.
He was observed, after dinner, carefully to gather up the remnants
left at his table (not many, nor very choice fragments, you may credit
me)--and, in an especial manner, these disreputable morsels, which
he would convey away, and secretly stow in the settle that stood at
his bed-side. None saw when he ate them. It was rumoured that he
privately devoured them in the night. He was watched, but no traces
of such midnight practices were discoverable. Some reported, that, on
leave-days, he had been seen to carry out of the bounds a large blue
check handkerchief, full of something. This then must be the accursed
thing. Conjecture next was at work to imagine how he could dispose
of it. Some said he sold it to the beggars. This belief generally
prevailed. He went about moping. None spake to him. No one would play
with him. He was excommunicated; put out of the pale of the school.
He was too powerful a boy to be beaten, but he underwent every
mode of that negative punishment, which is more grievous than many
stripes. Still he persevered. At length he was observed by two of his
school-fellows, who were determined to get at the secret, and had
traced him one leave-day for that purpose, to enter a large worn-out
building, such as there exist specimens of in Chancery-lane, which are
let out to various scales of pauperism with open door, and a common
staircase. After him they silently slunk in, and followed by stealth
up four flights, and saw him tap at a poor wicket, which was opened by
an aged woman, meanly clad. Suspicion was now ripened into certainty.
The informers had secured their victim. They had him in their toils.
Accusation was formally preferred, and retribution most signal was
looked for. Mr. Hathaway, the then steward (for this happened a little
after my time), with that patient sagacity which tempered all his
conduct, determined to investigate the matter, before he proceeded to
sentence. The result was, that the supposed mendicants, the receivers
or purchasers of the mysterious scraps, turned out to be the parents
of ----, an honest couple come to decay,--whom this seasonable supply
had, in all probability, saved from mendicancy; and that this young
stork, at the expense of his own good name, had all this while been
only feeding the old birds!--The governors on this occasion, much
to their honour, voted a present relief to the family of ----, and
presented him with a silver medal. The lesson which the steward read
upon RASH JUDGMENT, on the occasion of publicly delivering the medal
to ----, I believe, would not be lost upon his auditory.--I had left
school then, but I well remember ----. He was a tall, shambling youth,
with a cast in his eye, not at all calculated to conciliate hostile
prejudices. I have since seen him carrying a baker's basket. I think
I heard he did not do quite so well by himself, as he had done by the
old folks.
I was a hypochondriac lad; and the sight of a boy in fetters, upon the
day of my first putting on the blue clothes, was not exactly fitted
to assuage the natural terrors of initiation. I was of tender years,
barely turned of seven; and had only read of such things in books, or
seen them but in dreams. I was told he had _run away_. This was the
punishment for the first offence.--As a novice I was soon after taken
to see the dungeons. These were little, square, Bedlam cells, where a
boy could just lie at his length upon straw and a blanket--a mattress,
I think, was afterwards substituted--with a peep of light, let in
askance, from a prison-orifice at top, barely enough to read by. Here
the poor boy was locked in by himself all day, without sight of any
but the porter who brought him his bread and water--who _might not
speak to him_;--or of the beadle, who came twice a week to call him
out to receive his periodical chastisement, which was almost welcome,
because it separated him for a brief interval from solitude:--and here
he was shut up by himself of _nights_, out of the reach of any sound,
to suffer whatever horrors the weak nerves, and superstition incident
to his time of life, might subject him to.[2] This was the penalty for
the second offence.--Wouldst thou like, reader, to see what became of
him in the next degree?
The culprit, who had been a third time an offender, and whose
expulsion was at this time deemed irreversible, was brought forth, as
at some solemn _auto da fe_, arrayed in uncouth and most appalling
attire--all trace of his late "watchet weeds" carefully effaced, he
was exposed in a jacket, resembling those which London lamplighters
formerly delighted in, with a cap of the same. The effect of
this divestiture was such as the ingenious devisers of it could
have anticipated. With his pale and frighted features, it was
as if some of those disfigurements in Dante had seized upon
him. In this disguisement he was brought into the hall (_L.'s
favourite state-room_), where awaited him the whole number of his
school-fellows, whose joint lessons and sports he was thenceforth to
share no more; the awful presence of the steward, to be seen for the
last time; of the executioner beadle, clad in his state robe for the
occasion; and of two faces more, of direr import, because never but
in these extremities visible. These were governors; two of whom, by
choice, or charter, were always accustomed to officiate at these
_Ultima Supplicia_; not to mitigate (so at least we understood it),
but to enforce the uttermost stripe. Old Bamber Gascoigne, and Peter
Aubert, I remember, were colleagues on one occasion, when the beadle
turning rather pale, a glass of brandy was ordered to prepare him for
the mysteries. The scourging was, after the old Roman fashion, long
and stately. The lictor accompanied the criminal quite round the hall.
We were generally too faint with attending to the previous disgusting
circumstances, to make accurate report with our eyes of the degree
of corporal suffering inflicted. Report, of course, gave out the
back knotty and livid. After scourging, he was made over, in his
_San Benito_, to his friends, if he had any (but commonly such poor
runagates were friendless), or to his parish officer, who, to enhance
the effect of the scene, had his station allotted to him on the
outside of the hall gate.
These solemn pageantries were not played off so often as to spoil
the general mirth of the community. We had plenty of exercise and
recreation _after_ school hours; and, for myself, I must confess,
that I was never happier, than _in_ them. The Upper and the Lower
Grammar Schools were held in the same room; and an imaginary line only
divided their bounds. Their character was as different as that of the
inhabitants on the two sides of the Pyrennees. The Rev. James Boyer
was the Upper Master; but the Rev. Matthew Field presided over that
portion of the apartment, of which I had the good fortune to be a
member. We lived a life as careless as birds. We talked and did just
what we pleased, and nobody molested us. We carried an accidence, or
a grammar, for form; but, for any trouble it gave us, we might take
two years in getting through the verbs deponent, and another two in
forgetting all that we had learned about them. There was now and then
the formality of saying a lesson, but if you had not learned it, a
brush across the shoulders (just enough to disturb a fly) was the sole
remonstrance. Field never used the rod; and in truth he wielded the
cane with no great good will--holding it "like a dancer." It looked
in his hands rather like an emblem than an instrument of authority;
and an emblem, too, he was ashamed of. He was a good easy man, that
did not care to ruffle his own peace, nor perhaps set any great
consideration upon the value of juvenile time. He came among us, now
and then, but often staid away whole days from us; and when he came,
it made no difference to us--he had his private room to retire to, the
short time he staid, to be out of the sound of our noise. Our mirth
and uproar went on. We had classics of our own, without being beholden
to "insolent Greece or haughty Rome," that passed current among
us--Peter Wilkins--the Adventures of the Hon. Capt. Robert Boyle--the
Fortunate Blue Coat Boy--and the like. Or we cultivated a turn for
mechanic or scientific operations; making little sun-dials of paper;
or weaving those ingenious parentheses, called _cat-cradles_; or
making dry peas to dance upon the end of a tin pipe; or studying the
art military over that laudable game "French and English," and a
hundred other such devices to pass away the time--mixing the useful
with the agreeable--as would have made the souls of Rousseau and John
Locke chuckle to have seen us.
Matthew Field belonged to that class of modest divines who affect
to mix in equal proportion the _gentleman_, the _scholar_, and the
_Christian_; but, I know not how, the first ingredient is generally
found to be the predominating dose in the composition. He was engaged
in gay parties, or with his courtly bow at some episcopal levee, when
he should have been attending upon us. He had for many years the
classical charge of a hundred children, during the four or five first
years of their education; and his very highest form seldom proceeded
further than two or three of the introductory fables of Phaedrus. How
things were suffered to go on thus, I cannot guess. Boyer, who was the
proper person to have remedied these abuses, always affected, perhaps
felt, a delicacy in interfering in a province not strictly his own.
I have not been without my suspicions, that he was not altogether
displeased at the contrast we presented to his end of the school.
We were a sort of Helots to his young Spartans. He would sometimes,
with ironic deference, send to borrow a rod of the Under Master, and
then, with Sardonic grin, observe to one of his upper boys, "how neat
and fresh the twigs looked." While his pale students were battering
their brains over Xenophon and Plato, with a silence as deep as that
enjoined by the Samite, we were enjoying ourselves at our ease in our
little Goshen. We saw a little into the secrets of his discipline, and
the prospect did but the more reconcile us to our lot. His thunders
rolled innocuous for us; his storms came near, but never touched us;
contrary to Gideon's miracle, while all around were drenched, our
fleece was dry.[3] His boys turned out the better scholars; we, I
suspect, have the advantage in temper. His pupils cannot speak of him
without something of terror allaying their gratitude; the remembrance
of Field comes back with all the soothing images of indolence, and
summer slumbers, and work like play, and innocent idleness, and
Elysian exemptions, and life itself a "playing holiday."
Though sufficiently removed from the jurisdiction of Boyer, we were
near enough (as I have said) to understand a little of his system.
We occasionally heard sounds of the _Ululantes_, and caught glances
of Tartarus. B. was a rabid pedant. His English style was crampt to
barbarism. His Easter anthems (for his duty obliged him to those
periodical flights) were grating as scrannel pipes.[4]--He would
laugh, ay, and heartily, but then it must be at Flaccus's quibble
about _Rex_--or at the _tristis severitas in vultu_, or _inspicere in
patinas_, of Terence--thin jests, which at their first broaching could
hardly have had _vis_ enough to move a Roman muscle.--He had two wigs,
both pedantic, but of differing omen. The one serene, smiling, fresh
powdered, betokening a mild day. The other, an old discoloured,
unkempt, angry caxon, denoting frequent and bloody execution. Woe to
the school, when he made his morning appearance in his _passy_, or
_passionate wig_. No comet expounded surer.--J.B. had a heavy hand. I
have known him double his knotty fist at a poor trembling child (the
maternal milk hardly dry upon its lips) with a "Sirrah, do you presume
to set your wits at me?"--Nothing was more common than to see him make
a head-long entry into the school-room, from his inner recess, or
library, and, with turbulent eye, singling out a lad, roar out, "Od's
my life, Sirrah," (his favourite adjuration) "I have a great mind to
whip you,"--then, with as sudden a retracting impulse, fling back into
his lair--and, after a cooling lapse of some minutes (during which
all but the culprit had totally forgotten the context) drive headlong
out again, piecing out his imperfect sense, as if it had been some
Devil's Litany, with the expletory yell--"_and I WILL, too._"--In
his gentler moods, when the _rabidus furor_ was assuaged, he had
resort to an ingenious method, peculiar, for what I have heard, to
himself, of whipping the boy, and reading the Debates, at the same
time; a paragraph, and a lash between; which in those times, when
parliamentary oratory was most at a height and flourishing in these
realms, was not calculated to impress the patient with a veneration
for the diffuser graces of rhetoric.
Once, and but once, the uplifted rod was known to fall ineffectual
from his hand--when droll squinting W---- having been caught putting
the inside of the master's desk to a use for which the architect had
clearly not designed it, to justify himself, with great simplicity
averred, that _he did not know that the thing had been forewarned_.
This exquisite irrecognition of any law antecedent to the _oral_ or
_declaratory_, struck so irresistibly upon the fancy of all who
heard it (the pedagogue himself not excepted) that remission was
unavoidable.
L. has given credit to B.'s great merits as an instructor. Coleridge,
in his literary life, has pronounced a more intelligible and ample
encomium on them. The author of the Country Spectator doubts not to
compare him with the ablest teachers of antiquity. Perhaps we cannot
dismiss him better than with the pious ejaculation of C.--when he
heard that his old master was on his death-bed--"Poor J.B.!--may all
his faults be forgiven; and may he be wafted to bliss by little cherub
boys, all head and wings, with no _bottoms_ to reproach his sublunary
infirmities."
Under him were many good and sound scholars bred.--First Grecian of
my time was Lancelot Pepys Stevens, kindest of boys and men, since
Co-grammar-master (and inseparable companion) with Dr. T----e. What
an edifying spectacle did this brace of friends present to those who
remembered the anti-socialities of their predecessors!--You never met
the one by chance in the street without a wonder, which was quickly
dissipated by the almost immediate sub-appearance of the other.
Generally arm in arm, these kindly coadjutors lightened for each
other the toilsome duties of their profession, and when, in advanced
age, one found it convenient to retire, the other was not long in
discovering that it suited him to lay down the fasces also. Oh, it
is pleasant, as it is rare, to find the same arm linked in yours
at forty, which at thirteen helped it to turn over the _Cicero De
Amicitia_, or some tale of Antique Friendship, which the young heart
even then was burning to anticipate!--Co-Grecian with S. was Th----,
who has since executed with ability various diplomatic functions at
the Northern courts. Th---- was a tall, dark, saturnine youth, sparing
of speech, with raven locks.--Thomas Fanshaw Middleton followed him
(now Bishop of Calcutta) a scholar and a gentleman in his teens. He
has the reputation of an excellent critic; and is author (besides
the Country Spectator) of a Treatise on the Greek Article, against
Sharpe.--M. is said to bear his mitre high in India, where the _regni
novitas_ (I dare say) sufficiently justifies the bearing. A humility
quite as primitive as that of Jewel or Hooker might not be exactly
fitted to impress the minds of those Anglo-Asiatic diocesans with a
reverence for home institutions, and the church which those fathers
watered. The manners of M. at school, though firm, were mild, and
unassuming.--Next to M. (if not senior to him) was Richards, author of
the Aboriginal Britons, the most spirited of the Oxford Prize Poems; a
pale, studious Grecian.--Then followed poor S----, ill-fated M----! of
these the Muse is silent.
Finding some of Edward's race
Unhappy, pass their annals by.
Come back into memory, like as thou wert in the day-spring of thy
fancies, with hope like a fiery column before thee--the dark pillar
not yet turned--Samuel Taylor Coleridge--Logician, Metaphysician,
Bard!--How have I seen the casual passer through the Cloisters stand
still, intranced with admiration (while he weighed the disproportion
between the _speech_ and the _garb_ of the young Mirandula), to hear
thee unfold, in thy deep and sweet intonations, the mysteries of
Jamblichus, or Plotinus (for even in those years thou waxedst not
pale at such philosophic draughts), or reciting Homer in his Greek,
or Pindar--while the walls of the old Grey Friars re-echoed to the
accents of the _inspired charity-boy_!--Many were the "wit-combats,"
(to dally awhile with the words of old Fuller,) between him and C.V.
Le G----, "which two I behold like a Spanish great gallion, and an
English man of war; Master Coleridge, like the former, was built far
higher in learning, solid, but slow in his performances. C.V.L., with
the English man of war, lesser in bulk, but lighter in sailing, could
turn with all tides, tack about, and take advantage of all winds, by
the quickness of his wit and invention."
Nor shall thou, their compeer, be quickly forgotten, Allen, with the
cordial smile, and still more cordial laugh, with which thou wert wont
to make the old Cloisters shake, in thy cognition of some poignant
jest of theirs; or the anticipation of some more material, and,
peradventure, practical one, of thine own. Extinct are those smiles,
with that beautiful countenance, with which (for thou wert the _Nircus
formosus_ of the school), in the days of thy maturer waggery, thou
didst disarm the wrath of infuriated town-damsel, who, incensed by
provoking pinch, turning tigress-like round, suddenly converted by
thy angel-look, exchanged the half-formed terrible "_bl----_," for a
gentler greeting--"_bless thy handsome face_!"
Next follow two, who ought to be now alive, and the friends of
Elia--the junior Le G---- and F----; who impelled, the former by
a roving temper, the latter by too quick a sense of neglect--ill
capable of enduring the slights poor Sizars are sometimes subject to
in our seats of learning--exchanged their Alma Mater for the camp;
perishing, one by climate, and one on the plains of Salamanca:--Le
G----, sanguine, volatile, sweet-natured; F----, dogged, faithful,
anticipative of insult, warm-hearted, with something of the old Roman
height about him.
Fine, frank-hearted Fr----, the present master of Hertford, with
Marmaduke T----, mildest of Missionaries--and both my good friends
still--close the catalogue of Grecians in my time.
[Footnote 1: Recollections of Christ's Hospital.]
[Footnote 2: One or two instances of lunacy, or attempted suicide,
accordingly, at length convinced the governors of the impolicy of
this part of the sentence, and the midnight torture to the spirits
was dispensed with.--This fancy of dungeons for children was a sprout
of Howard's brain; for which (saving the reverence due to Holy Paul)
methinks, I could willingly spit upon his statue.]
[Footnote 3: Cowley.]
[Footnote 4: In this and every thing B. was the antipodes of his
co-adjutor. While the former was digging his brains for crude anthems,
worth a pig-nut, F. would be recreating his gentlemanly fancy in the
more flowery walks of the Muses. A little dramatic effusion of his,
under the name of Vertumnus and Pomona, is not yet forgotten by the
chroniclers of that sort of literature. It was accepted by Garrick,
but the town did not give it their sanction.--B. used to say of it, in
a way of half-compliment, half-irony, that it was _too classical for
representation_.]
THE TWO RACES OF MEN
The human species, according to the best theory I can form of it, is
composed of two distinct races, _the men who borrow_, and _the men
who lend_. To these two original diversities may be reduced all those
impertinent classifications of Gothic and Celtic tribes, white men,
black men, red men. All the dwellers upon earth, "Parthians, and
Medes, and Elamites," flock hither, and do naturally fall in with
one or other of these primary distinctions. The infinite superiority
of the former, which I choose to designate as the _great race_,
is discernible in their figure, port, and a certain instinctive
sovereignty. The latter are born degraded. "He shall serve his
brethren." There is something in the air of one of this cast, lean and
suspicious; contrasting with the open, trusting, generous manners of
the other.
Observe who have been the greatest borrowers of all
ages--Alcibiades--Falstaff--Sir Richard Steele--our late incomparable
Brinsley--what a family likeness in all four!
What a careless, even deportment hath your borrower! what rosy gills!
what a beautiful reliance on Providence doth he manifest,--taking
no more thought than lilies! What contempt for money,--accounting
it (yours and mine especially) no better than dross! What a liberal
confounding of those pedantic distinctions of _meum_ and _tuum_!
or rather what a noble simplification of language (beyond Tooke),
resolving these supposed opposites into one clear, intelligible
pronoun adjective!--What near approaches doth he make to the primitive
_community_,--to the extent of one half of the principle at least!--
He is the true taxer who "calleth all the world up to be taxed:" and
the distance is as vast between him and _one of us_, as subsisted
betwixt the Augustan Majesty and the poorest obolary Jew that paid
it tribute-pittance at Jerusalem!--His exactions, too, have such a
cheerful, voluntary air! So far removed from your sour parochial or
state-gatherers,--those ink-horn varlets, who carry their want of
welcome in their faces! He cometh to you with a smile, and troubleth
you with no receipt; confining himself to no set season. Every day is
his Candlemas, or his Feast of Holy Michael. He applieth the _lene
tormentum_ of a pleasant look to your purse,--which to that gentle
warmth expands her silken leaves, as naturally as the cloak of the
traveller, for which sun and wind contended! He is the true Propontic
which never ebbeth! The sea which taketh handsomely at each man's
hand. In vain the victim, whom he delighteth to honour, struggles with
destiny; he is in the net. Lend therefore cheerfully, O man ordained
to lend--that thou lose not in the end, with thy worldly penny, the
reversion promised. Combine not preposterously in thine own person the
penalties of Lazarus and of Dives!--but, when thou seest the proper
authority coming, meet it smilingly, as it were half-way. Come,
a handsome sacrifice! See how light _he_ makes of it! Strain not
courtesies with a noble enemy.
Reflections like the foregoing were forced upon my mind by the death
of my old friend, Ralph Bigod, Esq., who departed this life on
Wednesday evening; dying, as he had lived, without much trouble. He
boasted himself a descendant from mighty ancestors of that name, who
heretofore held ducal dignities in this realm. In his actions and
sentiments he belied not the stock to which he pretended. Early in
life he found himself invested with ample revenues; which, with that
noble disinterestedness which I have noticed as inherent in men of the
_great race_, he took almost immediate measures entirely to dissipate
and bring to nothing: for there is something revolting in the idea of
a king holding a private purse; and the thoughts of Bigod were all
regal. Thus furnished, by the very act of disfurnishment; getting rid
of the cumbersome luggage of riches, more apt (as one sings)
To slacken virtue, and abate her edge,
Than prompt her to do aught may merit praise,
he set forth, like some Alexander, upon his great enterprise,
"borrowing and to borrow!"
In his periegesis, or triumphant progress throughout this island, it
has been calculated that he laid a tythe part of the inhabitants under
contribution. I reject this estimate as greatly exaggerated:--but
having had the honour of accompanying my friend, divers times, in his
perambulations about this vast city, I own I was greatly struck at
first with the prodigious number of faces we met, who claimed a sort
of respectful acquaintance with us. He was one day so obliging as to
explain the phenomenon. It seems, these were his tributaries; feeders
of his exchequer; gentlemen, his good friends (as he was pleased to
express himself), to whom he had occasionally been beholden for a
loan. Their multitudes did no way disconcert him. He rather took
a pride in numbering them; and, with Comus, seemed pleased to be
"stocked with so fair a herd."
With such sources, it was a wonder how he contrived to keep his
treasury always empty. He did it by force of an aphorism, which he had
often in his mouth, that "money kept longer than three days stinks."
So he made use of it while it was fresh. A good part he drank away
(for he was an excellent toss-pot), some he gave away, the rest he
threw away, literally tossing and hurling it violently from him--as
boys do burrs, or as if it had been infectious,--into ponds, or
ditches, or deep holes,--inscrutable cavities of the earth;--or he
would bury it (where he would never seek it again) by a river's
side under some bank, which (he would facetiously observe) paid no
interest--but out away from him it must go peremptorily, as Hagar's
offspring into the wilderness, while it was sweet. He never missed
it. The streams were perennial which fed his fisc. When new supplies
became necessary, the first stranger, was sure to contribute to the
deficiency. For Bigod had an _undeniable_ way with him. He had a
cheerful, open exterior, a quick jovial eye, a bald forehead, just
touched with grey (_cana fides_). He anticipated no excuse, and found
none. And, waiving for a while my theory as to the _great race_, I
would put it to the most untheorising reader, who may at times have
disposable coin in his pocket, whether it is not more repugnant to the
kindliness of his nature to refuse such a one as I am describing, than
to say _no_ to a poor petitionary rogue (your bastard borrower), who,
by his mumping visnomy, tells you, that he expects nothing better;
and, therefore, whose preconceived notions and expectations you do in
reality so much less shock in the refusal.
When I think of this man; his fiery glow of heart; his swell of
feeling; how magnificent, how _ideal_ he was; how great at the
midnight hour; and when I compare with him the companions with whom I
have associated since, I grudge the saving of a few idle ducats, and
think that I am fallen into the society of _lenders_, and _little
men_.
To one like Elia, whose treasures are rather cased in leather covers
than closed in iron coffers, there is a class of alienators more
formidable than that which I have touched upon; I mean your _borrowers
of books_--those mutilators of collections, spoilers of the symmetry
of shelves, and creators of odd volumes. There is Comberbatch,
matchless in his depredations!
That foul gap in the bottom shelf facing you, like a great eye-tooth
knocked out--(you are now with me in my little back study in
Bloomsbury, reader!)--with the huge Switzer-like tomes on each side
(like the Guildhall giants, in their reformed posture, guardant of
nothing) once held the tallest of my folios, _Opera Bonaventurae_,
choice and massy divinity, to which its two supporters (school
divinity also, but of a lesser calibre,--Bellarmine, and Holy Thomas),
showed but as dwarfs,--itself an Ascapart!--_that_ Comberbatch
abstracted upon the faith of a theory he holds, which is more easy, I
confess, for me to suffer by than to refute, namely, that "the title
to property in a book (my Bonaventure, for instance), is in exact
ratio to the claimant's powers of understanding and appreciating the
same." Should he go on acting upon this theory, which of our shelves
is safe?
The slight vacuum in the left-hand case--two shelves from the
ceiling--scarcely distinguishable but by the quick eye of a loser--was
whilom the commodious resting-place of Brown on Urn Burial. C. will
hardly allege that he knows more about that treatise than I do, who
introduced it to him, and was indeed the first (of the moderns) to
discover its beauties--but so have I known a foolish lover to praise
his mistress in the presence of a rival more qualified to carry her
off than himself.--Just below, Dodsley's dramas want their fourth
volume, where Vittoria Corombona is! The remainder nine are as
distasteful as Priam's refuse sons, when the Fates _borrowed_ Hector.
Here stood the Anatomy of Melancholy, in sober state.--There loitered
the Complete Angler; quiet as in life, by some stream side.--In yonder
nook, John Buncle, a widower-volume, with "eyes closed," I mourns his
ravished mate.
One justice I must do my friend, that if he sometimes, like the sea,
sweeps away a treasure, at another time, sea-like, he throws up as
rich an equivalent to match it. I have a small under-collection of
this nature (my friend's gathering's in his various calls), picked
up, he has forgotten at what odd places, and deposited with as little
memory as mine. I take in these orphans, the twice-deserted. These
proselytes of the gate are welcome as the true Hebrews. There they
stand in conjunction; natives, and naturalised. The latter seem as
little disposed to inquire out their true lineage as I am.--I charge
no warehouse-room for these deodands, nor shall ever put myself to the
ungentlemanly trouble of advertising a sale of them to pay expenses.
To lose a volume to C. carries some sense and meaning in it. You are
sure that he will make one hearty meal on your viands, if he can give
no account of the platter after it. But what moved thee, wayward,
spiteful K., to be so importunate to carry off with thee, in spite of
tears and adjurations to thee to forbear, the Letters of that princely
woman, the thrice noble Margaret Newcastle?--knowing at the time,
and knowing that I knew also, thou most assuredly wouldst never turn
over one leaf of the illustrious folio:--what but the mere spirit
of contradiction, and childish love of getting the better of thy
friend?--Then, worst cut of all! to transport it with thee to the
Gallican land--
Unworthy land to harbour such a sweetness,
A virtue in which all ennobling thoughts dwelt,
Pure thoughts, kind thoughts, high thoughts, her sex's wonder!
--hadst thou not thy play-books, and books of jests and fancies,
about thee, to keep thee merry, even as thou keepest all companies
with thy quips and mirthful tales?--Child of the Green-room, it was
unkindly done of thee. Thy wife, too, that part-French, better-part
Englishwoman!--that _she_ could fix upon no other treatise to bear
away, in kindly token of remembering us, than the works of Fulke
Greville, Lord Brook--of which no Frenchman, nor woman of France,
Italy, or England, was ever by nature constituted to comprehend a
tittle! _Was there not Zimmerman on Solitude?_
Reader, if haply thou art blessed with a moderate collection, be shy
of showing it; or if thy heart overfloweth to lend them, lend thy
books; but let it be to such a one as S.T.C.--he will return them
(generally anticipating the time appointed) with usury; enriched with
annotations, tripling their value. I have had experience. Many are
these precious MSS. of his--(in _matter_ oftentimes, and almost in
_quantity_ not unfrequently, vying with the originals)--in no very
clerkly hand--legible in my Daniel; in old Burton; in Sir Thomas
Browne; and those abstruser cogitations of the Greville, now, alas!
wandering in Pagan lands.--I counsel thee, shut not thy heart, nor thy
library, against S.T.C.
NEW YEAR'S EVE
Every man hath two birth-days: two days, at least, in every year,
which set him upon revolving the lapse of time, as it affects his
mortal duration. The one is that which in an especial manner he
termeth _his_. In the gradual desuetude of old observances, this
custom of solemnizing our proper birth-day hath nearly passed away, or
is left to children, who reflect nothing at all about the matter, nor
understand any thing in it beyond cake and orange. But the birth of
a New Year is of an interest too wide to be pretermitted by king or
cobbler. No one ever regarded the First of January with indifference.
It is that from which all date their time, and count upon what is
left. It is the nativity of our common Adam.
Of all sounds of all bells--(bells, the music nighest bordering upon
heaven)--most solemn and touching is the peal which rings out the
Old Year. I never hear it without a gathering-up of my mind to a
concentration of all the images that have been diffused over the past
twelvemonth; all I have done or suffered, performed or neglected--in
that regretted time. I begin to know its worth, as when a person
dies. It takes a personal colour; nor was it a poetical flight in a
contemporary, when he exclaimed
I saw the skirts of the departing Year.
It is no more than what in sober sadness every one of us seems to be
conscious of, in that awful leave-taking. I am sure I felt it, and all
felt it with me, last night; though some of my companions affected
rather to manifest an exhilaration at the birth of the coming year,
than any very tender regrets for the decease of its predecessor. But I
am none of those who--
Welcome the coming, speed the parting guest.
I am naturally, beforehand, shy of novelties; new books, new faces,
new years,--from some mental twist which makes it difficult in me to
face the prospective. I have almost ceased to hope; and am sanguine
only in the prospects of other (former) years. I plunge into
foregone visions and conclusions. I encounter pell-mell with past
disappointments. I am armour-proof against old discouragements. I
forgive, or overcome in fancy, old adversaries. I play over again _for
love_, as the gamesters phrase it, games, for which I once paid so
dear. I would scarce now have any of those untoward accidents and
events of my life reversed. I would no more alter them than the
incidents of some well-contrived novel. Methinks, it is better that I
should have pined away seven of my goldenest years, when I was thrall
to the fair hair, and fairer eyes, of Alice W----n, than that so
passionate a love-adventure should be lost. It was better that our
family should have missed that legacy, which old Dorrell cheated us
of, than that I should have at this moment two thousand pounds _in
banco_, and be without the idea of that specious old rogue.
In a degree beneath manhood, it is my infirmity to look back upon
those early days. Do I advance a paradox, when I say, that, skipping
over the intervention of forty years, a man may have leave to love
_himself_, without the imputation of self-love?
If I know aught of myself, no one whose mind is introspective--and
mine is painfully so--can have a less respect for his present
identity, than I have for the man Elia. I know him to be light, and
vain, and humorsome; a notorious ***; addicted to ****: averse
from counsel, neither taking it, nor offering it;--*** besides;
a stammering buffoon; what you will; lay it on, and spare not; I
subscribe to it all, and much more, than thou canst be willing to lay
at his door--but for the child Elia--that "other me," there, in the
back-ground--I must take leave to cherish the remembrance of that
young master--with as little reference, I protest, to this stupid
changeling of five-and-forty, as if it had been a child of some other
house, and not of my parents. I can cry over its patient small-pox at
five, and rougher medicaments I can lay its poor fevered head upon the
sick pillow at Christ's and wake with it in surprise at the gentle
posture of maternal tenderness hanging over it, that unknown had
watched its sleep. I know how it shrank from any the least colour
of falsehood.--God help thee, Elia, how art thou changed! Thou art
sophisticated.--I know how honest, how courageous (for a weakling) it
was--how religious, how imaginative, how hopeful! From what have I
not fallen, if the child I remember was indeed myself--and not some
dissembling guardian presenting a false identity, to give the rule to
my unpractised steps, and regulate the tone of my moral being!
That I am fond of indulging, beyond a hope of sympathy, in such
retrospection, may be the symptom of some sickly idiosyncrasy. Or
is it owing to another cause; simply, that being without wife or
family, I have not learned to project myself enough out of myself;
and having no offspring of my own to dally with, I turn back upon
memory and adopt my own early idea, as my heir and favourite? If
these speculations seem fantastical to thee, reader--(a busy man,
perchance), if I tread out of the way of thy sympathy, and am
singularly-conceited only, I retire, impenetrable to ridicule, under
the phantom cloud of Elia.
The elders, with whom I was brought up, were of a character not likely
to let slip the sacred observance of any old institution; and the
ringing out of the Old Year was kept by them with circumstances of
peculiar ceremony.--In those days the sound of those midnight chimes,
though it seemed to raise hilarity in all around me, never failed to
bring a train of pensive imagery into my fancy. Yet I then scarce
conceived what it meant, or thought of it as a reckoning that
concerned me. Not childhood alone, but the young man till thirty,
never feels practically that he is mortal. He knows it indeed, and,
if need were, he could preach a homily on the fragility of life; but
he brings it not home to himself, any more than in a hot June we can
appropriate to our imagination the freezing days of December. But now,
shall I confess a truth?--I feel these audits but too powerfully. I
begin to count the probabilities of my duration, and to grudge at the
expenditure of moments and shortest periods, like miser's farthings.
In proportion as the years both lessen and shorten, I set more count
upon their periods, and would fain lay my ineffectual finger upon
the spoke of the great wheel. I am not content to pass away "like a
weaver's shuttle." Those metaphors solace me not, nor sweeten the
unpalatable draught of mortality. I care not to be carried with the
tide, that smoothly bears human life to eternity; and reluct at the
inevitable course of destiny. I am in love with this green earth; the
face of town and country; the unspeakable rural solitudes, and the
sweet security of streets. I would set up my tabernacle here. I am
content to stand still at the age to which I am arrived; I, and my
friends: to be no younger, no richer, no handsomer. I do not want to
be weaned by age; or drop, like mellow fruit, as they say, into the
grave.--Any alteration, on this earth of mine, in diet or in lodging,
puzzles and discomposes me. My household-gods plant a terrible fixed
foot, and are not rooted up without blood. They do not willingly seek
Lavinian shores. A new state of being staggers me. Sun, and sky, and
breeze, and solitary walks, and summer holidays, and the greenness of
fields, and the delicious juices of meats and fishes, and society, and
the cheerful glass, and candle-light, and fire-side conversations, and
innocent vanities, and jests, and _irony itself_--do these things go
out with life?
Can a ghost laugh, or shake his gaunt sides, when you are pleasant
with him?
And you, my midnight darlings, my Folios! must I part with the intense
delight of having you (huge armfuls) in my embraces? Must knowledge
come to me, if it come at all, by some awkward experiment of
intuition, and no longer by this familiar process of reading?
Shall I enjoy friendships there, wanting the smiling indications which
point me to them here,--the recognisable face--the "sweet assurance of
a look"--?
In winter this intolerable disinclination to dying--to give it its
mildest name--does more especially haunt and beset me. In a genial
August noon, beneath a sweltering sky, death is almost problematic.
At those times do such poor snakes as myself enjoy an immortality.
Then we expand and burgeon. Then are we as strong again, as valiant
again, as wise again, and a great deal taller. The blast that nips
and shrinks me, puts me in thoughts of death. All things allied to
the insubstantial, wait upon that master feeling; cold, numbness,
dreams, perplexity; moonlight itself, with its shadowy and spectral
appearances,--that cold ghost of the sun, or Phoebus' sickly sister,
like that innutritious one denounced in the Canticles:--I am none of
her minions--I hold with the Persian.
Whatsoever thwarts, or puts me out of my way, brings death into
my mind. All partial evils, like humours, run into that capital
plague-sore.--I have heard some profess an indifference to life. Such
hail the end of their existence as a port of refuge; and speak of
the grave as of some soft arms, in which they may slumber as on a
pillow. Some have wooed death--but out upon thee, I say, thou foul,
ugly phantom! I detest, abhor, execrate, and (with Friar John) give
thee to six-score thousand devils, as in no instance to be excused
or tolerated, but shunned as a universal viper; to be branded,
proscribed, and spoken evil of! In no way can I be brought to digest
thee, thou thin, melancholy _Privation_, or more frightful and
confounding _Positive!_'
Those antidotes, prescribed against the fear of thee, are altogether
frigid and insulting, like thyself. For what satisfaction hath a man,
that he shall "lie down with kings and emperors in death," who in his
life-time never greatly coveted the society of such bed-fellows?--or,
forsooth, that "so shall the fairest face appear?"--why, to comfort
me, must Alice W----n be a goblin? More than all, I conceive disgust
at those impertinent and misbecoming familiarities, inscribed upon
your ordinary tombstones. Every dead man must take upon himself to be
lecturing me with his odious truism, that "such as he now is, I must
shortly be." Not so shortly, friend, perhaps, as thou imaginest. In
the meantime I am alive. I move about. I am worth twenty of thee.
Know thy betters! Thy New Years' Days are past. I survive, a jolly
candidate for 1821. Another cup of wine--and while that turn-coat
bell, that just now mournfully chanted the obsequies of 1820 departed,
with changed notes lustily rings in a successor, let us attune to
its peal the song made on a like occasion, by hearty, cheerful Mr.
Cotton.--
THE NEW YEAR
Hark, the cock crows, and yon bright star
Tells us, the day himself's not far;
And see where, breaking from the night,
He gilds the western hills with light.
With him old Janus doth appear,
Peeping into the future year,
With such a look as seems to say,
The prospect is not good that way.
Thus do we rise ill sights to see,
And 'gainst ourselves to prophesy;
When the prophetic fear of things
A more tormenting mischief brings,
More full of soul-tormenting gall,
Than direst mischiefs can befall.
But stay! but stay! methinks my sight,
Better inform'd by clearer light,
Discerns sereneness in that brow,
That all contracted seem'd but now.
His revers'd face may show distaste,
And frown upon the ills are past;
But that which this way looks is clear,
And smiles upon the New-born Year.
He looks too from a place so high,
The Year lies open to his eye;
And all the moments open are
To the exact discoverer.
Yet more and more he smiles upon
The happy revolution.
Why should we then suspect or fear
The influences of a year,
So smiles upon us the first morn,
And speaks us good so soon as born?
Plague on't! the last was ill enough,
This cannot but make better proof;
Or, at the worst, as we brush'd through
The last, why so we may this too;
And then the next in reason shou'd
Be superexcellently good:
For the worst ills (we daily see)
Have no more perpetuity,
Than the best fortunes that do fall;
Which also bring us wherewithal
Longer their being to support,
Than those do of the other sort:
And who has one good year in three,
And yet repines at destiny,
Appears ungrateful in the case,
And merits not the good he has.
Then let us welcome the New Guest
With lusty brimmers of the best;
Mirth always should Good Fortune meet,
And renders e'en Disaster sweet:
And though the Princess turn her back,
Let us but line ourselves with sack,
We better shall by far hold out,
Till the next Year she face about.
How say you, reader--do not these verses smack of the rough
magnanimity of the old English vein? Do they not fortify like a
cordial; enlarging the heart, and productive of sweet blood, and
generous spirits, in the concoction? Where be those puling fears of
death, just now expressed or affected?--Passed like a cloud--absorbed
in the purging sunlight of clear poetry--clean washed away by a wave
of genuine Helicon, your only Spa for these hypochondries--And now
another cup of the generous! and a merry New Year, and many of them,
to you all, my masters!
MRS. BATTLE'S OPINIONS ON WHIST
"A clear fire, a clean hearth, and the rigour of the game." This was
the celebrated _wish_ of old Sarah Battle (now with God) who, next
to her devotions, loved a good game at whist. She was none of your
lukewarm gamesters, your half and half players, who have no objection
to take a hand, if you want one to make up a rubber; who affirm that
they have no pleasure in winning; that they like to win one game,
and lose another; that they can while away an hour very agreeably at
a card-table, but are indifferent whether they play or no; and will
desire an adversary, who has slipt a wrong card, to take it up and
play another. These insufferable triflers are the curse of a table.
One of these flies will spoil a whole pot. Of such it may be said,
that they do not play at cards, but only play at playing at them.
Sarah Battle was none of that breed. She detested them, as I do, from
her heart and soul; and would not, save upon a striking emergency,
willingly seat herself at the same table with them. She loved a
thorough-paced partner, a determined enemy. She took, and gave,
no concessions. She hated favours. She never made a revoke, nor
ever passed it over in her adversary without exacting the utmost
forfeiture. She fought a good fight: cut and thrust. She held not her
good sword (her cards) "like a dancer." She sate bolt upright; and
neither showed you her cards, nor desired to see yours. All people
have their blind side--their superstitions; and I have heard her
declare, under the rose, that Hearts was her favourite suit.
I never in my life--and I knew Sarah Battle many of the best years of
it--saw her take out her snuff-box when it was her turn to play; or
snuff a candle in the middle of a game; or ring for a servant, till it
was fairly over. She never introduced, or connived at, miscellaneous
conversation during its process. As she emphatically observed,
cards were cards: and if I ever saw unmingled distaste in her fine
last-century countenance, it was at the airs of a young gentleman of a
literary turn, who had been with difficulty persuaded to take a hand;
and who, in his excess of candour, declared, that he thought there was
no harm in unbending the mind now and then, after serious studies,
in recreations of that kind! She could not bear to have her noble
occupation, to which she wound up her faculties, considered in that
light. It was her business, her duty, the thing she came into the
world to do,--and she did it. She unbent her mind afterwards--over a
book.
Pope was her favourite author: his Rape of the Lock her favourite
work. She once did me the favour to play over with me (with the cards)
his celebrated game of Ombre in that poem; and to explain to me how
far it agreed with, and in what points it would be found to differ
from, tradrille. Her illustrations were apposite and poignant; and I
had the pleasure of sending the substance of them to Mr. Bowles: but
I suppose they came too late to be inserted among his ingenious notes
upon that author.
Quadrille, she has often told me, was her first love; but whist
had engaged her maturer esteem. The former, she said, was showy
and specious, and likely to allure young persons. The uncertainty
and quick shifting of partners--a thing which the constancy of
whist abhors;--the dazzling supremacy and regal investiture of
Spadille--absurd, as she justly observed, in the pure aristocracy of
whist, where his crown and garter give him no proper power above his
brother-nobility of the Aces;--the giddy vanity, so taking to the
inexperienced, of playing alone:--above all, the overpowering
attractions of a _Sans Prendre Vole_,--to the triumph of which there
is certainly nothing parallel or approaching, in the contingencies of
whist;--all these, she would say, make quadrille a game of captivation
to the young and enthusiastic. But whist was the _solider_ game:
that was her word. It was a long meal; not, like quadrille, a feast
of snatches. One or two rubbers might coextend in duration with an
evening. They gave time to form rooted friendships, to cultivate
steady enmities. She despised the chance-started, capricious, and ever
fluctuating alliances of the other. The skirmishes of quadrille, she
would say, reminded her of the petty ephemeral embroilments of the
little Italian states, depicted by Machiavel; perpetually changing
postures and connexions; bitter foes to-day, sugared darlings
to-morrow; kissing and scratching in a breath;--but the wars of
whist were comparable to the long, steady, deep-rooted, rational,
antipathies of the great French and English nations.
A grave simplicity was what she chiefly admired in her favourite game.
There was nothing silly in it, like the nob in cribbage--nothing
superfluous. No _flushes_--that most irrational of all pleas that
a reasonable being can set up:--that any one should claim four by
virtue of holding cards of the same mark and colour, without reference
to the playing of the game, or the individual worth or pretensions
of the cards themselves! She held this to be a solecism; as pitiful
an ambition at cards as alliteration is in authorship. She despised
superficiality, and looked deeper than the colours of things.--Suits
were soldiers, she would say, and must have a uniformity of array to
distinguish them: but what should we say to a foolish squire, who
should claim a merit from dressing up his tenantry in red jackets,
that never were to be marshalled--never to take the field?--She even
wished that whist were more simple than it is; and, in my mind, would
have stript it of some appendages, which, in the state of human
frailty, may be venially, and even commendably allowed of. She saw no
reason for the deciding of the trump by the turn of the card. Why not
one suit always trumps?--Why two colours, when the mark of the suits
would have sufficiently distinguished them without it?--
"But the eye, my dear Madam, is agreeably refreshed with the variety.
Man is not a creature of pure reason he must have his senses
delightfully appealed to. We see it in Roman Catholic countries, where
the music and the paintings draw in many to worship, whom your quaker
spirit of unsensualizing would have kept out.--You, yourself, have a
pretty collection of paintings--but confess to me, whether, walking
in your gallery at Sandham, among those clear Vandykes, or among the
Paul Potters in the ante-room, you ever felt your bosom glow with
an elegant delight, at all comparable to _that_ you have it in your
power to experience most evenings over a well-arranged assortment
of the court cards?--the pretty antic habits, like heralds in a
procession--the gay triumph-assuring scarlets--the contrasting
deadly-killing sables--the 'hoary majesty of spades'--Pam in all his
glory!--
"All these might be dispensed with; and, with their naked names upon
the drab pasteboard, the game might go on very well, picture-less.
But the _beauty_ of cards would be extinguished for ever. Stripped
of all that is imaginative in them, they must degenerate into mere
gambling.--Imagine a dull deal board, or drum head, to spread them on,
instead of that nice verdant carpet (next to nature's), fittest arena
for those courtly combatants to play their gallant jousts and turneys
in!--Exchange those delicately-turned ivory markers--(work of Chinese
artist, unconscious of their symbol,--or as profanely slighting their
true application as the arrantest Ephesian journeyman that turned out
those little shrines for the goddess)--exchange them for little bits
of leather (our ancestors' money) or chalk and a slate!"--
The old lady, with a smile, confessed the soundness of my logic;
and to her approbation of my arguments on her favourite topic that
evening, I have always fancied myself indebted for the legacy of a
curious cribbage board, made of the finest Sienna marble, which her
maternal uncle (old Walter Plumer, whom I have elsewhere celebrated)
brought with him from Florence:--this, and a trifle of five hundred
pounds, came to me at her death.
The former bequest (which I do not least value) I have kept with
religious care; though she herself, to confess a truth, was never
greatly taken with cribbage. It was an essentially vulgar game, I have
heard her say,--disputing with her uncle, who was very partial to
it. She could never heartily bring her mouth to pronounce "_go_"--or
"_that's a go_." She called it an ungrammatical game. The pegging
teased her. I once knew her to forfeit a rubber (a five dollar stake),
because she would not take advantage of the turn-up knave, which would
have given it her, but which she must have claimed by the disgraceful
tenure of declaring "_two for his heels_." There is something
extremely genteel in this sort of self-denial. Sarah Battle was a
gentlewoman born.
Piquet she held the best game at the cards for two persons, though she
would ridicule the pedantry of the terms--such as pique--repique--the
capot--they savoured (she thought) of affectation. But games for two,
or even three, she never greatly cared for. She loved the quadrate,
or square. She would argue thus:--Cards are warfare: the ends are
gain, with glory. But cards are war, in disguise of a sport: when
single adversaries encounter, the ends proposed are too palpable.
By themselves, it is too close a fight; with spectators, it is not
much bettered. No looker on can be interested, except for a bet,
and then it is a mere affair of money; he cares not for your luck
_sympathetically_, or for your play.--Three are still worse; a mere
naked war of every man against every man, as in cribbage, without
league or alliance; or a rotation of petty and contradictory
interests, a succession of heartless leagues, and not much more hearty
infractions of them, as in tradrille.--But in square games (_she
meant whist_) all that is possible to be attained in card-playing is
accomplished. There are the incentives of profit with honour, common
to every species--though the _latter_ can be but very imperfectly
enjoyed in those other games, where the spectator is only feebly a
participator. But the parties in whist are spectators and principals
too. They are a theatre to themselves, and a looker-on is not
wanted. He is rather worse than nothing, and an impertinence. Whist
abhors neutrality, or interest beyond its sphere. You glory in some
surprising stroke of skill or fortune, not because a cold--or even
an interested--by-stander witnesses it, but because your _partner_
sympathises in the contingency. You win for two. You triumph for
two. Two are exalted. Two again are mortified; which divides their
disgrace, as the conjunction doubles (by taking off the invidiousness)
your glories. Two losing to two are better reconciled, than one to one
in that close butchery. The hostile feeling is weakened by multiplying
the channels. War becomes a civil game.--By such reasonings as these
the old lady was accustomed to defend her favourite pastime.
No inducement could ever prevail upon her to play at any game, where
chance entered into the composition, _for nothing_. Chance, she would
argue--and here again, admire the subtlety of her conclusion!--chance
is nothing, but where something else depends upon it. It is obvious,
that cannot be _glory_. What rational cause of exultation could it
give to a man to turn up size ace a hundred times together by himself?
or before spectators, where no stake was depending?--Make a lottery
of a hundred thousand tickets with but one fortunate number--and what
possible principle of our nature, except stupid wonderment, could it
gratify to gain that number as many times successively, without a
prize?--Therefore she disliked the mixture of chance in backgammon,
where it was not played for money. She called it foolish, and
those people idots, who were taken with a lucky hit under such
circumstances. Games of pure skill were as little to her fancy. Played
for a stake, they were a mere system of over-reaching. Played for
glory, they were a mere setting of one man's wit,--his memory, or
combination-faculty rather--against another's; like a mock-engagement
at a review, bloodless and profitless.--She could not conceive a
_game_ wanting the spritely infusion of chance,--the handsome excuses
of good fortune. Two people playing at chess in a corner of a room,
whilst whist was stirring in the centre, would inspire her with
insufferable horror and ennui. Those well-cut similitudes of Castles,
and Knights, the _imagery_ of the board, she would argue, (and I think
in this case justly) were entirely misplaced and senseless. Those hard
head-contests can in no instance ally with the fancy. They reject form
and colour. A pencil and dry slate (she used to say) were the proper
arena for such combatants.
To those puny objectors against cards, as nurturing the bad passions,
she would retort, that man is a gaming animal. He must be always
trying to get the better in something or other:--that this passion can
scarcely be more safely expended than upon a game at cards: that cards
are a temporary illusion; in truth, a mere drama; for we do but _play_
at being mightily concerned, where a few idle shillings are at stake,
yet, during the illusion, we _are_ as mightily concerned as those
whose stake is crowns and kingdoms. They are a sort of dream-fighting;
much ado; great battling, and little bloodshed; mighty means for
disproportioned ends; quite as diverting, and a great deal more
innoxious, than many of those more serious _games_ of life, which men
play, without esteeming them to be such.--
With great deference to the old lady's judgment on these matters, I
think I have experienced some moments in my life, when playing at
cards _for nothing_ has even been agreeable. When I am in sickness, or
not in the best spirits, I sometimes call for the cards, and play a
game at piquet _for love_ with my cousin Bridget--Bridget Elia.
I grant there is something sneaking in it; but with a toothache, or a
sprained ancle,--when you are subdued and humble,--you are glad to put
up with an inferior spring of action.
There is such a thing in nature, I am convinced, as _sick whist_.--
I grant it is not the highest style of man--I deprecate the manes of
Sarah Battle--she lives not, alas! to whom I should apologise.--
At such times, those _terms_ which my old friend objected to, come in
as something admissible.--I love to get a tierce or a quatorze, though
they mean nothing. I am subdued to an inferior interest. Those shadows
of winning amuse me.
That last game I had with my sweet cousin (I capotted her)--(dare I
tell thee, how foolish I am?)--I wished it might have lasted for ever,
though we gained nothing, and lost nothing, though it was a mere shade
of play: I would be content to go on in that idle folly for ever. The
pipkin should be ever boiling, that was to prepare the gentle lenitive
to my foot, which Bridget was doomed to apply after the game was over:
and, as I do not much relish appliances, there it should ever bubble.
Bridget and I should be ever playing.
A CHAPTER ON EARS
I have no ear.--
Mistake me not, reader,--nor imagine that I am by nature destitute
of those exterior twin appendages, hanging ornaments, and
(architecturally speaking) handsome volutes to the human capital.
Better my mother had never borne me.--I am, I think, rather delicately
than copiously provided with those conduits; and I feel no disposition
to envy the mule for his plenty, or the mole for her exactness,
in those ingenious labyrinthine inlets--those indispensable
side-intelligencers.
Neither have I incurred, or done any thing to incur, with Defoe,
that hideous disfigurement, which constrained him to draw upon
assurance--to feel "quite unabashed," and at ease upon that article.
I was never, I thank my stars, in the pillory; nor, if I read them
aright, is it within the compass of my destiny, that I ever should be.
When therefore I say that I have no ear, you will understand me
to mean--_for music_.--To say that this heart never melted at the
concourse of sweet sounds, would be a foul self-libel.--"_Water
parted from the sea_" never fails to move it strangely. So does "_In
Infancy_." But they were used to be sung at her harpsichord (the
old-fashioned instrument in vogue in those days) by a gentlewoman--the
gentlest, sure, that ever merited the appellation--the sweetest--why
should I hesitate to name Mrs. S----, once the blooming Fanny
Weatheral of the Temple--who had power to thrill the soul of Elia,
small imp as he was, even in his long coats; and to make him glow,
tremble, and blush with a passion, that not faintly indicated the
day-spring of that absorbing sentiment, which was afterwards destined
to overwhelm and subdue his nature quite, for Alice W----n.
I even think that _sentimentally_ I am disposed to harmony. But
_organically_ I am incapable of a tune. I have been practising "_God
save the King_" all my life; whistling and humming of it over to
myself in solitary corners; and am not yet arrived, they tell me,
within many quavers of it. Yet hath the loyalty of Elia never been
impeached.
I am not without suspicion, that I have an undeveloped faculty of
music within me. For, thrumming, in my wild way, on my friend A.'s
piano, the other morning, while he was engaged in an adjoining
parlour,--on his return he was pleased to say, "_he thought it could
not be the maid_!" On his first surprise at hearing the keys touched
in somewhat an airy and masterful way, not dreaming of me, his
suspicions had lighted on _Jenny_. But a grace, snatched from a
superior refinement, soon convinced him that some being,--technically
perhaps deficient, but higher informed from a principle common to all
the fine arts,--had swayed the keys to a mood which Jenny, with all
her (less-cultivated) enthusiasm, could never have elicited from them.
I mention this as a proof of my friend's penetration, and not with any
view of disparaging Jenny.
Scientifically I could never be made to understand (yet have I taken
some pains) what a note in music is; or how one note should differ
from another. Much less in voices can I distinguish a soprano from a
tenor. Only sometimes the thorough bass I contrive to guess at, from
its being supereminently harsh and disagreeable. I tremble, however,
for my misapplication of the simplest terms of _that_ which I
disclaim. While I profess my ignorance, I scarce know what to _say_ I
am ignorant of I hate, perhaps, by misnomers. _Sostenuto_ and _adagio_
stand in the like relation of obscurity to me; and _Sol_, _Fa_, _Mi_,
_Re_, is as conjuring as _Baralipton_.
It is hard to stand alone--in an age like this,--(constituted to the
quick and critical perception of all harmonious combinations, I verily
believe, beyond all preceding ages, since Jubal stumbled upon the
gamut)--to remain, as it were, singly unimpressible to the magic
influences of an art, which is said to have such an especial stroke at
soothing, elevating, and refining the passions.--Yet rather than break
the candid current of my confessions, I must avow to you, that I have
received a great deal more pain than pleasure from this so cried-up
faculty.
I am constitutionally susceptible of noises. A carpenter's hammer, in
a warm summer noon, will fret me into more than midsummer madness. But
those unconnected, unset sounds are nothing to the measured malice of
music. The ear is passive to those single strokes; willingly enduring
stripes, while it hath no task to con. To music it cannot be passive.
It will strive--mine at least will--'spite of its inaptitude, to thrid
the maze; like an unskilled eye painfully poring upon hieroglyphics.
I have sat through an Italian Opera, till, for sheer pain, and
inexplicable anguish, I have rushed out into the noisiest places of
the crowded streets, to solace myself with sounds, which I was not
obliged to follow, and get rid of the distracting torment of endless,
fruitless, barren attention! I take refuge in the unpretending
assemblage of honest common-life sounds;--and the purgatory of the
Enraged Musician becomes my paradise.
I have sat at an Oratorio (that profanation of the purposes of the
cheerful playhouse) watching the faces of the auditory in the pit
(what a contrast to Hogarth's Laughing Audience!) immoveable, or
affecting some faint emotion,--till (as some have said, that our
occupations in the next world will be but a shadow of what delighted
us in this) I have imagined myself in some cold Theatre in Hades,
where some of the _forms_ of the earthly one should be kept up, with
none of the _enjoyment_; or like that--
--Party in a parlour,
All silent, and all DAMNED!
Above all, those insufferable concertos, and pieces of music, as
they are called, do plague and embitter my apprehension.--Words are
something; but to be exposed to an endless battery of mere sounds; to
be long a dying, to lie stretched upon a rack of roses; to keep up
languor by unintermitted effort; to pile honey upon sugar, and sugar
upon honey, to an interminable tedious sweetness; to fill up sound
with feeling, and strain ideas to keep pace with it; to gaze on empty
frames, and be forced to make the pictures for yourself; to read a
book, _all stops_, and be obliged to supply the verbal matter; to
invent extempore tragedies to answer to the vague gestures of an
inexplicable rambling mime--these are faint shadows of what I have
undergone from a series of the ablest-executed pieces of this empty
_instrumental music_.
I deny not, that in the opening of a concert, I have experienced
something vastly lulling and agreeable:--afterwards followeth the
languor, and the oppression. Like that disappointing book in Patmos;
or, like the comings on of melancholy, described by Burton, doth
music make her first insinuating approaches:--"Most pleasant it is
to such as are melancholy given, to walk alone in some solitary
grove, betwixt wood and water, by some brook side, and to meditate
upon some delightsome and pleasant subject, which shall affect him
most, _amabilis insania_, and _mentis gratissimus error_. A most
incomparable delight to build castles in the air, to go smiling to
themselves, acting an infinite variety of parts, which they suppose,
and strongly imagine, they act, or that they see done.--So delightsome
these toys at first, they could spend whole days and nights without
sleep, even whole years in such contemplations, and fantastical
meditations, which are like so many dreams, and will hardly be drawn
from them--winding and unwinding themselves as so many clocks, and
still pleasing their humours, until at last the SCENE TURNS UPON A
SUDDEN, and they being now habitated to such meditations and solitary
places, can endure no company, can think of nothing but harsh and
distasteful subjects. Fear, sorrow, suspicion, _subrusticus pudor_,
discontent, cares, and weariness of life, surprise them on a sudden,
and they can think of nothing else: continually suspecting, no sooner
are their eyes open, but this infernal plague of melancholy seizeth on
them, and terrifies their souls, representing some dismal object to
their minds; which now, by no means, no labour, no persuasions they
can avoid, they cannot be rid of it, they cannot resist."
Something like this "SCENE-TURNING" I have experienced at the evening
parties, at the house of my good Catholic friend _Nov----_; who, by
the aid of a capital organ, himself the most finished of players,
converts his drawing-room into a chapel, his week days into Sundays,
and these latter into minor heavens.[1]
When my friend commences upon one of those solemn anthems, which
peradventure struck upon my heedless ear, rambling in the side
aisles of the dim abbey, some five and thirty years since, waking
a new sense, and putting a soul of old religion into my young
apprehension--(whether it be _that_, in which the psalmist, weary of
the persecutions of bad men, wisheth to himself dove's wings--or _that
other_, which, with a like measure of sobriety and pathos, inquireth
by what means the young man shall best cleanse his mind)--a holy calm
pervadeth me.--I am for the time
--rapt above earth,
And possess joys not promised at my birth.
But when this master of the spell, not content to have laid a soul
prostrate, goes on, in his power, to inflict more bliss than lies in
her capacity to receive,--impatient to overcome her "earthly" with his
"heavenly,"--still pouring in, for protracted hours, fresh waves and
fresh from the sea of sound, or from that inexhausted _German_ ocean,
above which, in triumphant progress, dolphin-seated, ride those
Arions _Haydn_ and _Mozart_, with their attendant tritons, _Bach_,
_Beethoven_, and a countless tribe, whom to attempt to reckon up
would but plunge me again in the deeps,--I stagger under the weight
of harmony, reeling to and fro at my wit's end;--clouds, as of
frankincense, oppress me--priests, altars, censers, dazzle before
me--the genius of _his_ religion hath me in her toils--a shadowy
triple tiara invests the brow of my friend, late so naked, so
ingenuous he is Pope, and by him sits, like as in the anomaly of
dreams, a she-Pope too,--tri-coroneted like himself!--I am converted,
and yet a Protestant;--at once _malleus hereticorum_, and myself grand
heresiarch: or three heresies centre in my person:--I am Marcion,
Ebion, and Cerinthus--Gog and Magog--what not?--till the coming in of
the friendly supper-tray dissipates the figment, and a draught of true
Lutheran beer (in which chiefly my friend shows himself no bigot) at
once reconciles me to the rationalities of a purer faith; and restores
to me the genuine unterrifying aspects of my pleasant-countenanced
host and hostess.
[Footnote 1:
I have been there, and still would go;
'Tis like a little heaven below.--_Dr. Watts_.]
ALL FOOLS' DAY
The compliments of the season to my worthy masters, and a merry first
of April to us all!
Many happy returns of this day to you--and you--and _you_, Sir--nay,
never frown, man, nor put a long face upon the matter. Do not we know
one another? what need of ceremony among friends? we have all a touch
of _that same_--you understand me--a speck of the motley. Beshrew
the man who on such a day as this, the _general festival_, should
affect to stand aloof. I am none of those sneakers. I am free of the
corporation, and care not who knows it. He that meets me in the forest
to-day, shall meet with no wise-acre, I can tell him. _Stultus sum_.
Translate me that, and take the meaning of it to yourself for your
pains. What, man, we have four quarters of the globe on our side, at
the least computation.
Fill us a cup of that sparkling gooseberry--we will drink no wise,
melancholy, politic port on this day--and let us troll the catch of
Amiens--_duc ad me_--_duc ad me_--how goes it?
Here shall he see
Gross fools as he.
Now would I give a trifle to know historically and authentically, who
was the greatest fool that ever lived. I would certainly give him in
a bumper. Marry, of the present breed, I think I could without much
difficulty name you the party.
Remove your cap a little further, if you please: it hides my bauble.
And now each man bestride his hobby, and dust away his bells to what
tune he pleases. I will give you, for my part,
--The crazy old church clock.
And the bewildered chimes.
Good master Empedocles, you are welcome. It is long since you went a
salamander-gathering down AEtna. Worse than samphire-picking by some
odds. 'Tis a mercy your worship did not singe your mustachios.
Ha! Cleombrotus! and what salads in faith did you light upon at the
bottom of the Mediterranean? You were founder, I take it, of the
disinterested sect of the Calenturists.
Gebir, my old free-mason, and prince of plasterers at Babel, bring
in your trowel, most Ancient Grand! You have claim to a seat here at
my right hand, as patron of the stammerers. You left your work, if
I remember Herodotus correctly, at eight hundred million toises, or
thereabout, above the level of the sea. Bless us, what a long bell you
must have pulled, to call your top workmen to their nuncheon on the
low grounds of Sennaar. Or did you send up your garlick and onions by
a rocket? I am a rogue if I am not ashamed to show you our Monument on
Fish-street Hill, after your altitudes. Yet we think it somewhat.
What, the magnanimous Alexander in tears?--cry, baby, put its finger
in its eye, it shall have another globe, round as an orange, pretty
moppet!
Mister Adams--'odso, I honour your coat--pray do us the favour to read
to us that sermon, which you lent to Mistress Slipslop--the twenty and
second in your portmanteau there--on Female Incontinence--the same--it
will come in most irrelevantly and impertinently seasonable to the
time of the day.
Good Master Raymund Lully, you look wise. Pray correct that error.--
Duns, spare your definitions. I must fine you a bumper, or a paradox.
We will have nothing said or done syllogistically this day. Remove
those logical forms, waiter, that no gentleman break the tender shins
of his apprehension stumbling across them.
Master Stephen, you are late.--Ha! Cokes, is it you?--Aguecheek,
my dear knight, let me pay my devoir to you.--Master Shallow, your
worship's poor servant to command.--Master Silence, I will use few
words with you.--Slender, it shall go hard if I edge not you in
somewhere.--You six will engross all the poor wit of the company
to-day.--I know it, I know it.
Ha! honest R----, my fine old Librarian of Ludgate, time out of mind,
art thou here again? Bless thy doublet, it is not over-new, threadbare
as thy stories:--what dost thou flitting about the world at this
rate?--Thy customers are extinct, defunct, bed-rid, have ceased to
read long ago.--Thou goest still among them, seeing if, peradventure,
thou canst hawk a volume or two.--Good Granville S----, thy last
patron, is flown.
King Pandion, he is dead,
All thy friends are lapt in lead.--
Nevertheless, noble R----, come in, and take your seat here, between
Armado and Quisada: for in true courtesy, in gravity, in fantastic
smiling to thyself, in courteous smiling upon others, in the goodly
ornature of well-apparelled speech, and the commendation of wise
sentences, thou art nothing inferior to those accomplished Dons of
Spain. The spirit of chivalry forsake me for ever, when I forget thy
singing the song of Macheath, which declares that he might be _happy
with either_, situated between those two ancient spinsters--when I
forget the inimitable formal love which thou didst make, turning now
to the one, and now to the other, with that Malvolian smile--as if
Cervantes, not Gay, had written it for his hero; and as if thousands
of periods must revolve, before the mirror of courtesy could have
given his invidious preference between a pair of so goodly-propertied
and meritorious-equal damsels, * * * * *
To descend from these altitudes, and not to protract our Fools'
Banquet beyond its appropriate day,--for I fear the second of April
is not many hours distant--in sober verity I will confess a truth to
thee, reader. I love a _Fool_--as naturally, as if I were of kith and
kin to him. When a child, with child-like apprehensions, that dived
not below the surface of the matter, I read those _Parables_--not
guessing at their involved wisdom--I had more yearnings towards
that simple architect, that built his house upon the sand, than I
entertained for his more cautious neighbour; I grudged at the
hard censure pronounced upon the quiet soul that kept his talent;
and--prizing their simplicity beyond the more provident, and, to my
apprehension, somewhat _unfeminine_ wariness of their competitors--I
felt a kindliness, that almost amounted to a _tendre_, for those five
thoughtless virgins.--I have never made an acquaintance since, that
lasted; or a friendship, that answered; with any that had not some
tincture of the absurd in their characters. I venerate an honest
obliquity of understanding. The more laughable blunders a man shall
commit in your company, the more tests he giveth you, that he will
not betray or overreach you. I love the safety, which a palpable
hallucination warrants; the security, which a word out of season
ratifies. And take my word for this, reader, and say a fool
told it you, if you please, that he who hath not a dram of
folly in his mixture, hath pounds of much worse matter in his
composition. It is observed, that "the foolisher the fowl or
fish,--woodcocks,--dotterels,--cod's-heads, &c. the finer the flesh
thereof," and what are commonly the world's received fools, but such
whereof the world is not worthy? and what have been some of the
kindliest patterns of our species, but so many darlings of absurdity,
minions of the goddess, and, her white boys?--Reader, if you wrest my
words beyond their fair construction, it is you, and not I, that are
the _April Fool_.
A QUAKER'S MEETING
Still-born Silence! thou that art
Flood-gate of the deeper heart!
Offspring of a heavenly kind!
Frost o' the mouth, and thaw o' the mind!
Secrecy's confident, and he
Who makes religion mystery!
Admiration's speaking'st tongue!
Leave, thy desert shades among,
Reverend hermits' hallowed cells,
Where retired devotion dwells!
With thy enthusiasms come,
Seize our tongues, and strike us dumb![1]
Reader, would'st thou know what true peace and quiet mean; would'st
thou find a refuge from the noises and clamours of the multitude;
would'st thou enjoy at once solitude and society; would'st thou
possess the depth of thy own spirit in stillness, without being shut
out from the consolatory faces of thy species; would'st thou be alone,
and yet accompanied; solitary, yet not desolate; singular, yet not
without some to keep thee in countenance; a unit in aggregate; a
simple in composite:--come with me into a Quaker's Meeting.
Dost thou love silence deep as that "before the winds were made?" go
not out into the wilderness, descend not into the profundities of the
earth; shut not up thy casements; nor pour wax into the little cells
of thy ears, with little-faith'd self-mistrusting Ulysses.--Retire
with me into a Quaker's Meeting.
For a man to refrain even from good words, and to hold his peace, it
is commendable; but for a multitude, it is great mastery.
What is the stillness of the desert, compared with this place? what
the uncommunicating muteness of fishes?--here the goddess reigns and
revels.--"Boreas, and Cesias, and Argestes loud," do not with their
inter-confounding uproars more augment the brawl--nor the waves of the
blown Baltic with their clubbed sounds--than their opposite (Silence
her sacred self) is multiplied and rendered more intense by numbers,
and by sympathy. She too hath her deeps, that call unto deeps.
Negation itself hath a positive more and less; and closed eyes would
seem to obscure the great obscurity of midnight.
There are wounds, which an imperfect solitude cannot heal. By
imperfect I mean that which a man enjoyeth by himself. The perfect
is that which he can sometimes attain in crowds, but nowhere so
absolutely as in a Quaker's Meeting.--Those first hermits did
certainly understand this principle, when they retired into Egyptian
solitudes, not singly, but in shoals, to enjoy one another's want of
conversation. The Carthusian is bound to his brethren by this agreeing
spirit of incommunicativeness. In secular occasions, what so pleasant
as to be reading a book through a long winter evening, with a friend
sitting by--say, a wife--he, or she, too, (if that be probable),
reading another, without interruption, or oral communication?--can
there be no sympathy without the gabble of words?--away with this
inhuman, shy, single, shade-and-cavern-haunting solitariness. Give me,
Master Zimmerman, a sympathetic solitude.
To pace alone in the cloisters, or side aisles of some cathedral,
time-stricken;
Or under hanging mountains,
Or by the fall of fountains;
is but a vulgar luxury, compared with that which those enjoy, who come
together for the purposes of more complete, abstracted solitude. This
is the loneliness "to be felt."--The Abbey Church of Westminster hath
nothing so solemn, so spirit-soothing, as the naked walls and benches
of a Quaker's Meeting. Here are no tombs, no inscriptions,
--sands, ignoble things,
Dropt from the ruined sides of kings--
but here is something, which throws Antiquity herself into
the fore-ground--SILENCE--eldest of things--language of old
Night--primitive Discourser--to which the insolent decays of
mouldering grandeur have but arrived by a violent, and, as we may say,
unnatural progression.
How reverend is the view of these hushed heads,
Looking tranquillity!
Nothing-plotting, nought-caballing, unmischievous synod! convocation
without intrigue! parliament without debate! what a lesson dost
thou read to council, and to consistory!--if my pen treat of you
lightly--as haply it will wander--yet my spirit hath gravely felt the
wisdom of your custom, when sitting among you in deepest peace, which
some out-welling tears would rather confirm than disturb, I have
reverted to the times of your beginnings, and the sowings of the seed
by Fox and Dewesbury.--I have witnessed that, which brought before
my eyes your heroic tranquillity, inflexible to the rude jests and
serious violences of the insolent soldiery, republican or royalist,
sent to molest you--for ye sate betwixt the fires of two persecutions,
the out-cast and off-scowering of church and presbytery.--I have seen
the reeling sea-ruffian, who had wandered into your receptacle, with
the avowed intention of disturbing your quiet, from the very spirit of
the place receive in a moment a new heart, and presently sit among ye
as a lamb amidst lambs. And I remembered Penn before his accusers, and
Fox in the bail-dock, where he was lifted up in spirit, as he tells
us, and "the Judge and the Jury became as dead men under his feet."
Reader, if you are not acquainted with it, I would recommend to you,
above all church-narratives, to read Sewel's History of the Quakers.
It is in folio, and is the abstract of the journals of Fox, and the
primitive Friends. It is far more edifying and affecting than any
thing you will read of Wesley and his colleagues. Here is nothing to
stagger you, nothing to make you mistrust, no suspicion of alloy,
no drop or dreg of the worldly or ambitious spirit. You will here
read the true story of that much-injured, ridiculed man (who perhaps
hath been a by-word in your mouth,)--James Naylor: what dreadful
sufferings, with what patience, he endured even to the boring through
of his tongue with red-hot irons without a murmur; and with what
strength of mind, when the delusion he had fallen into, which they
stigmatised for blasphemy, had given way to clearer thoughts, he could
renounce his error, in a strain of the beautifullest humility, yet
keep his first grounds, and be a Quaker still!--so different from
the practice of your common converts from enthusiasm, who, when they
apostatize, _apostatize all_, and think they can never get far enough
from the society of their former errors, even to the renunciation of
some saving truths, with which they had been mingled, not implicated.
Get the Writings of John Woolman by heart; and love the early Quakers.
How far the followers of these good men in our days have kept to
the primitive spirit, or in what proportion they have substituted
formality for it, the Judge of Spirits can alone determine. I have
seen faces in their assemblies, upon which the dove sate visibly
brooding. Others again I have watched, when my thoughts should have
been better engaged, in which I could possibly detect nothing but a
blank inanity. But quiet was in all, and the disposition to unanimity,
and the absence of the fierce controversial workings.--If the
spiritual pretensions of the Quakers have abated, at least they make
few pretences. Hypocrites they certainly are not, in their preaching.
It is seldom indeed that you shall see one get up amongst them to hold
forth. Only now and then a trembling, female, generally _ancient_,
voice is heard--you cannot guess from what part of the meeting it
proceeds--with a low, buzzing, musical sound, laying out a few words
which "she thought might suit the condition of some present," with a
quaking diffidence, which leaves no possibility of supposing that any
thing of female vanity was mixed up, where the tones were so full of
tenderness, and a restraining modesty.--The men, for what I observed,
speak seldomer.
Once only, and it was some years ago, I witnessed a sample of the
old Foxian orgasm. It was a man of giant stature, who, as Wordsworth
phrases it, might have danced "from head to foot equipt in iron mail."
His frame was of iron too. But _he_ was malleable. I saw him shake
all over with the spirit--I dare not say, of delusion. The strivings
of the outer man were unutterable--he seemed not to speak, but to
be spoken from. I saw the strong man bowed down, and his knees to
fail--his joints all seemed loosening--it was a figure to set off
against Paul Preaching--the words he uttered were few, and sound--he
was evidently resisting his will--keeping down his own word-wisdom
with more mighty effort, than the world's orators strain for theirs.
"He had been a WIT in his youth," he told us, with expressions of a
sober remorse. And it was not till long after the impression had begun
to wear away, that I was enabled, with something like a smile, to
recall the striking incongruity of the confession--understanding the
term in its worldly acceptation--with the frame and physiognomy of the
person before me. His brow would have scared away the Levities--the
Jocos Risus-que--faster than the Loves fled the face of Dis at
Enna.--By _wit_, even in his youth, I will be sworn he understood
something far within the limits of an allowable liberty.
More frequently the Meeting is broken up without a word having been
spoken. But the mind has been fed. You go away with a sermon, not made
with hands. You have been in the milder caverns of Trophonius; or as
in some den, where that fiercest and savagest of all wild creatures,
the TONGUE, that unruly member, has strangely lain tied up and
captive. You have bathed with stillness.--O when the spirit is sore
fretted, even tired to sickness of the janglings, and nonsense-noises
of the world, what a balm and a solace it is, to go and seat yourself,
for a quiet half hour, upon some undisputed corner of a bench, among
the gentle Quakers!
Their garb and stillness conjoined, present an uniformity, tranquil
and herd-like--as in the pasture--"forty feeding like one."--
The very garments of a Quaker seem incapable of receiving a soil;
and cleanliness in them to be something more than the absence of its
contrary. Every Quakeress is a lily; and when they come up in bands
to their Whitsun-conferences, whitening the easterly streets of the
metropolis, from all parts of the United Kingdom, they show like
troops of the Shining Ones.
[Footnote 1: From "Poems of all sorts," by Richard Fleckno, 1653.]
THE OLD AND THE NEW SCHOOLMASTER
My reading has been lamentably desultory and immethodical. Odd, out of
the way, old English plays, and treatises, have supplied me with most
of my notions, and ways of feeling. In every thing that relates to
_science_, I am a whole Encyclopaedia behind the rest of the world.
I should have scarcely cut a figure among the franklins, or country
gentlemen, in king John's days. I know less geography than a
school-boy of six weeks' standing. To me a map of old Ortelius is as
authentic as Arrowsmith. I do not know whereabout Africa merges into
Asia; whether Ethiopia lie in one or other of those great divisions;
nor can form the remotest conjecture of the position of New South
Wales, or Van Diemen's Land. Yet do I hold a correspondence with a
very dear friend in the first-named of these two Terrae Incognitae.
I have no astronomy. I do not know where to look for the Bear, or
Charles's Wain; the place of any star; or the name of any of them at
sight. I guess at Venus only by her brightness--and if the sun on
some portentous morn were to make his first appearance in the West, I
verily believe, that, while all the world were gasping in apprehension
about me, I alone should stand unterrified, from sheer incuriosity
and want of observation. Of history and chronology I possess some
vague points, such as one cannot help picking up in the course of
miscellaneous study; but I never deliberately sat down to a chronicle,
even of my own country. I have most dim apprehensions of the four
great monarchies; and sometimes the Assyrian, sometimes the Persian,
floats as _first_ in my fancy. I make the widest conjectures
concerning Egypt, and her shepherd kings. My friend _M._, with great
painstaking, got me to think I understood the first proposition in
Euclid, but gave me over in despair at the second. I am entirely
unacquainted with the modern languages; and, like a better man than
myself, have "small Latin and less Greek." I am a stranger to the
shapes and texture of the commonest trees, herbs, flowers--not from
the circumstance of my being town-born--for I should have brought the
same inobservant spirit into the world with me, had I first seen it
in "on Devon's leafy shores,"--and am no less at a loss among purely
town-objects, tools, engines, mechanic processes.--Not that I affect
ignorance--but my head has not many mansions, nor spacious; and I have
been obliged to fill it with such cabinet curiosities as it can hold
without aching. I sometimes wonder, how I have passed my probation
with so little discredit in the world, as I have done, upon so meagre
a stock. But the fact is, a man may do very well with a very little
knowledge, and scarce be found out, in mixed company; every body is so
much more ready to produce his own, than to call for a display of your
acquisitions. But in a _tete-a-tete_ there is no shuffling. The truth
will out. There is nothing which I dread so much, as the being left
alone for a quarter of an hour with a sensible, well-informed man,
that does not know me. I lately got into a dilemma of this sort.--
In one of my daily jaunts between Bishopsgate and Shacklewell, the
coach stopped to take up a staid-looking gentleman, about the wrong
side of thirty, who was giving his parting directions (while the
steps were adjusting), in a tone of mild authority, to a tall youth,
who seemed to be neither his clerk, his son, nor his servant, but
something partaking of all three. The youth was dismissed, and
we drove on. As we were the sole passengers, he naturally enough
addressed his conversation to me; and we discussed the merits of the
fare, the civility and punctuality of the driver; the circumstance of
an opposition coach having been lately set up, with the probabilities
of its success--to all which I was enabled to return pretty
satisfactory answers, having been drilled into this kind of etiquette
by some years' daily practice of riding to and fro in the stage
aforesaid--when he suddenly alarmed me by a startling question,
whether I had seen the show of prize cattle that morning in
Smithfield? Now as I had not seen it, and do not greatly care for
such sort of exhibitions, I was obliged to return a cold negative. He
seemed a little mortified, as well as astonished, at my declaration,
as (it appeared) he was just come fresh from the sight, and doubtless
had hoped to compare notes on the subject. However he assured me that
I had lost a fine treat, as it far exceeded the show of last year. We
were now approaching Norton Falgate, when the sight of some shop-goods
_ticketed_ freshened him up into a dissertation upon the cheapness of
cottons this spring. I was now a little in heart, as the nature of my
morning avocations had brought me into some sort of familiarity with
the raw material; and I was surprised to find how eloquent I was
becoming on the state of the India market--when, presently, he dashed
my incipient vanity to the earth at once, by inquiring whether I had
ever made any calculation as to the value of the rental of all the
retail shops in London. Had he asked of me, what song the Sirens sang,
or what name Achilles assumed when he hid himself among women, I
might, with Sir Thomas Browne, have hazarded a "wide solution."[1] My
companion saw my embarrassment, and, the almshouses beyond Shoreditch
just coming in view, with great good-nature and dexterity shifted
his conversation to the subject of public charities; which led to
the comparative merits of provision for the poor in past and present
times, with observations on the old monastic institutions, and
charitable orders;--but, finding me rather dimly impressed with
some glimmering notions from old poetic associations, than strongly
fortified with any speculations reducible to calculation on the
subject, he gave the matter up; and, the country beginning to open
more and more upon us, as we approached the turnpike at Kingsland (the
destined termination of his journey), he put a home thrust upon me, in
the most unfortunate position he could have chosen, by advancing some
queries relative to the North Pole Expedition. While I was muttering
out something about the Panorama of those strange regions (which I had
actually seen), by way of parrying the question, the coach stopping
relieved me from any further apprehensions. My companion getting out,
left me in the comfortable possession of my ignorance; and I heard
him, as he went off, putting questions to an outside passenger, who
had alighted with him, regarding an epidemic disorder, that had been
rife about Dalston; and which, my friend assured him, had gone through
five or six schools in that neighbourhood. The truth now flashed upon
me, that my companion was a schoolmaster; and that the youth, whom he
had parted from at our first acquaintance, must have been one of the
bigger boys, or the usher.--He was evidently a kind-hearted man, who
did not seem so much desirous of provoking discussion by the questions
which he put, as of obtaining information at any rate. It did not
appear that he took any interest, either, in such kind of inquiries,
for their own sake; but that he was in some way bound to seek for
knowledge. A greenish- coat, which he had on, forbade me to
surmise that he was a clergyman. The adventure gave birth to some
reflections on the difference between persons of his profession in
past and present times.
Rest to the souls of those fine old Pedagogues; the breed, long
since extinct, of the Lilys, and the Linacres: who believing that
all learning was contained in the languages which they taught, and
despising every other acquirement as superficial and useless, came to
their task as to a sport! Passing from infancy to age, they dreamed
away all their days as in a grammar-school. Revolving in a perpetual
cycle of declensions, conjugations, syntaxes, and prosodies; renewing
constantly the occupations which had charmed their studious childhood;
rehearsing continually the part of the past; life must have slipped
from them at last like one day. They were always in their first
garden, reaping harvests of their golden time, among their _Flori_ and
their _Spici-legia_; in Arcadia still, but kings; the ferule of their
sway not much harsher, but of like dignity with that mild sceptre
attributed to king Basileus; the Greek and Latin, their stately Pamela
and their Philoclea; with the occasional duncery of some untoward
Tyro, serving for a refreshing interlude of a Mopsa, or a clown
Damaetas!
With what a savour doth the Preface to Colet's, or (as it is sometimes
called) Paul's Accidence, set forth! "To exhort every man to the
learning of grammar, that intendeth to attain the understanding of
the tongues, wherein is contained a great treasury of wisdom and
knowledge, it would seem but vain and lost labour; for so much as it
is known, that nothing can surely be ended, whose beginning is either
feeble or faulty; and no building be perfect, whereas the foundation
and ground-work is ready to fall, and unable to uphold the burden of
the frame." How well doth this stately preamble (comparable to those
which Milton commendeth as "having been the usage to prefix to some
solemn law, then first promulgated by Solon, or Lycurgus") correspond
with and illustrate that pious zeal for conformity, expressed in a
succeeding clause, which would fence about grammar-rules with the
severity of faith-articles!--"as for the diversity of grammars, it
is well profitably taken away by the king majesties wisdom, who
foreseeing the inconvenience, and favourably providing the remedie,
caused one kind of grammar by sundry learned men to be diligently
drawn, and so to be set out, only everywhere to be taught for the use
of learners, and for the hurt in changing of schoolmaisters." What a
_gusto_ in that which follows: "wherein it is profitable that he can
orderly decline his noun, and his verb." _His_ noun!
The fine dream is fading away fast; and the least concern of a teacher
in the present day is to inculcate grammar-rules.
The modern schoolmaster is expected to know a little of every thing,
because his pupil is required not to be entirely ignorant of any
thing. He must be superficially, if I may so say, omniscient. He is to
know something of pneumatics; of chemistry; of whatever is curious,
or proper to excite the attention of the youthful mind; an insight
into mechanics is desirable, with a touch of statistics; the quality
of soils, &c. botany, the constitution of his country, _cum multis
aliis_. You may get a notion of some part of his expected duties by
consulting the famous Tractate on Education addressed to Mr. Hartlib.
All these things--these, or the desire of them--he is expected to
instil, not by set lessons from professors, which he may charge in the
bill, but at school-intervals, as he walks the streets, or saunters
through green fields (those natural instructors), with his pupils.
The least part of what is expected from him, is to be done in
school-hours. He must insinuate knowledge at the _mollia tempera
fandi_. He must seize every occasion--the season of the year--the time
of the day--a passing cloud--a rainbow--a wagon of hay--a regiment of
soldiers going by--to inculcate something useful. He can receive no
pleasure from a casual glimpse of Nature, but must catch at it as an
object of instruction. He must interpret beauty into the picturesque.
He cannot relish a beggar-man, or a gipsy, for thinking of the
suitable improvement. Nothing comes to him, not spoiled by the
sophisticating medium of moral uses. The Universe--that Great Book, as
it has been called--is to him indeed, to all intents and purposes, a
book, out of which he is doomed to read tedious homilies to distasting
schoolboys.--Vacations themselves are none to him, he is only rather
worse off than before; for commonly he has some intrusive upper-boy
fastened upon him at such times; some cadet of a great family; some
neglected lump of nobility, or gentry; that he must drag after him to
the play, to the Panorama, to Mr. Bartley's Orrery, to the Panopticon,
or into the country, to a friend's house, or to his favourite
watering-place. Wherever he goes, this uneasy shadow attends him. A
boy is at his board, and in his path, and in all his movements. He is
boy-rid, sick of perpetual boy.
Boys are capital fellows in their own way, among their mates; but
they are unwholesome companions for grown people. The restraint is
felt no less on the one side, than on the other.--Even a child, that
"plaything for an hour," tires _always_. The noises of children,
playing their own fancies--as I now hearken to them by fits, sporting
on the green before my window, while I am engaged in these grave
speculations at my neat suburban retreat at Shacklewell--by distance
made more sweet--inexpressibly take from the labour of my task. It is
like writing to music. They seem to modulate my periods. They ought at
least to do so--for in the voice of that tender age there is a kind of
poetry, far unlike the harsh prose-accents of man's conversation.--I
should but spoil their sport, and diminish my own sympathy for them,
by mingling in their pastime.
I would not be domesticated all my days with a person of very
superior capacity to my own--not, if I know myself at all, from any
considerations of jealousy or self-comparison, for the occasional
communion with such minds has constituted the fortune and felicity of
my life--but the habit of too constant intercourse with spirits above
you, instead of raising you, keeps you down. Too frequent doses of
original thinking from others, restrain what lesser portion of that
faculty you may possess of your own. You get entangled in another
man's mind, even as you lose yourself in another man's grounds. You
are walking with a tall varlet, whose strides out-pace yours to
lassitude. The constant operation of such potent agency would reduce
me, I am convinced, to imbecility. You may derive thoughts from
others; your way of thinking, the mould in which your thoughts are
cast, must be your own. Intellect may be imparted, but not each man's
intellectual frame.--
As little as I should wish to be always thus dragged upwards, as
little (or rather still less) is it desirable to be stunted downwards
by your associates. The trumpet does not more stun you by its
loudness, than a whisper teases you by its provoking inaudibility.
Why are we never quite at our ease in the presence of a
schoolmaster?--because we are conscious that he is not quite at his
ease in ours. He is awkward, and out of place, in the society of his
equals. He comes like Gulliver from among his little people, and he
cannot fit the stature of his understanding to yours. He cannot meet
you on the square. He wants a point given him, like an indifferent
whist-player. He is so used to teaching, that he wants to be teaching
_you_. One of these professors, upon my complaining that these little
sketches of mine were any thing but methodical, and that I was unable
to make them otherwise, kindly offered to instruct me in the method by
which young gentlemen in _his_ seminary were taught to compose English
themes.--The jests of a schoolmaster are coarse, or thin. They do
not _tell_ out of school. He is under the restraint of a formal and
didactive hypocrisy in company, as a clergyman is under a moral one.
He can no more let his intellect loose in society, than the other
can his inclinations.--He is forlorn among his co-evals; his juniors
cannot be his friends.
"I take blame to myself," said a sensible man of this profession,
writing to a friend respecting a youth who had quitted his school
abruptly, "that your nephew was not more attached to me. But persons
in my situation are more to be pitied, than can well be imagined. We
are surrounded by young, and, consequently, ardently affectionate
hearts, but _we_ can never hope to share an atom of their affections.
The relation of master and scholar forbids this. _How pleasing this
must be to you, how I envy your feelings_, my friends will sometimes
say to me, when they see young men, whom I have educated, return after
some years absence from school, their eyes shining with pleasure,
while they shake hands with their old master, bringing a present of
game to me, or a toy to my wife, and thanking me in the warmest terms
for my care of their education. A holiday is begged for the boys;
the house is a scene of happiness; I, only, am sad at heart--This
fine-spirited and warm-hearted youth, who fancies he repays his master
with gratitude for the care of his boyish years--this young man--in
the eight long years I watched over him with a parent's anxiety, never
could repay me with one look of genuine feeling. He was proud, when
I praised; he was submissive, when I reproved him; but he did never
_love_ me--and what he now mistakes for gratitude and kindness for me,
is but the pleasant sensation, which all persons feel at revisiting
the scene of their boyish hopes and fears; and the seeing on equal
terms the man they were accustomed to look up to with reverence.
My wife too," this interesting correspondent goes on to say, "my
once darling Anna, is the wife of a schoolmaster.--When I married
her--knowing that the wife of a schoolmaster ought to be a busy
notable creature, and fearing that my gentle Anna would ill supply the
loss of my dear bustling mother, just then dead, who never sat still,
was in every part of the house in a moment, and whom I was obliged
sometimes to threaten to fasten down in a chair, to save her from
fatiguing herself to death--I expressed my fears, that I was bringing
her into a way of life unsuitable to her; and she, who loved me
tenderly, promised for my sake to exert herself to perform the duties
of her new situation. She promised, and she has kept her word. What
wonders will not woman's love perform?--My house is managed with a
propriety and decorum, unknown in other schools; my boys are well
fed, look healthy, and have every proper accommodation; and all this
performed with a careful economy, that never descends to meanness. But
I have lost my gentle, _helpless_ Anna!--When we sit down to enjoy an
hour of repose after the fatigue of the day, I am compelled to listen
to what have been her useful (and they are really useful) employments
through the day, and what she proposes for her to-morrow's task. Her
heart and her features are changed by the duties of her situation. To
the boys, she never appears other than the _master's wife_, and she
looks up to me as the _boys' master_; to whom all show of love and
affection would be highly improper, and unbecoming the dignity of her
situation and mine. Yet _this_ my gratitude forbids me to hint to
her. For my sake she submitted to be this altered creature, and can
I reproach her for it?"--For the communication of this letter, I am
indebted to my cousin Bridget.
[Footnote 1: Urn Burial.]
VALENTINE'S DAY
Hail to thy returning festival, old Bishop Valentine! Great is thy
name in the rubric, thou venerable Archflamen of Hymen! Immortal
Go-between! who and what manner of person art thou? Art thou but a
_name_, typifying the restless principle which impels poor humans to
seek perfection in union? or wert thou indeed a mortal prelate, with
thy tippet and thy rochet, thy apron on, and decent lawn sleeves?
Mysterious personage! like unto thee, assuredly, there is no other
mitred father in the calendar; not Jerome, nor Ambrose, nor Cyril;
nor the consigner of undipt infants to eternal torments, Austin, whom
all mothers hate; nor he who hated all mothers, Origen; nor Bishop
Bull, nor Archbishop Parker, nor Whitgift. Thou comest attended with
thousands and ten thousands of little Loves, and the air is
Brush'd with the hiss of rustling wings.
Singing Cupids are thy choristers and thy precentors; and instead of
the crosier, the mystical arrow is borne before thee.
In other words, this is the day on which those charming little
missives, ycleped Valentines, cross and intercross each other at every
street and turning. The weary and all forspent twopenny postman sinks
beneath a load of delicate embarrassments, not his own. It is scarcely
credible to what an extent this ephemeral courtship is carried on in
this loving town, to the great enrichment of porters, and detriment
of knockers and bell-wires. In these little visual interpretations,
no emblem is so common as the _heart_,--that little three-cornered
exponent of all our hopes and fears,--the bestuck and bleeding heart;
it is twisted and tortured into more allegories and affectations
than an opera hat. What authority we have in history or mythology
for placing the head-quarters and metropolis of God Cupid in this
anatomical seat rather than in any other, is not very clear; but we
have got it, and it will serve as well as any other. Else we might
easily imagine, upon some other system which might have prevailed
for any thing which our pathology knows to the contrary, a lover
addressing his mistress, in perfect simplicity of feeling, "Madam,
my _liver_ and fortune are entirely at your disposal;" or putting
a delicate question, "Amanda, have you a _midriff_ to bestow?" But
custom has settled these things, and awarded the seat of sentiment to
the aforesaid triangle, while its less fortunate neighbours wait at
animal and anatomical distance.
Not many sounds in life, and I include all urban and all rural sounds,
exceed in interest a _knock at the door_. It "gives a very echo to
the throne where Hope is seated." But its issues seldom answer to
this oracle within. It is so seldom that just the person we want to
see comes. But of all the clamorous visitations the welcomest in
expectation is the sound that ushers in, or seems to usher in, a
Valentine. As the raven himself was hoarse that announced the fatal
entrance of Duncan, so the knock of the postman on this day is light,
airy, confident, and befitting one that bringeth good tidings. It is
less mechanical than on other days; you will say, "That is not the
post, I am sure." Visions of Love, of Cupids, of Hymens!--delightful
eternal common-places, which "having been will always be;" which no
school-boy nor school-man can write away; having your irreversible
throne in the fancy and affections--what are your transports, when the
happy maiden, opening with careful finger, careful not to break the
emblematic seal, bursts upon the sight of some well-designed allegory,
some type, some youthful fancy, not without verses--
Lovers all,
A madrigal,
or some such device, not over abundant in sense--young Love disclaims
it,--and not quite silly--something between wind and water, a chorus
where the sheep might almost join the shepherd, as they did, or as I
apprehend they did, in Arcadia.
All Valentines are not foolish; and I shall not easily forget thine,
my kind friend (if I may have leave to call you so) E. B.--E.B. lived
opposite a young maiden, whom he had often seen, unseen, from his
parlour window in C--e-street. She was all joyousness and innocence,
and just of an age to enjoy receiving a Valentine, and just of a
temper to bear the disappointment of missing one with good humour.
E.B. is an artist of no common powers; in the fancy parts of
designing, perhaps inferior to none; his name is known at the bottom
of many a well executed vignette in the way of his profession, but no
further; for E.B. is modest, and the world meets nobody half-way. E.B.
meditated how he could repay this young maiden for many a favour which
she had done him unknown; for when a kindly face greets us, though but
passing by, and never knows us again, nor we it, we should feel it as
an obligation; and E.B. did. This good artist set himself at work to
please the damsel. It was just before Valentine's day three years
since. He wrought, unseen and unsuspected, a wondrous work. We need
not say it was on the finest gilt paper with borders--full, not of
common hearts and heartless allegory, but all the prettiest stories
of love from Ovid, and older poets than Ovid (for E.B. is a scholar.)
There was Pyramus and Thisbe, and be sure Dido was not forgot, nor
Hero and Leander, and swans more than sang in Cayster, with mottos
and fanciful devices, such as beseemed,--a work in short of magic.
Iris dipt the woof. This on Valentine's eve he commended to the
all-swallowing indiscriminate orifice--(O ignoble trust!)--of the
common post; but the humble medium did its duty, and from his watchful
stand, the next morning, he saw the cheerful messenger knock, and by
and by the precious charge delivered. He saw, unseen, the happy girl
unfold the Valentine, dance about, clap her hands, as one after one
the pretty emblems unfolded themselves. She danced about, not with
light love, or foolish expectations, for she had no lover; or, if she
had, none she knew that could have created those bright images which
delighted her. It was more like some fairy present; a God-send, as
our familiarly pious ancestors termed a benefit received, where the
benefactor was unknown. It would do her no harm. It would do her good
for ever after. It is good to love the unknown. I only give this as a
specimen of E.B. and his modest way of doing a concealed kindness.
Good-morrow to my Valentine, sings poor Ophelia; and no better wish,
but with better auspices, we wish to all faithful lovers, who are not
too wise to despise old legends, but are content to rank themselves
humble diocesans of old Bishop Valentine, and his true church.
IMPERFECT SYMPATHIES
I am of a constitution so general, that it consorts and sympathized
with all things, I have no antipathy, or rather idiosyncracy in any
thing. Those national repugnancies do not touch me, nor do I behold with
prejudice the French, Italian, Spaniard, or Dutch.--_Religio Medici_.
That the author of the Religio Medici, mounted upon the airy stilts
of abstraction, conversant about notional and conjectural essences;
in whose categories of Being the possible took the upper hand of
the actual; should have overlooked the impertinent individualities
of such poor concretions as mankind, is not much to be admired.
It is rather to be wondered at, that in the genus of animals he
should have condescended to distinguish that species at all. For
myself--earth-bound and fettered to the scene of my activities,--
Standing on earth, not rapt above the sky,
I confess that I do feel the differences of mankind, national or
individual, to an unhealthy excess. I can look with no indifferent
eye upon things or persons. Whatever is, is to me a matter of taste
or distaste; or when once it becomes indifferent, it begins to be
disrelishing. I am, in plainer words, a bundle of prejudices--made up
of likings and dislikings--the veriest thrall to sympathies, apathies,
antipathies. In a certain sense, I hope it may be said of me that I am
a lover of my species. I can feel for all indifferently, but I cannot
feel towards all equally. The more purely-English word that expresses
sympathy will better explain my meaning. I can be a friend to a worthy
man, who upon another account cannot be my mate or _fellow_. I cannot
_like_ all people alike.[1]
I have been trying all my life to like Scotchmen, and am obliged to
desist from the experiment in despair. They cannot like me--and in
truth, I never knew one of that nation who attempted to do it. There
is something more plain and ingenuous in their mode of proceeding.
We know one another at first sight. There is an order of imperfect
intellects (under which mine must be content to rank) which in its
constitution is essentially anti-Caledonian. The owners of the
sort of faculties I allude to, have minds rather suggestive than
comprehensive. They have no pretences to much clearness or precision
in their ideas, or in their manner of expressing them. Their
intellectual wardrobe (to confess fairly) has few whole pieces in it.
They are content with fragments and scattered pieces of Truth. She
presents no full front to them--a feature or side-face at the most.
Hints and glimpses, germs and crude essays at a system, is the utmost
they pretend to. They beat up a little game peradventure--and leave
it to knottier heads, more robust constitutions, to run it down.
The light that lights them is not steady and polar, but mutable and
shifting: waxing, and again waning. Their conversation is accordingly.
They will throw out a random word in or out of season, and be content
to let it pass for what it is worth. They cannot speak always as
if they were upon their oath--but must be understood, speaking
or writing, with some abatement. They seldom wait to mature a
proposition, but e'en bring it to market in the green ear. They
delight to impart their defective discoveries as they arise, without
waiting for their full developement. They are no systematizers, and
would but err more by attempting it. Their minds, as I said before,
are suggestive merely. The brain of a true Caledonian (if I am not
mistaken) is constituted upon quite a different plan. His Minerva is
born in panoply. You are never admitted to see his ideas in their
growth--if, indeed, they do grow, and are not rather put together upon
principles of clock-work. You never catch his mind in an undress. He
never hints or suggests any thing, but unlades his stock of ideas
in perfect order and completeness. He brings his total wealth into
company, and gravely unpacks it. His riches are always about him. He
never stoops to catch a glittering something in your presence, to
share it with you, before he quite knows whether it be true touch or
not. You cannot cry _halves_ to any thing that he finds. He does not
find, but bring. You never witness his first apprehension of a thing.
His understanding is always at its meridian--you never see the first
dawn, the early streaks.--He has no falterings of self-suspicion.
Surmises, guesses, misgivings, half-intuitions, semi-consciousnesses,
partial illuminations, dim instincts, embryo conceptions, have no
place in his brain, or vocabulary. The twilight of dubiety never falls
upon him. Is he orthodox--he has no doubts. Is he an infidel--he has
none either. Between the affirmative and the negative there is no
border-land with him. You cannot hover with him upon the confines of
truth, or wander in the maze of a probable argument. He always keeps
the path. You cannot make excursions with him--for he sets you right.
His taste never fluctuates. His morality never abates. He cannot
compromise, or understand middle actions. There can be but a right
and a wrong. His conversation is as a book. His affirmations have the
sanctity of an oath. You must speak upon the square with him. He stops
a metaphor like a suspected person in an enemy's country. "A healthy
book!"--said one of his countrymen to me, who had ventured to give
that appellation to John Buncle,--"did I catch rightly what you said?
I have heard of a man in health, and of a healthy state of body, but I
do not see how that epithet can be properly applied to a book." Above
all, you must beware of indirect expressions before a Caledonian.
Clap an extinguisher upon your irony, if you are unhappily blest
with a vein of it. Remember you are upon your oath. I have a print
of a graceful female after Leonardo da Vinci, which I was showing
off to Mr. ****. After he had examined it minutely, I ventured to
ask him how he liked MY BEAUTY (a foolish name it goes by among my
friends)--when he very gravely assured me, that "he had considerable
respect for my character and talents" (so he was pleased to say), "but
had not given himself much thought about the degree of my personal
pretensions." The misconception staggered me, but did not seem much
to disconcert him.--Persons of this nation are particularly fond
of affirming a truth--which nobody doubts. They do not so properly
affirm, as annunciate it. They do indeed appear to have such a love of
truth (as if, like virtue, it were valuable for itself) that all truth
becomes equally valuable, whether the proposition that contains it be
new or old, disputed, or such as is impossible to become a subject of
disputation. I was present not long since at a party of North Britons,
where a son of Burns was expected; and happened to drop a silly
expression (in my South British way), that I wished it were the father
instead of the son--when four of them started up at once to inform
me, that "that was impossible, because he was dead." An impracticable
wish, it seems, was more than they could conceive. Swift has hit off
this part of their character, namely their love of truth, in his
biting way, but with an illiberality that necessarily confines the
passage to the margin.[2] The tediousness of these people is certainly
provoking. I wonder if they ever tire one another!--In my early life
I had a passionate fondness for the poetry of Burns. I have sometimes
foolishly hoped to ingratiate myself with his countrymen by expressing
it. But I have always found that a true Scot resents your admiration
of his compatriot, even more than he would your contempt of him. The
latter he imputes to your "imperfect acquaintance with many of the
words which he uses;" and the same objection makes it a presumption
in you to suppose that you can admire him.--Thomson they seem to have
forgotten. Smollett they have neither forgotten nor forgiven for his
delineation of Rory and his companion, upon their first introduction
to our metropolis.--peak of Smollett as a great genius, and they will
retort upon you Hume's History compared with _his_ Continuation of it.
What if the historian had continued Humphrey Clinker?
I have, in the abstract, no disrespect for Jews. They are a piece of
stubborn antiquity, compared with which Stonehenge is in its nonage.
They date beyond the pyramids. But I should not care to be in habits
of familiar intercourse with any of that nation. I confess that I
have not the nerves to enter their synagogues. Old prejudices cling
about me. I cannot shake off the story of Hugh of Lincoln. Centuries
of injury, contempt, and hate, on the one side,--of cloaked revenge,
dissimulation, and hate, on the other, between our and their fathers,
must, and ought, to affect the blood of the children. I cannot believe
it can run clear and kindly yet; or that a few fine words, such as
candour, liberality, the light of a nineteenth century, can close up
the breaches of so deadly a disunion. A Hebrew is nowhere congenial
to me. He is least distasteful on 'Change--for the mercantile spirit
levels all distinctions, as all are beauties in the dark. I boldly
confess that I do not relish the approximation of Jew and Christian,
which has become so fashionable. The reciprocal endearments have, to
me, something hypocritical and unnatural in them. I do not like to see
the Church and Synagogue kissing and congeeing in awkward postures of
an affected civility. If _they_ are converted, why do they not come
over to us altogether? Why keep up a form of separation, when the
life of it is fled? If they can sit with us at table, why do they
keck at our cookery? I do not understand these half convertites. Jews
christianizing--Christians judaizing--puzzle me. I like fish or flesh.
A moderate Jew is a more confounding piece of anomaly than a wet
Quaker. The spirit of the synagogue is essentially _separative_. B----
would have been more in keeping if he had abided by the faith of his
forefathers. There is a fine scorn in his face, which nature meant to
be of ---- Christians. The Hebrew spirit is strong in him, in spite of
his proselytism. He cannot conquer the Shibboleth. How it breaks out,
when he sings, "The Children of Israel passed through the Red Sea!"
The auditors, for the moment, are as Egyptians to him, and he rides
over our necks in triumph. There is no mistaking him.--B---- has a
strong expression of sense in his countenance, and it is confirmed by
his singing. The foundation of his vocal excellence is sense. He sings
with understanding, as Kemble delivered dialogue. He would sing the
Commandments, and give an appropriate character to each prohibition.
His nation, in general, have not ever-sensible countenances. How
should they?--but you seldom see a silly expression among them.
Gain, and the pursuit of gain, sharpen a man's visage. I never heard
of an idiot being born among them.--Some admire the Jewish female
physiognomy. I admire it--but with trembling. Jael had those full dark
inscrutable eyes.
In the <DW64> countenance you will often meet with strong traits of
benignity. I have felt yearnings of tenderness towards some of these
faces--or rather masks--that have looked out kindly upon one in casual
encounters in the streets and highways. I love what Fuller beautifully
calls--these "images of God cut in ebony." But I should not like
to associate with them, to share my meals and my good-nights with
them--because they are black.
I love Quaker ways, and Quaker worship. I venerate the Quaker
principles. It does me good for the rest of the day when I meet any
of their people in my path. When I am ruffled or disturbed by any
occurrence, the sight, or quiet voice of a Quaker, acts upon me as a
ventilator, lightening the air, and taking off a load from the bosom.
But I cannot like the Quakers (as Desdemona would say) "to live with
them." I am all over sophisticated--with humours, fancies, craving
hourly sympathy. I must have books, pictures, theatres, chit-chat,
scandal, jokes, ambiguities, and a thousand whim-whams, which their
simpler taste can do without. I should starve at their primitive
banquet. My appetites are too high for the salads which (according to
Evelyn) Eve dressed for the angel, my gusto too excited
To sit a guest with Daniel at his pulse.
The indirect answers which Quakers are often found to return to a
question put to them may be explained, I think, without the vulgar
assumption, that they are more given to evasion and equivocating than
other people. They naturally look to their words more carefully, and
are more cautious of committing themselves. They have a peculiar
character to keep up on this head. They stand in a manner upon their
veracity. A Quaker is by law exempted from taking an oath. The custom
of resorting to an oath in extreme cases, sanctified as it is by all
religious antiquity, is apt (it must be confessed) to introduce into
the laxer sort of minds the notion of two kinds of truth--the one
applicable to the solemn affairs of justice, and the other to the
common proceedings of daily intercourse. As truth bound upon the
conscience by an oath can be but truth, so in the common affirmations
of the shop and the market-place a latitude is expected, and conceded
upon questions wanting this solemn covenant. Something less than truth
satisfies. It is common to hear a person say, "You do not expect me to
speak as if I were upon my oath." Hence a great deal of incorrectness
and inadvertency, short of falsehood, creeps into ordinary
conversation; and a kind of secondary or laic-truth is tolerated,
where clergy-truth--oath-truth, by the nature of the circumstances,
is not required. A Quaker knows none of this distinction. His simple
affirmation being received, upon the most sacred occasions, without
any further test, stamps a value upon the words which he is to use
upon the most indifferent topics of life. He looks to them, naturally,
with more severity. You can have of him no more than his word. He
knows, if he is caught tripping in a casual expression, he forfeits,
for himself, at least, his claim to the invidious exemption. He knows
that his syllables are weighed--and how far a consciousness of this
particular watchfulness, exerted against a person, has a tendency to
produce indirect answers, and a diverting of the question by honest
means, might be illustrated, and the practice justified, by a more
sacred example than is proper to be adduced upon this occasion. The
admirable presence of mind, which is notorious in Quakers upon all
contingencies, might be traced to this imposed self-watchfulness--if
it did not seem rather an humble and secular scion of that old stock
of religious constancy, which never bent or faltered, in the Primitive
Friends, or gave way to the winds of persecution, to the violence of
judge or accuser, under trials and racking examinations. "You will
never be the wiser, if I sit here answering your questions till
midnight," said one of those upright Justicers to Penn, who had been
putting law-cases with a puzzling subtlety. "Thereafter as the answers
may be," retorted the Quaker. The astonishing composure of this people
is sometimes ludicrously displayed in lighter instances.--I was
travelling in a stagecoach with three male Quakers, buttoned up in the
straitest non-conformity of their sect. We stopped to bait at Andover,
where a meal, partly tea apparatus, partly supper, was set before
us. My friends confined themselves to the tea-table. I in my way
took supper. When the landlady brought in the bill, the eldest of my
companions discovered that she had charged for both meals. This was
resisted. Mine hostess was very clamorous and positive. Some mild
arguments were used on the part of the Quakers, for which the heated
mind of the good lady seemed by no means a fit recipient. The guard
came in with his usual peremptory notice. The Quakers pulled out
their money, and formally tendered it.--so much for tea--I, in humble
imitation, tendering mine--for the supper which I had taken. She
would not relax in her demand. So they all three quietly put up their
silver, as did myself, and marched out of the room, the eldest and
gravest going first, with myself closing up the rear, who thought
I could not do better than follow the example of such grave and
warrantable personages. We got in. The steps went up. The coach drove
off. The murmurs of mine hostess, not very indistinctly or ambiguously
pronounced, became after a time inaudible--and now my conscience,
which the whimsical scene had for a while suspended, beginning to give
some twitches, I waited, in the hope that some justification would be
offered by these serious persons for the seeming injustice of their
conduct. To my great surprise, not a syllable was dropped on the
subject. They sate as mute as at a meeting. At length the eldest of
them broke silence, by inquiring of his next neighbour, "Hast thee
heard how indigos go at the India House?" and the question operated as
a soporific on my moral feeling as far as Exeter.
[Footnote 1: I would be understood as confining myself to the subject
of _imperfect sympathies_. To nations or classes of men there can be
no direct _antipathy_. There may be individuals born and constellated
so opposite to another individual nature, that the same sphere cannot
hold them. I have met with my moral antipodes, and can believe the
story of two persons meeting (who never saw one another before in
their lives) and instantly fighting.
--We by proof find there should be
Twixt man and man such an antipathy,
That though he can show no just reason why
For any former wrong or injury,
Can neither find a blemish in his fame,
Nor aught in face or feature justly blame,
Can challenge or accuse him of no evil,
Yet notwithstanding hates him as a devil.
The lines are from old Heywood's "Hierarchie of Angels," and he
subjoins a curious story in confirmation, of a Spaniard who attempted
to assassinate a King Ferdinand of Spain, and being put to the rack
could give no other reason for the deed but an inveterate antipathy
which he had taken to the first sight of the King.
--The cause which to that act compell'd him
Was, he ne'er loved him since he first beheld him.]
[Footnote 2: There are some people who think they sufficiently acquit
themselves, and entertain their company, with relating facts of no
consequence, not at all out of the road of such common incidents as
happen every day; and this I have observed more frequently among the
Scots than any other nation, who are very careful not to omit the
minutest circumstances of time or place; which kind of discourse, if
it were not a little relieved by the uncouth terms and phrases, as
well as accent and gesture peculiar to that country, would be hardly
tolerable.--_Hints towards an Essay on Conversation_.]
WITCHES, AND OTHER NIGHT-FEARS
We are too hasty when we set down our ancestors in the gross for
fools, for the monstrous inconsistencies (as they seem to us) involved
in their creed of witchcraft. In the relations of this visible
world we find them to have been as rational, and shrewd to detect an
historic anomaly, as ourselves. But when once the invisible world
was supposed to be opened, and the lawless agency of bad spirits
assumed, what measures of probability, of decency, of fitness, or
proportion--of that which distinguishes the likely from the palpable
absurd--could they have to guide them in the rejection or admission
of any particular testimony?--That maidens pined away, wasting
inwardly as their waxen images consumed before a fire--that corn was
lodged, and cattle lamed--that whirlwinds uptore in diabolic revelry
the oaks of the forest--or that spits and kettles only danced a
fearful-innocent vagary about some rustic's kitchen when no wind
was stirring--were all equally probable where no law of agency was
understood. That the prince of the powers of darkness, passing by the
flower and pomp of the earth, should lay preposterous siege to the
weak fantasy of indigent eld--has neither likelihood nor unlikelihood
_a priori_ to us, who have no measure to guess at his policy, or
standard to estimate what rate those anile souls may fetch in the
devil's market. Nor, when the wicked are expressly symbolized by
a goat, was it to be wondered at so much, that _he_ should come
sometimes in that body, and assert his metaphor.--That the intercourse
was opened at all between both worlds was perhaps the mistake--but
that once assumed, I see no reason for disbelieving one attested story
of this nature more than another on the score of absurdity. There
is no law to judge of the lawless, or canon by which a dream may be
criticised.
I have sometimes thought that I could not have existed in the days of
received witchcraft; that I could not have slept in a village where
one of those reputed hags dwelt. Our ancestors were bolder or more
obtuse. Amidst the universal belief that these wretches were in
league with the author of all evil, holding hell tributary to their
muttering, no simple Justice of the Peace seems to have scrupled
issuing, or silly Headborough serving, a warrant upon them--as if they
should subpoena Satan!--Prospero in his boat, with his books and wand
about him, suffers himself to be conveyed away at the mercy of his
enemies to an unknown island. He might have raised a storm or two, we
think, on the passage. His acquiescence is in exact analogy to the
non-resistance of witches to the constituted powers.--What stops the
Fiend in Spenser from tearing Guyon to pieces--or who had made it a
condition of his prey, that Guyon must take assay of the glorious
bait--we have no guess. We do not know the laws of that country.
From my childhood I was extremely inquisitive about witches and
witch-stories. My maid, and more legendary aunt, supplied me with good
store. But I shall mention the accident which directed my curiosity
originally into this channel. In my father's book-closet, the History
of the Bible, by Stackhouse, occupied a distinguished station. The
pictures with which it abounds--one of the ark, in particular,
and another of Solomon's temple, delineated with all the fidelity
of ocular admeasurement, as if the artist had been upon the
spot--attracted my childish attention. There was a picture, too, of
the Witch raising up Samuel, which I wish that I had never seen. We
shall come to that hereafter. Stackhouse is in two huge tomes--and
there was a pleasure in removing folios of that magnitude, which, with
infinite straining, was as much as I could manage, from the situation
which they occupied upon an upper shelf. I have not met with the work
from that time to this, but I remember it consisted of Old Testament
stories, orderly set down, with the _objection_ appended to each
story, and the _solution_ of the objection regularly tacked to that.
The _objection_ was a summary of whatever difficulties had been
opposed to the credibility of the history, by the shrewdness of
ancient or modern infidelity, drawn up with an almost complimentary
excess of candour. The _solution_ was brief, modest, and satisfactory.
The bane and antidote were, both before you. To doubts so put, and so
quashed, there seemed to be an end for ever. The dragon lay dead, for
the foot of the veriest babe to trample on. But--like as was rather
feared than realised from that slain monster in Spenser--from the womb
of those crushed errors young dragonets would creep, exceeding the
prowess of so tender a Saint George as myself to vanquish. The habit
of expecting objections to every passage, set me upon starting more
objections, for the glory of finding a solution of my own for them. I
became staggered and perplexed, a sceptic in long coats. The pretty
Bible stories which I had read, or heard read in church, lost their
purity and sincerity of impression, and were turned into so many
historic or chronologic theses to be defended against whatever
impugners. I was not to disbelieve them, but--the next thing to
that--I was to be quite sure that some one or other would or had
disbelieved them. Next to making a child an infidel, is the letting
him know that there are infidels at all. Credulity is the man's
weakness, but the child's strength. O, how ugly sound scriptural
doubts from the mouth of a babe and a suckling!--I should have lost
myself in these mazes, and have pined away, I think, with such unfit
sustenance as these husks afforded, but for a fortunate piece of
ill-fortune, which about this time befel me. Turning over the picture
of the ark with too much haste, I unhappily made a breach in its
ingenious fabric--driving my inconsiderate fingers right through the
two larger quadrupeds--the elephant, and the camel--that stare (as
well they might) out of the two last windows next the steerage in
that unique piece of naval architecture. Stackhouse was henceforth
locked up, and became an interdicted treasure. With the book, the
_objections_ and _solutions_ gradually cleared out of my head, and
have seldom returned since in any force to trouble me.--But there was
one impression which I had imbibed from Stackhouse, which no lock or
bar could shut out, and which was destined to try my childish nerves
rather more seriously.--That detestable picture!
I was dreadfully alive to nervous terrors. The night-time solitude,
and the dark, were my hell. The sufferings I endured in this nature
would justify the expression. I never laid my head on my pillow, I
suppose, from the fourth to the seventh or eighth year of my life--so
far as memory serves in things so long ago--without an assurance,
which realized its own prophecy, of seeing some frightful spectre. Be
old Stackhouse then acquitted in part, if I say, that to his picture
of the Witch raising up Samuel--(O that old man covered with a
mantle!) I owe--not my midnight terrors, the hell of my infancy--but
the shape and manner of their visitation. It was he who dressed up for
me a hag that nightly sate upon my pillow--a sure bed-fellow, when
my aunt or my maid was far from me. All day long, while the book was
permitted me, I dreamed waking over his delineation, and at night
(if I may use so bold an expression) awoke into sleep, and found
the vision true. I durst not, even in the day-light, once enter the
chamber where I slept, without my face turned to the window, aversely
from the bed where my witch-ridden pillow was.--Parents do not know
what they do when they leave tender babes alone to go to sleep in the
dark. The feeling about for a friendly arm--the hoping for a familiar
voice--when they wake screaming--and find none to soothe them--what a
terrible shaking it is to their poor nerves! The keeping them up till
midnight, through candle-light and the unwholesome hours, as they are
called,--would, I am satisfied, in a medical point of view, prove the
better caution.--That detestable picture, as I have said, gave the
fashion to my dreams--if dreams they were--for the scene of them was
invariably the room in which I lay. Had I never met with the picture,
the fears would have come self-pictured in some shape or other--
Headless bear, black man, or ape--
but, as it was, my imaginations took that form.--It is not book,
or picture, or the stories of foolish servants, which create these
terrors in children. They can at most but give them a direction. Dear
little T.H. who of all children has been brought up with the most
scrupulous exclusion of every taint of superstition--who was never
allowed to hear of goblin or apparition, or scarcely to be told of bad
men, or to read or hear of any distressing story--finds all this world
of fear, from which he has been so rigidly excluded _ab extra_, in his
own "thick-coming fancies;" and from his little midnight pillow, this
nurse-child of optimism will start at shapes, unborrowed of tradition,
in sweats to which the reveries of the cell-damned murderer are
tranquillity.
Gorgons, and Hydras, and Chimaeras--dire stories of Celaeno and the
Harpies--may reproduce themselves in the brain of superstition--but
they were there before. They are transcripts, types--the archetypes
are in us, and eternal. How else should the recital of that, which we
know in a waking sense to be false, come to affect us at all?--or
--Names, whose sense we see not,
Fray us with things that be not?
Is it that we naturally conceive terror from such objects, considered
in their capacity of being able to inflict upon us bodily injury?--O,
least of all! These terrors are of older standing. They date beyond
body--or, without the body, they would have been the same. All the
cruel, tormenting, defined devils in Dante--tearing, mangling,
choking, stifling, scorching demons--are they one half so fearful
to the spirit of a man, as the simple idea of a spirit unembodied
following him--
Like one that on a lonesome road
Doth walk in fear and dread,
And having once turn'd round, walks on,
And turns no more his head;
Because he knows a frightful fiend
Doth close behind him tread.[1]
That the kind of fear here treated of is purely spiritual--that it
is strong in proportion as it is objectless upon earth--that it
predominates in the period of sinless infancy--are difficulties,
the solution of which might afford some probable insight into our
antemundane condition, and a peep at least into the shadow-land of
pre-existence.
My night-fancies have long ceased to be afflictive. I confess an
occasional night-mare; but I do not, as in early youth, keep a stud of
them. Fiendish faces, with the extinguished taper, will come and look
at me; but I know them for mockeries, even while I cannot elude their
presence, and I fight and grapple with them. For the credit of my
imagination, I am almost ashamed to say how tame and prosaic my dreams
are grown. They are never romantic, seldom even rural. They are of
architecture and of buildings--cities abroad, which I have never seen,
and hardly have hope to see. I have traversed, for the seeming length
of a natural day, Rome, Amsterdam, Paris, Lisbon--their churches,
palaces, squares, market-places, shops, suburbs, ruins, with an
inexpressible sense of delight--a map-like distinctness of trace--and
a day-light vividness of vision, that was all but being awake.--I have
formerly travelled among the Westmoreland fells--my highest Alps,--but
they are objects too mighty for the grasp of my dreaming recognition;
and I have again and again awoke with ineffectual struggles of the
inner eye, to make out a shape in any way whatever, of Helvellyn.
Methought I was in that country, but the mountains were gone. The
poverty of my dreams mortifies me. There is Coleridge, at his will
can conjure up icy domes, and pleasure-houses for Kubla Khan, and
Abyssinian maids, and songs of Abara, and caverns,
Where Alph, the sacred river, runs,
to solace his night solitudes--when I cannot muster a fiddle. Barry
Cornwall has his tritons and his nereids gamboling before him in
nocturnal visions, and proclaiming sons born to Neptune--when my
stretch of imaginative activity can hardly, in the night season,
raise up the ghost of a fish-wife. To set my failures in somewhat a
mortifying light--it was after reading the noble Dream of this poet,
that my fancy ran strong upon these marine spectra; and the poor
plastic power, such as it is, within me set to work, to humour my
folly in a sort of dream that very night. Methought I was upon the
ocean billows at some sea nuptials, riding and mounted high, with the
customary train sounding their conchs before me, (I myself, you may be
sure, the _leading god_,) and jollily we went careering over the main,
till just where Ino Leucothea should have greeted me (I think it was
Ino) with a white embrace, the billows gradually subsiding, fell from
a sea-roughness to a sea-calm, and thence to a river-motion, and that
river (as happens in the familiarization of dreams) was no other than
the gentle Thames, which landed me, in the wafture of a placid wave
or two, alone, safe and inglorious, somewhere at the foot of Lambeth
palace.
The degree of the soul's creativeness in sleep might furnish no
whimsical criterion of the quantum of poetical faculty resident in the
same soul waking. An old gentleman, a friend of mine, and a humorist,
used to carry this notion so far, that when he saw any stripling of
his acquaintance ambitious of becoming a poet, his first question
would be,--"Young man, what sort of dreams have you?" I have so much
faith in my old friend's theory, that when I feel that idle vein
returning upon me, I presently subside into my proper element of
prose, remembering those eluding nereids, and that inauspicious
inland landing.
[Footnote 1: Mr. Coleridge's Ancient Mariner.]
MY RELATIONS
I am arrived at that point of life, at which a man may account it a
blessing, as it is a singularity, if he have either of his parents
surviving. I have not that felicity--and sometimes think feelingly of
a passage in Browne's Christian Morals, where he speaks of a man that
hath lived sixty or seventy years in the world. "In such a compass of
time," he says, "a man may have a close apprehension what it is to
be forgotten, when he hath lived to find none who could remember his
father, or scarcely the friends of his youth, and may sensibly see
with what a face in no long time OBLIVION will look upon himself."
I had an aunt, a dear and good one. She was one whom single
blessedness had soured to the world. She often used to say, that I
was the only thing in it which she loved; and, when she thought I was
quitting it, she grieved over me with mother's tears. A partiality
quite so exclusive my reason cannot altogether approve. She was from
morning till night poring over good books, and devotional exercises.
Her favourite volumes were Thomas a Kempis, in Stanhope's Translation;
and a Roman Catholic Prayer Book, with the _matins_ and _complines_
regularly set down,--terms which I was at that time too young to
understand. She persisted in reading them, although admonished daily
concerning their Papistical tendency; and went to church every
Sabbath, as a good Protestant should do. These were the only books
she studied; though, I think, at one period of her life, she told me,
she had read with great satisfaction the Adventures of an Unfortunate
Young Nobleman. Finding the door of the chapel in Essex-street open
one day--it was in the infancy of that heresy--she went in, liked the
sermon, and the manner of worship, and frequented it at intervals
for some time after. She came not for doctrinal points, and never
missed them. With some little asperities in her constitution, which
I have above hinted at, she was a steadfast, friendly being, and a
fine _old Christian_. She was a woman of strong sense, and a shrewd
mind--extraordinary at a _repartee;_ one of the few occasions of her
breaking silence--else she did not much value wit. The only secular
employment I remember to have seen her engaged in, was, the splitting
of French beans, and dropping them into a China basin of fair water.
The odour of those tender vegetables to this day comes back upon my
sense, redolent of soothing recollections. Certainly it is the most
delicate of culinary operations.
Male aunts, as somebody calls them, I had none--to remember. By the
uncle's side I may be said to have been born an orphan. Brother, or
sister, I never had any--to know them. A sister, I think, that should
have been Elizabeth, died in both our infancies. What a comfort,
or what a care, may I not have missed in her!--But I have cousins,
sprinkled about in Hertfordshire--besides _two_, with whom I have been
all my life in habits of the closest intimacy, and whom I may term
cousins _par excellence_. These are James and Bridget Elia. They are
older than myself by twelve, and ten, years; and neither of them seems
disposed, in matters of advice and guidance, to waive any of the
prerogatives which primogeniture confers. May they continue still in
the same mind; and when they shall be seventy-five, and seventy-three,
years old (I cannot spare them sooner), persist in treating me in my
grand climacteric precisely as a stripling, or younger brother!
James is an inexplicable cousin. Nature hath her unities, which not
every critic can penetrate; or, if we feel, we cannot explain them.
The pen of Yorick, and of none since his, could have drawn J.E.
entire--those fine Shandian lights and shades, which make up his
story. I must limp after in my poor antithetical manner, as the fates
have given me grace and talent. J.E. then--to the eye of a common
observer at least--seemeth made up of contradictory principles.--The
genuine child of impulse, the frigid philosopher of prudence--the
phlegm of my cousin's doctrine is invariably at war with his
temperament, which is high sanguine. With always some fire-new project
in his brain, J.E. is the systematic opponent of innovation, and crier
down of every thing that has not stood the test of age and experiment.
With a hundred fine notions chasing one another hourly in his fancy,
he is startled at the least approach to the romantic in others; and,
determined by his own sense in every thing, commends _you_ to the
guidance of common sense on all occasions.--With a touch of the
eccentric in all which he does, or says, he is only anxious that _you_
should not commit yourself by doing any thing absurd or singular.
On my once letting slip at table, that I was not fond of a certain
popular dish, he begged me at any rate not to _say_ so--for the world
would think me mad. He disguises a passionate fondness for works of
high art (whereof he hath amassed a choice collection), under the
pretext of buying only to sell again--that his enthusiasm may give no
encouragement to yours. Yet, if it were so, why does that piece of
tender, pastoral Dominichino hang still by his wall?--is the ball of
his sight much more dear to him?--or what picture-dealer can talk like
him?
Whereas mankind in general are observed to warp their speculative
conclusions to the bent of their individual humours, _his_ theories
are sure to be in diametrical opposition to his constitution. He is
courageous as Charles of Sweden, upon instinct; chary of his person,
upon principle, as a travelling Quaker.--He has been preaching up to
me, all my life, the doctrine of bowing to the great--the necessity
of forms, and manner, to a man's getting on in the world. He himself
never aims at either, that I can discover,--and has a spirit, that
would stand upright in the presence of the Cham of Tartary. It is
pleasant to hear him discourse of patience--extolling it as the truest
wisdom--and to see him during the last seven minutes that his dinner
is getting ready. Nature never ran up in her haste a more restless
piece of workmanship than when she moulded this impetuous cousin--and
Art never turned out a more elaborate orator than he can display
himself to be, upon his favourite topic of the advantages of quiet,
and contentedness in the state, whatever it may be, that we are
placed in. He is triumphant on this theme, when he has you safe in
one of those short stages that ply for the western road, in a very
obstructing manner, at the foot of John Murray's street--where you get
in when it is empty, and are expected to wait till the vehicle hath
completed her just freight--a trying three quarters of an hour to some
people. He wonders at your fidgetiness,--"where could we be better
than we are, _thus silting, thus consulting_?"--"prefers, for his
part, a state of rest to locomotion,"--with an eye all the while upon
the coachman--till at length, waxing out of all patience, at _your
want of it_, he breaks out into a pathetic remonstrance at the fellow
for detaining us so long over the time which he had professed, and
declares peremptorily, that "the gentleman in the coach is determined
to get out, if he does not drive on that instant."
Very quick at inventing an argument, or detecting a sophistry, he is
incapable of attending _you_ in any chain of arguing. Indeed he makes
wild work with logic; and seems to jump at most admirable conclusions
by some process, not at all akin to it. Consonantly enough to this,
he hath been heard to deny, upon certain occasions, that there exists
such a faculty at all in man as _reason_; and wondereth how man came
first to have a conceit of it--enforcing his negation with all the
might of _reasoning_ he is master of. He has some speculative notions
against laughter, and will maintain that laughing is not natural
to _him_--when peradventure the next moment his lungs shall crow
like Chanticleer. He says some of the best things in the world--and
declareth that wit is his aversion. It was he who said, upon seeing
the Eton boys at play in their grounds--_What a pity to think, that
these fine ingenuous lads in a few years will all be changed into
frivolous Members of Parliament!_
His youth was fiery, glowing, tempestuous--and in age he discovereth
no symptom of cooling. This is that which I admire in him. I hate
people who meet Time half-way. I am for no compromise with that
inevitable spoiler. While he lives, J.E. will take his swing.--It does
me good, as I walk towards the street of my daily avocation, on some
fine May morning, to meet him marching in a quite opposite direction,
with a jolly handsome presence, and shining sanguine face, that
indicates some purchase in his eye--a Claude--or a Hobbima--for much
of his enviable leisure is consumed at Christie's, and Phillips's--or
where not, to pick up pictures, and such gauds. On these occasions
he mostly stoppeth me, to read a short lecture on the advantage a
person like me possesses above himself, in having his time occupied
with business which he _must do_--assureth me that he often feels
it hang heavy on his hands--wishes he had fewer holidays--and goes
off--Westward Ho!--chanting a tune, to Pall Mall--perfectly convinced
that he has convinced me--while I proceed in my opposite direction
tuneless.
It is pleasant again to see this Professor of Indifference doing the
honours of his new purchase, when he has fairly housed it. You must
view it in every light, till _he_ has found the best--placing it at
this distance, and at that, but always suiting the focus of your sight
to his own. You must spy at it through your fingers, to catch the
aerial perspective--though you assure him that to you the landscape
shows much more agreeable without that artifice. Wo be to the luckless
wight, who does not only not respond to his rapture, but who should
drop an unseasonable intimation of preferring one of his anterior
bargains to the present!--The last is always his best hit--his
"Cynthia of the minute."--Alas! how many a mild Madonna have I
known to _come in_--a Raphael!--keep its ascendancy for a few brief
moons--then, after certain intermedial degradations, from the front
drawing-room to the back gallery, thence to the dark parlour,--adopted
in turn by each of the Carracci, under successive lowering ascriptions
of filiation, mildly breaking its fall--consigned to the oblivious
lumber-room, _go out_ at last a Lucca Giordano, or plain Carlo
Maratti!--which things when I beheld--musing upon the chances and
mutabilities of fate below, hath made me to reflect upon the altered
condition of great personages, or that woful Queen of Richard the
Second--
--set forth in pomp,
She came adorned hither like sweet May.
Sent back like Hollowmass or shortest day.
With great love for _you_, J.E. hath but a limited sympathy with what
you feel or do. He lives in a world of his own, and makes slender
guesses at what passes in your mind. He never pierces the marrow of
your habits. He will tell an old established play-goer, that Mr.
Such-a-one, of So-and-so (naming one of the theatres), is a very
lively comedian--as a piece of news! He advertised me but the other
day of some pleasant green lanes which he had found out for me,
_knowing me to be a great walker_, in my own immediate vicinity--who
have haunted the identical spot any time these twenty years! He has
not much respect for that class of feelings which goes by the name
of sentimental. He applies the definition of real evil to bodily
sufferings exclusively--and rejecteth all others as imaginary. He
is affected by the sight, or the bare supposition, of a creature in
pain, to a degree which I have never witnessed out of womankind. A
constitutional acuteness to this class of sufferings may in part
account for this. The animal tribe in particular he taketh under his
especial protection. A broken-winded or spur-galled horse is sure to
find an advocate in him. An over-loaded ass is his client for ever. He
is the apostle to the brute kind--the never-failing friend of those
who have none to care for them. The contemplation of a lobster boiled,
or eels skinned _alive_, will wring him so, that "all for pity he
could die." It will take the savour from his palate, and the rest from
his pillow, for days and nights. With the intense feeling of Thomas
Clarkson, he wanted only the steadiness of pursuit, and unity of
purpose, of that "true yolk-fellow with Time," to have effected as
much for the _Animal_, as _he_ hath done for the _Negro Creation_. But
my uncontrollable cousin is but imperfectly formed for purposes which
demand co-operation. He cannot wait. His amelioration-plans must be
ripened in a day. For this reason he has cut but an equivocal figure
in benevolent societies, and combinations for the alleviation of human
sufferings. His zeal constantly makes him to outrun, and put out, his
coadjutors. He thinks of relieving,--while they think of debating.
He was black-balled out of a society for the Relief of **********,
because the fervor of his humanity toiled beyond the formal
apprehension, and creeping processes, of his associates. I shall
always consider this distinction as a patent of nobility in the Elia
family! Do I mention these seeming inconsistencies to smile at, or
upbraid, my unique cousin? Marry, heaven, and all good manners, and
the understanding that should be between kinsfolk, forbid!--With all
the strangenesses of this _strangest of the Elias_--I would not have
him in one jot or tittle other than he is; neither would I barter or
exchange my wild kinsman for the most exact, regular, and everyway
consistent kinsman breathing.
In my next, reader, I may perhaps give you some account of my cousin
Bridget--if you are not already surfeited with cousins--and take you
by the hand, if you are willing to go with us, on an excursion which
we made a summer or two since, in search of _more cousins_--
Through the green plains of pleasant Hertfordshire.
MACKERY END, IN HERTFORDSHIRE
Bridget Elia has been my housekeeper for many a long year. I have
obligations to Bridget, extending beyond the period of memory. We
house together, old bachelor and maid, in a sort of double singleness;
with such tolerable comfort, upon the whole, that I, for one, find in
myself no sort of disposition to go out upon the mountains, with the
rash king's offspring, to bewail my celibacy. We agree pretty well
in our tastes and habits--yet so, as "with a difference." We are
generally in harmony, with occasional bickerings--as it should be
among near relations. Our sympathies are rather understood, than
expressed; and once, upon my dissembling a tone in my voice more kind
than ordinary, my cousin burst into tears, and complained that I was
altered. We are both great readers in different directions. While I am
hanging over (for the thousandth time) some passage in old Burton, or
one of his strange contemporaries, she is abstracted in some modern
tale, or adventure, whereof our common reading-table is daily fed with
assiduously fresh supplies. Narrative teazes me. I have little concern
in the progress of events. She must have a story--well, ill, or
indifferently told--so there be life stirring in it, and plenty of
good or evil accidents. The fluctuations of fortune in fiction--and
almost in real life--have ceased to interest, or operate but dully
upon me. Out-of-the-way humours and opinions--heads with some
diverting twist in them--the oddities of authorship please me most. My
cousin has a native disrelish of any thing that sounds odd or bizarre.
Nothing goes down with her, that is quaint, irregular, or out of the
road of common sympathy. She "holds Nature more clever." I can pardon
her blindness to the beautiful obliquities of the Religio Medici; but
she must apologise to me for certain disrespectful insinuations, which
she has been pleased to throw out latterly, touching the intellectuals
of a dear favourite of mine, of the last century but one--the thrice
noble, chaste, and virtuous,--but again somewhat fantastical, and
original-brain'd, generous Margaret Newcastle.
It has been the lot of my cousin, oftener perhaps than I
could have wished, to have had for her associates and mine,
free-thinkers--leaders, and disciples, of novel philosophies and
systems; but she neither wrangles with, nor accepts, their opinions.
That which was good and venerable to her, when a child, retains its
authority over her mind still. She never juggles or plays tricks with
her understanding.
We are both of us inclined to be a little too positive; and I have
observed the result of our disputes to be almost uniformly this--that
in matters of fact, dates, and circumstances, it turns out, that I was
in the right, and my cousin in the wrong. But where we have differed
upon moral points; upon something proper to be done, or let alone;
whatever heat of opposition, or steadiness of conviction, I set out
with, I am sure always, in the long run, to be brought over to her way
of thinking.
I must touch upon the foibles of my kinswoman with a gentle hand,
for Bridget does not like to be told of her faults. She hath an
awkward trick (to say no worse of it) of reading in company: at which
times she will answer _yes_ or _no_ to a question, without fully
understanding its purport--which is provoking, and derogatory in the
highest degree to the dignity of the putter of the said question. Her
presence of mind is equal to the most pressing trials of life, but
will sometimes desert her upon trifling occasions. When the purpose
requires it, and is a thing of moment, she can speak to it greatly;
but in matters which are not stuff of the conscience, she hath been
known sometimes to let slip a word less seasonably.
Her education in youth was not much attended to; and she happily
missed all that train of female garniture, which passeth by the name
of accomplishments. She was tumbled early, by accident or design, into
a spacious closet of good old English reading, without much selection
or prohibition, and browsed at will upon that fair and wholesome
pasturage. Had I twenty girls, they should be brought up exactly in
this fashion. I know not whether their chance in wedlock might not be
diminished by it; but I can answer for it, that it makes (if the worst
come to the worst) most incomparable old maids.
In a season of distress, she is the truest comforter; but in the
teazing accidents, and minor perplexities, which do not call out the
_will_ to meet them, she sometimes maketh matters worse by an excess
of participation. If she does not always divide your trouble, upon
the pleasanter occasions of life she is sure always to treble your
satisfaction. She is excellent to be at a play with, or upon a visit;
but best, when she goes a journey with you.
We made an excursion together a few summers since, into Hertfordshire,
to beat up the quarters of some of our less-known relations in that
fine corn country.
The oldest thing I remember is Mackery End; or Mackarel End, as it
is spelt, perhaps more properly, in some old maps of Hertfordshire;
a farm-house,--delightfully situated within a gentle walk from
Wheathampstead. I can just remember having been there, on a visit to a
great-aunt, when I was a child, under the care of Bridget; who, as I
have said, is older than myself by some ten years. I wish that I could
throw into a heap the remainder of our joint existences, that we might
share them in equal division. But that is impossible. The house was at
that time in the occupation of a substantial yeoman, who had married
my grandmother's sister. His name was Gladman. My grandmother was a
Bruton, married to a Field. The Gladmans and the Brutons are still
flourishing in that part of the county, but the Fields are almost
extinct. More than forty years had elapsed since the visit I speak of;
and, for the greater portion of that period, we had lost sight of the
other two branches also. Who or what sort of persons inherited Mackery
End--kindred or strange folk--we were afraid almost to conjecture, but
determined some day to explore.
By somewhat a circuitous route, taking the noble park at Luton in
our way from Saint Alban's, we arrived at the spot of our anxious
curiosity about noon. The sight of the old farm-house, though every
trace of it was effaced from my recollection, affected me with a
pleasure which I had not experienced for many a year. For though _I_
had forgotten it, _we_ had never forgotten being there together, and
we had been talking about Mackery End all our lives, till memory on my
part became mocked with a phantom of itself, and I thought I knew the
aspect of a place, which, when present, O how unlike it was to _that_,
which I had conjured up so many times instead of it!
Still the air breathed balmily about it; the season was in the "heart
of June," and I could say with the poet,
But them, that didst appear so fair
To fond imagination,
Dost rival in the light of day
Her delicate creation!
Bridget's was more a waking bliss than mine, for she easily remembered
her old acquaintance again--some altered features, of course, a little
grudged at. At first, indeed, she was ready to disbelieve for joy;
but the scene soon re-confirmed itself in her affections--and she
traversed every out-post of the old mansion, to the wood-house, the
orchard, the place where the pigeon-house had stood (house and birds
were alike flown)--with a breathless impatience of recognition, which
was more pardonable perhaps than decorous at the age of fifty odd. But
Bridget in some things is behind her years.
The only thing left was to get into the house--and that was a
difficulty which to me singly would have been insurmountable; for I
am terribly shy in making myself known to strangers and out-of-date
kinsfolk. Love, stronger than scruple, winged my cousin in without
me; but she soon returned with a creature that might have sat to
a sculptor for the image of Welcome. It was the youngest of the
Gladmans; who, by marriage with a Bruton, had become mistress of the
old mansion. A comely brood are the Brutons. Six of them, females,
were noted as the handsomest young women in the county. But this
adopted Bruton, in my mind, was better than they all--more comely. She
was born too late to have remembered me. She just recollected in early
life to have had her cousin Bridget once pointed out to her, climbing
a style. But the name of kindred, and of cousinship, was enough. Those
slender ties, that prove slight as gossamer in the rending atmosphere
of a metropolis, bind faster, as we found it, in hearty, homely,
loving Hertfordshire. In five minutes we were as thoroughly acquainted
as if we had been born and bred up together; were familiar, even to
the calling each other by our Christian names. So Christians should
call one another. To have seen Bridget, and her--it was like the
meeting of the two scriptural cousins! There was a grace and dignity,
an amplitude of form and stature, answering to her mind, in this
farmer's wife, which would have shined in a palace--or so we thought
it. We were made welcome by husband and wife equally--we, and our
friend that was with us--I had almost forgotten him--but B.F. will not
so soon forget that meeting, if peradventure he shall read this on the
far distant shores where the Kangaroo haunts. The fatted calf was made
ready, or rather was already so, as if in anticipation of our coming;
and, after an appropriate glass of native wine, never let me forget
with what honest pride this hospitable cousin made us proceed to
Wheathampstead, to introduce us (as some new-found rarity) to her
mother and sister Gladmans, who did indeed know something more of
us, at a time when she almost knew nothing.--With what corresponding
kindness we were received by them also--how Bridget's memory, exalted
by the occasion, warmed into a thousand half-obliterated recollections
of things and persons, to my utter astonishment, and her own--and to
the astoundment of B.F. who sat by, almost the only thing that was not
a cousin there,--old effaced images of more than half-forgotten names
and circumstances still crowding back upon her, as words written in
lemon come out upon exposure to a friendly warmth,--when I forget
all this, then may my country cousins forget me; and Bridget no more
remember, that in the days of weakling infancy I was her tender
charge--as I have been her care in foolish manhood since--in those
pretty pastoral walks, long ago, about Mackery End, in Hertfordshire.
MODERN GALLANTRY
In comparing modern with ancient manners, we are pleased to compliment
ourselves upon the point of gallantry; a certain obsequiousness, or
deferential respect, which we are supposed to pay to females, as
females.
I shall believe that this principle actuates our conduct, when I can
forget, that in the nineteenth century of the era from which we date
our civility, we are but just beginning to leave off the very frequent
practice of whipping females in public, in common with the coarsest
male offenders.
I shall believe it to be influential, when I can shut my eyes to the
fact, that in England women are still occasionally--hanged.
I shall believe in it, when actresses are no longer subject to be
hissed off a stage by gentlemen.
I shall believe in it, when Dorimant hands a fish-wife across the
kennel; or assists the apple-woman to pick up her wandering fruit,
which some unlucky dray has just dissipated.
I shall believe in it, when the Dorimants in humbler life, who would
be thought in their way notable adepts in this refinement, shall act
upon it in places where they are not known, or think themselves not
observed--when I shall see the traveller for some rich tradesman part
with his admired box-coat, to spread it over the defenceless shoulders
of the poor woman, who is passing to her parish on the roof of the
same stage-coach with him, drenched in the rain--when I shall no
longer see a woman standing up in the pit of a London theatre, till
she is sick and faint with the exertion, with men about her, seated
at their ease, and jeering at her distress; till one, that seems to
have more manners or conscience than the rest, significantly declares
"she should be welcome to his seat, if she were a little younger and
handsomer." Place this dapper warehouseman, or that rider, in a circle
of their own female acquaintance, and you shall confess you have not
seen a politer-bred man in Lothbury.
Lastly, I shall begin to believe that there is some such principle
influencing our conduct, when more than one-half of the drudgery and
coarse servitude of the world shall cease to be performed by women.
Until that day comes, I shall never believe this boasted point to be
any thing more than a conventional fiction; a pageant got up between
the sexes, in a certain rank, and at a certain time of life, in which
both find their account equally.
I shall be even disposed to rank it among the salutary fictions of
life, when in polite circles I shall see the same attentions paid
to age as to youth, to homely features as to handsome, to coarse
complexions as to clear--to the woman, as she is a woman, not as she
is a beauty, a fortune, or a title.
I shall believe it to be something more than a name, when a
well-dressed gentleman in a well-dressed company can advert to the
topic of _female old age_ without exciting, and intending to excite,
a sneer:--when the phrases "antiquated virginity," and such a one
has "overstoocl her market," pronounced in good company, shall raise
immediate offence in man, or woman, that shall hear them spoken.
Joseph Paice, of Bread-street-hill, merchant, and one of the Directors
of the South-Sea company--the same to whom Edwards, the Shakspeare
commentator, has addressed a fine sonnet--was the only pattern of
consistent gallantry I have met with. He took me under his shelter at
an early age, and bestowed some pains upon me. I owe to his precepts
and example whatever there is of the man of business (and that is not
much) in my composition. It was not his fault that I did not profit
more. Though bred a Presbyterian, and brought up a merchant, he was
the finest gentleman of his time. He had not _one_ system of attention
to females in the drawing-room, and _another_ in the shop, or at the
stall. I do not mean that he made no distinction. But he never lost
sight of sex, or overlooked it in the casualties of a disadvantageous
situation. I have seen him stand bare-headed--smile if you please--to
a poor servant girl, while she has been inquiring of him the way to
some street--in such a posture of unforced civility, as neither to
embarrass her in the acceptance, nor himself in the offer, of it. He
was no dangler, in the common acceptation of the word, after women:
but he reverenced and upheld, in every form in which it came before
him, _womanhood_. I have seen him--nay, smile not--tenderly escorting
a marketwoman, whom he had encountered in a shower, exalting his
umbrella over her poor basket of fruit, that it might receive no
damage, with as much carefulness as if she had been a Countess. To the
reverend form of Female Eld he would yield the wall (though it were to
an ancient beggar-woman) with more ceremony than we can afford to show
our grandams. He was the Preux Chevalier of Age; the Sir Calidore,
or Sir Tristan, to those who have no Calidores or Tristans to defend
them. The roses, that had long faded thence, still bloomed for him in
those withered and yellow cheeks.
He was never married, but in his youth he paid his addresses to the
beautiful Susan Winstanley--old Winstanley's daughter of Clapton--who
dying in the early days of their courtship, confirmed in him the
resolution of perpetual bachelorship. It was during their short
courtship, he told me, that he had been one day treating his mistress
with a profusion of civil speeches--the common gallantries--to which
kind of thing she had hitherto manifested no repugnance--but in
this instance with no effect. He could not obtain from her a decent
acknowledgment in return. She rather seemed to resent his compliments.
He could not set it down to caprice, for the lady had always shown
herself above that littleness. When he ventured on the following day,
finding her a little better humoured, to expostulate with her on her
coldness of yesterday, she confessed, with her usual frankness, that
she had no sort of dislike to his attentions; that she could even
endure some high-flown compliments; that a young woman placed in her
situation had a right to expect all sort of civil things said to
her; that she hoped she could digest a dose of adulation, short of
insincerity, with as little injury to her humility as most young
women: but that--a little before he had commenced his compliments--she
had overheard him by accident, in rather rough language, rating
a young woman, who had not brought home his cravats quite to the
appointed time, and she thought to herself, "As I am Miss Susan
Winstanley, and a young lady--a reputed beauty, and known to be a
fortune,--I can have my choice of the finest speeches from the mouth
of this very fine gentleman who is courting me--but if I had been poor
Mary Such-a-one (_naming the milliner_),--and had failed of bringing
home the cravats to the appointed hour--though perhaps I had sat up
half the night to forward them--what sort of compliments should I have
received then?--And my woman's pride came to my assistance; and I
thought, that if it were only to do _me_ honour, a female, like
myself, might have received handsomer usage: and I was determined
not to accept any fine speeches, to the compromise of that sex, the
belonging to which was after all my strongest claim and title to
them."
I think the lady discovered both generosity, and a just way of
thinking, in this rebuke which she gave her lover; and I have
sometimes imagined, that the uncommon strain of courtesy, which
through life regulated the actions and behaviour of my friend towards
all of womankind indiscriminately, owed its happy origin to this
seasonable lesson from the lips of his lamented mistress.
I wish the whole female world would entertain the same notion of these
things that Miss Winstanley showed. Then we should see something
of the spirit of consistent gallantry; and no longer witness the
anomaly of the same man--a pattern of true politeness to a wife--of
cold contempt, or rudeness, to a sister--the idolater of his female
mistress--the disparager and despiser of his no less female aunt, or
unfortunate--still female--maiden cousin. Just so much respect as a
woman derogates from her own sex, in whatever condition placed--her
handmaid, or dependent--she deserves to have diminished from herself
on that score; and probably will feel the diminution, when youth, and
beauty, and advantages, not inseparable from sex, shall lose of their
attraction. What a woman should demand of a man in courtship, or after
it, is first--respect for her as she is a woman;--and next to that--to
be respected by him above all other women. But let her stand upon
her female character as upon a foundation; and let the attentions,
incident to individual preference, be so many pretty additaments and
ornaments--as many, and as fanciful, as you please--to that main
structure. Let her first lesson be--with sweet Susan Winstanley--to
_reverence her sex_.
THE OLD BENCHERS OF THE INNER TEMPLE
I was born, and passed the first seven years of my life, in the
Temple. Its church, its halls, its gardens, its fountain, its river,
I had almost said--for in those young years, what was this king of
rivers to me but a stream that watered our pleasant places?--these are
of my oldest recollections. I repeat, to this day, no verses to myself
more frequently, or with kindlier emotion, than those of Spenser,
where he speaks of this spot.
There when they came, whereas those bricky towers,
The which on Themmes brode aged back doth ride,
Where now the studious lawyers have their bowers,
There whylome wont the Templer knights to bide;
Till they decayd through pride.
Indeed, it is the most elegant spot in the metropolis. What a
transition for a countryman visiting London for the first time--the
passing from the crowded Strand or Fleet-street, by unexpected
avenues, into its magnificent ample squares, its classic green
recesses! What a cheerful, liberal look hath that portion of it,
which, from three sides, overlooks the greater garden: that goodly
pile
Of building strong, albeit of Paper hight,
confronting, with massy contrast, the lighter, older, more
fantastically shrouded one, named of Harcourt, with the cheerful
Crown-office Row (place of my kindly engendure), right opposite the
stately stream, which washes the garden-foot with her yet scarcely
trade-polluted waters, and seems but just weaned from her Twickenham
Naiades! a man would give something to have been born in such places.
What a collegiate aspect has that fine Elizabethan hall, where the
fountain plays, which I have made to rise and fall, how many times!
to the astoundment of the young urchins, my contemporaries, who,
not being able to guess at its recondite machinery, were almost
tempted to hail the wondrous work as magic! What an antique air had
the now almost effaced sundials, with their moral inscriptions,
seeming coevals with that Time which they measured, and to take
their revelations of its flight immediately from heaven, holding
correspondence with the fountain of light! How would the dark line
steal imperceptibly on, watched by the eye of childhood, eager to
detect its movement, never catched, nice as an evanescent cloud, or
the first arrests of sleep!
Ah! yet doth beauty like a dial-hand
Steal from his figure, and no pace perceived!
What a dead thing is a clock, with its ponderous embowelments of lead
and brass, its pert or solemn dulness of communication, compared with
the simple altar-like structure, and silent heart-language of the
old dial! It stood as the garden god of Christian gardens. Why is it
almost every where vanished? If its business-use be superseded by more
elaborate inventions, its moral uses, its beauty, might have pleaded
for its continuance. It spoke of moderate labours, of pleasures not
protracted after sun-set, of temperance, and good-hours. It was the
primitive clock, the horologe of the first world. Adam could scarce
have missed it in Paradise. It was the measure appropriate for sweet
plants and flowers to spring by, for the birds to apportion their
silver warblings by, for flocks to pasture and be led to fold by. The
shepherd "carved it out quaintly in the sun;" and, turning philosopher
by the very occupation, provided it with mottos more touching than
tombstones. It was a pretty device of the gardener, recorded by
Marvell, who, in the days of artificial gardening, made a dial out of
herbs and flowers. I must quote his verses a little higher up, for
they are full, as all his serious poetry was, of a witty delicacy.
They will not come in awkwardly, I hope, in a talk of fountains and
sun-dials. He is speaking of sweet garden scenes:
What wondrous life in this I lead!
Ripe apples drop about my head.
The luscious clusters of the vine
Upon my mouth do crush their wine.
The nectarine, and curious peach,
Into my hands themselves do reach.
Stumbling on melons, as I pass,
Insnared with flowers, I fall on grass.
Meanwhile the mind from pleasure less
Withdraws into its happiness.
The mind, that ocean, where each kind
Does straight its own resemblance find;
Yet it creates, transcending these,
Far other worlds, and other seas;
Annihilating all that's made
To a green thought in a green shade.
Here at the fountain's sliding foot,
Or at some fruit-tree's mossy root,
Casting the body's vest aside,
My soul into the boughs does glide:
There, like a bird, it sits and sings,
Then whets and claps its silver wings;
And, till prepared for longer flight,
Waves in its plumes the various light.
How well the skilful gardener drew,
Of flowers and herbs, this dial new!
Where, from above, the milder sun
Does through a fragrant zodiac run:
And, as it works, the industrious bee
Computes its time as well as we.
How could such sweet and wholesome hours
Be reckon'd, but with herbs and flowers?[1]
The artificial fountains of the metropolis are, in like manner, fast
vanishing. Most of them are dried up, or bricked over. Yet, where one
is left, as in that little green nook behind the South-Sea House,
what a freshness it gives to the dreary pile! Four little winged
marble boys used to play their virgin fancies, spouting out ever
fresh streams from their innocent-wanton lips, in the square of
Lincoln's-inn, when I was no bigger than they were figured. They are
gone, and the spring choked up. The fashion, they tell me, is gone by,
and these things are esteemed childish. Why not then gratify children,
by letting them stand? Lawyers, I suppose, were children once. They
are awakening images to them at least. Why must every thing smack of
man, and mannish? Is the world all grown up? Is childhood dead? Or is
there not in the bosoms of the wisest and the best some of the child's
heart left, to respond to its earliest enchantments? The figures were
grotesque. Are the stiff-wigged living figures, that still flitter and
chatter about that area, less gothic in appearance? or is the splutter
of their hot rhetoric one half so refreshing and innocent as the
little cool playful streams those exploded cherubs uttered?
They have lately gothicised the entrance to the Inner Temple-hall, and
the library front, to assimilate them, I suppose, to the body of the
hall, which they do not at all resemble. What is become of the winged
horse that stood over the former? a stately arms! and who has removed
those frescoes of the Virtues, which Italianized the end of the
Paper-buildings?--my first hint of allegory! They must account to me
for these things, which I miss so greatly.
The terrace is, indeed, left, which we used to call the parade; but
the traces are passed away of the footsteps which made its pavement
awful! It is become common and profane. The old benchers had it almost
sacred to themselves, in the forepart of the day at least. They might
not be sided or jostled. Their air and dress asserted the parade.
You left wide spaces betwixt you, when you passed them. We walk on
even terms with their successors. The roguish eye of J----ll, ever
ready to be delivered of a jest, almost invites a stranger to vie
a repartee with it. But what insolent familiar durst have mated
Thomas Coventry?--whose person was a quadrate, his step massy and
elephantine, his face square as the lion's, his gait peremptory and
path-keeping, indivertible from his way as a moving column, the
scarecrow of his inferiors, the brow-beater of equals and superiors,
who made a solitude of children wherever he came, for they fled his
insufferable presence, as they would have shunned an Elisha bear. His
growl was as thunder in their ears, whether he spake to them in mirth
or in rebuke, his invitatory notes being, indeed, of all, the most
repulsive and horrid. Clouds of snuff, aggravating the natural terrors
of his speech, broke from each majestic nostril, darkening the air. He
took it, not by pinches, but a palmful at once, diving for it under
the mighty flaps of his old-fashioned waistcoat pocket; his waistcoat
red and angry, his coat dark rappee, tinctured by dye original, and by
adjuncts, with buttons of obsolete gold. And so he paced the terrace.
By his side a milder form was sometimes to be seen; the pensive
gentility of Samuel Salt. They were coevals, and had nothing but
that and their benchership in common. In politics Salt was a whig,
and Coventry a staunch tory. Many a sarcastic growl did the latter
cast out--for Coventry had a rough spinous humour--at the political
confederates of his associate, which rebounded from the gentle bosom
of the latter like cannon-balls from wool. You could not ruffle Samuel
Salt.
S. had the reputation of being a very clever man, and of excellent
discernment in the chamber practice of the law. I suspect his
knowledge did not amount to much. When a case of difficult disposition
of money, testamentary or otherwise, came before him, he ordinarily
handed it over with a few instructions to his man Lovel, who was
a quick little fellow, and would despatch it out of hand by the
light of natural understanding, of which he had an uncommon share.
It was incredible what repute for talents S. enjoyed by the mere
trick of gravity. He was a shy man; a child might pose him in a
minute--indolent and procrastinating to the last degree. Yet men would
give him credit for vast application in spite of himself. He was not
to be trusted with himself with impunity. He never dressed for a
dinner party but he forgot his sword--they wore swords then--or some
other necessary part of his equipage. Lovel had his eye upon him on
all these occasions, and ordinarily gave him his cue. If there was
anything which he could speak unseasonably, he was sure to do it.--He
was to dine at a relative's of the unfortunate Miss Blandy on the day
of her execution;--and L. who had a wary foresight of his probable
hallucinations, before he set out, schooled him with great anxiety not
in any possible manner to allude to her story that day. S. promised
faithfully to observe the injunction. He had not been seated in the
parlour, where the company was expecting the dinner summons, four
minutes, when, a pause in the conversation ensuing, he got up, looked
out of window, and pulling down his ruffles--an ordinary motion with
him--observed, "it was a gloomy day," and added, "Miss Blandy must
be hanged by this time, I suppose." Instances of this sort were
perpetual. Yet S. was thought by some of the greatest men of his time
a fit person to be consulted, not alone in matters pertaining to the
law, but in the ordinary niceties and embarrassments of conduct--from
force of manner entirely. He never laughed. He had the same good
fortune among the female world,--was a known toast with the ladies,
and one or two are said to have died for love of him--I suppose,
because he never trifled or talked gallantry with them, or paid them,
indeed, hardly common attentions. He had a fine face and person, but
wanted, methought, the spirit that should have shown them off with
advantage to the women. His eye lacked lustre.--Not so, thought Susan
P----; who, at the advanced age of sixty, was seen, in the cold
evening time, unaccompanied, wetting the pavement of B----d Row, with
tears that fell in drops which might be heard, because her friend had
died that day--he, whom she had pursued with a hopeless passion for
the last forty years--a passion, which years could not extinguish or
abate; nor the long resolved, yet gently enforced, puttings off of
unrelenting bachelorhood dissuade from its cherished purpose. Mild
Susan P----, thou hast now thy friend in heaven!
Thomas Coventry was a cadet of the noble family of that name. He
passed his youth in contracted circumstances, which gave him early
those parsimonious habits which in after-life never forsook him; so
that, with one windfall or another, about the time I knew him he was
master of four or five hundred thousand pounds; nor did he look,
or walk, worth a moidore less. He lived in a gloomy house opposite
the pump in Serjeant's-inn, Fleet-street. J., the counsel, is doing
self-imposed penance in it, for what reason I divine not, at this day.
C. had an agreeable seat at North Cray, where he seldom spent above
a day or two at a time in the summer; but preferred, during the hot
months, standing at his window in this damp, close, well-like mansion,
to watch, as he said, "the maids drawing water all day long." I
suspect he had his within-door reasons for the preference. _Hic currus
et arma fuere_. He might think his treasures more safe. His house had
the aspect of a strong box. C. was a close hunks--a hoarder rather
than a miser--or, if a miser, none of the mad Elwes breed, who have
brought discredit upon a character, which cannot exist without certain
admirable points of steadiness and unity of purpose. One may hate a
true miser, but cannot, I suspect, so easily despise him. By taking
care of the pence, he is often enabled to part with the pounds,
upon a scale that leaves us careless generous fellows halting at an
immeasurable distance behind. C. gave away 30,000_l_. at once in his
life-time to a blind charity. His house-keeping was severely looked
after, but he kept the table of a gentleman. He would know who came
in and who went out of his house, but his kitchen chimney was never
suffered to freeze.
Salt was his opposite in this, as in all--never knew what he was worth
in the world; and having but a competency for his rank, which his
indolent habits were little calculated to improve, might have suffered
severely if he had not had honest people about him. Lovel took care of
every thing. He was at once his clerk, his good servant, his dresser,
his friend, his "flapper," his guide, stop-watch, auditor, treasurer.
He did nothing without consulting Lovel, or failed in any thing
without expecting and fearing his admonishing. He put himself almost
too much in his hands, had they not been the purest in the world. He
resigned his title almost to respect as a master, if L. could ever
have forgotten for a moment that he was a servant.
I knew this Lovel. He was a man of an incorrigible and losing honesty.
A good fellow withal, and "would strike." In the cause of the
oppressed he never considered inequalities, or calculated the number
of his opponents. He once wrested a sword out of the hand of a man of
quality that had drawn upon him; and pommelled him severely with the
hilt of it. The swordsman had offered insult to a female--an occasion
upon which no odds against him could have prevented the interference
of Lovel. He would stand next day bare-headed to the same person,
modestly to excuse his interference--for L. never forgot rank, where
something better was not concerned. L. was the liveliest little fellow
breathing, had a face as gay as Garrick's, whom he was said greatly
to resemble (I have a portrait of him which confirms it), possessed a
fine turn for humorous poetry--next to Swift and Prior--moulded heads
in clay or plaster of Paris to admiration, by the dint of natural
genius merely; turned cribbage boards, and such small cabinet toys,
to perfection; took a hand at quadrille or bowls with equal facility;
made punch better than any man of his degree in England; had the
merriest quips and conceits, and was altogether as brimful of
rogueries and inventions as you could desire. He was a brother of the
angle, moreover, and just such a free, hearty, honest companion as Mr.
Isaac Walton would have chosen to go a fishing with. I saw him in his
old age and the decay of his faculties, palsy-smitten, in the last sad
stage of human weakness--"a remnant most forlorn of what he was,"--yet
even then his eye would light up upon the mention of his favourite
Garrick. He was greatest, he would say, in Bayes--"was upon the stage
nearly throughout the whole performance, and as busy as a bee." At
intervals, too, he would speak of his former life, and how he came up
a little boy from Lincoln to go to service, and how his mother cried
at parting with him, and how he returned, after some few years'
absence, in his smart new livery to see her, and she blessed herself
at the change, and could hardly be brought to believe that it was "her
own bairn." And then, the excitement subsiding, he would weep, till I
have wished that sad second-childhood might have a mother still to lay
its head upon her lap. But the common mother of us all in no long time
after received him gently into hers.
With Coventry, and with Salt, in their walks upon the terrace, most
commonly Peter Pierson would join, to make up a third. They did not
walk linked arm in arm in those days--"as now our stout triumvirs
sweep the streets,"--but generally with both hands folded behind them
for state, or with one at least behind, the other carrying a cane.
P. was a benevolent, but not a pre-possessing man. He had that in
his face which you could not term unhappiness; it rather implied
an incapacity of being happy. His cheeks were colourless, even to
whiteness. His look was uninviting, resembling (but without his
sourness) that of our great philanthropist. I know that he _did_ good
acts, but I could never make out what _he_ was. Contemporary with
these, but subordinate, was Daines Barrington--another oddity--he
walked burly and square--in imitation, I think, of Coventry--howbeit
he attained not to the dignity of his prototype. Nevertheless, he
did pretty well, upon the strength of being a tolerable antiquarian,
and having a brother a bishop. When the account of his year's
treasurership came to be audited, the following singular charge was
unanimously disallowed by the bench: "Item, disbursed Mr. Allen, the
gardener, twenty shillings, for stuff to poison the sparrows, by my
orders." Next to him was old Barton--a jolly negation, who took upon
him the ordering of the bills of fare for the parliament chamber,
where the benchers dine--answering to the combination rooms at
college--much to the easement of his less epicurean brethren. I know
nothing more of him.--Then Read, and Twopenny--Read, good-humoured
and personable--Twopenny, good-humoured, but thin, and felicitous in
jests upon his own figure. If T. was thin, Wharry was attenuated and
fleeting. Many must remember him (for he was rather of later date)
and his singular gait, which was performed by three steps and a jump
regularly succeeding. The steps were little efforts, like that of a
child beginning to walk; the jump comparatively vigorous, as a foot to
an inch. Where he learned this figure, or what occasioned it, I could
never discover. It was neither graceful in itself, nor seemed to
answer the purpose any better than common walking. The extreme tenuity
of his frame, I suspect, set him upon it. It was a trial of poising.
Twopenny would often rally him upon his leanness, and hail him as
Brother Lusty; but W. had no relish of a joke. His features were
spiteful. I have heard that he would pinch his cat's ears extremely,
when any thing had offended him. Jackson--the omniscient Jackson he
was called--was of this period. He had the reputation of possessing
more multifarious knowledge than any man of his time. He was the
Friar Bacon of the less literate portion of the Temple. I remember a
pleasant passage, of the cook applying to him, with much formality of
apology, for instructions how to write down _edge_ bone of beef in his
bill of commons. He was supposed to know, if any man in the world did.
He decided the orthography to be--as I have given it--fortifying his
authority with such anatomical reasons as dismissed the manciple (for
the time) learned and happy. Some do spell it yet perversely, _aitch_
bone, from a fanciful resemblance between its shape, and that of the
aspirate so denominated. I had almost forgotten Mingay with the iron
hand--but he was somewhat later. He had lost his right hand by some
accident, and supplied it with a grappling hook, which he wielded
with a tolerable adroitness. I detected the substitute, before I was
old enough to reason whether it were artificial or not. I remember
the astonishment it raised in me. He was a blustering, loud-talking
person; and I reconciled the phenomenon to my ideas as an emblem of
power--somewhat like the horns in the forehead of Michael Angelo's
Moses. Baron Maseres, who walks (or did till very lately) in the
costume of the reign of George the Second, closes my imperfect
recollections of the old benchers of the Inner Temple.
Fantastic forms, whither are ye fled? Or, if the like of you exist,
why exist they no more for me? Ye inexplicable, half-understood
appearances, why comes in reason to tear away the preternatural mist,
bright or gloomy, that enshrouded you? Why make ye so sorry a figure
in my relation, who made up to me--to my childish eyes--the mythology
of the Temple? In those days I saw Gods, as "old men covered with a
mantle," walking upon the earth. Let the dreams of classic idolatry
perish,--extinct be the fairies and fairy trumpery of legendary
fabling,--in the heart of childhood, there will, for ever, spring up a
well of innocent or wholesome superstition--the seeds of exaggeration
will be busy there, and vital--from every-day forms educing the
unknown and the uncommon. In that little Goshen there will be light,
when the grown world flounders about in the darkness of sense and
materiality. While childhood, and while dreams, reducing childhood,
shall be left, imagination shall not have spread her holy wings
totally to fly the earth.
* * * * *
P.S. I have done injustice to the soft shade of Samuel Salt. See
what it is to trust to imperfect memory, and the erring notices of
childhood! Yet I protest I always thought that he had been a bachelor!
This gentleman, R.N. informs me, married young, and losing his lady
in child-bed, within the first year of their union, fell into a deep
melancholy, from the effects of which, probably, he never thoroughly
recovered. In what a new light does this place his rejection (O
call it by a gentler name!) of mild Susan P----, unravelling
into beauty certain peculiarities of this very shy and retiring
character!--Henceforth let no one receive the narratives of Elia for
true records! They are, in truth, but shadows of fact-verisimilitudes,
not verities--or sitting but upon the remote edges and outskirts of
history. He is no such honest chronicler as R.N., and would have done
better perhaps to have consulted that gentleman, before he sent these
incondite reminiscences to press. But the worthy sub-treasurer--who
respects his old and his new masters--would but have been puzzled
at the indecorous liberties of Elia. The good man wots not,
peradventure, of the license which _Magazines_ have arrived at in this
plain-speaking age, or hardly dreams of their existence beyond the
_Gentleman's_--his furthest monthly excursions in this nature having
been long confined to the holy ground of honest _Urban's_ obituary.
May it be long before his own name shall help to swell those columns
of unenvied flattery!--Meantime, O ye New Benchers of the Inner
Temple, cherish him kindly, for he is himself the kindliest of human
creatures. Should infirmities over-take him--he is yet in green and
vigorous senility--make allowances for them, remembering that "ye
yourselves are old." So may the Winged Horse, your ancient badge
and cognisance, still flourish! so may future Hookers and Seldens
illustrate your church and chambers! so may the sparrows, in default
of more melodious quiristers, unpoisoned hop about your walks! so may
the fresh- and cleanly nursery maid, who, by leave, airs her
playful charge in your stately gardens, drop her prettiest blushing
curtsy as ye pass, reductive of juvenescent emotion! so may the
younkers of this generation eye you, pacing your stately terrace, with
the same superstitious veneration, with which the child Elia gazed on
the Old Worthies that solemnized the parade before ye!
[Footnote 1: From a copy of verses entitled The Garden.]
GRACE BEFORE MEAT
The custom of saying grace at meals had, probably, its origin in the
early times of the world, and the hunter-state of man, when dinners
were precarious things, and a full meal was something more than a
common blessing; when a belly-full was a windfall, and looked like
a special providence. In the shouts and triumphal songs with which,
after a season of sharp abstinence, a lucky booty of deer's or goat's
flesh would naturally be ushered home, existed, perhaps, the germ of
the modern grace. It is not otherwise easy to be understood, why the
blessing of food--the act of eating--should have had a particular
expression of thanksgiving annexed to it, distinct from that implied
and silent gratitude with which we are expected to enter upon
the enjoyment of the many other various gifts and good things of
existence.
I own that I am disposed to say grace upon twenty other occasions in
the course of the day besides my dinner. I want a form for setting out
upon a pleasant walk, for a moonlight ramble, for a friendly meeting,
or a solved problem. Why have we none for books, those spiritual
repasts--a grace before Milton--a grace before Shakspeare--a
devotional exercise proper to be said before reading the Fairy
Queen?--but, the received ritual having prescribed these forms to the
solitary ceremony of manducation, I shall confine my observations to
the experience which I have had of the grace, properly so called;
commending my new scheme for extension to a niche in the grand
philosophical, poetical, and perchance in part heretical, liturgy, now
compiling by my friend <DW25> Humanus, for the use of a certain snug
congregation of Utopian Rabelaesian Christians, no matter where
assembled.
The form then of the benediction before eating has its beauty at
a poor man's table, or at the simple and unprovocative repasts of
children. It is here that the grace becomes exceedingly graceful.
The indigent man, who hardly knows whether he shall have a meal the
next day or not, sits down to his fare with a present sense of the
blessing, which can be but feebly acted by the rich, into whose
minds the conception of wanting a dinner could never, but by some
extreme theory, have entered. The proper end of food--the animal
sustenance--is barely contemplated by them. The poor man's bread is
his daily bread, literally his bread for the day. Their courses are
perennial.
Again, the plainest diet seems the fittest to be preceded by the
grace. That which is least stimulative to appetite, leaves the mind
most free for foreign considerations. A man may feel thankful,
heartily thankful, over a dish of plain mutton with turnips, and have
leisure to reflect upon the ordinance and institution of eating;
when he shall confess a perturbation o f mind, inconsistent with the
purposes of the grace, at the presence of venison or turtle. When I
have sate (a _rarus hospes_) at rich men's tables, with the savoury
soup and messes steaming up the nostrils, and moistening the lips
of the guests with desire and a distracted choice, I have felt the
introduction of that ceremony to be unseasonable. With the ravenous
orgasm upon you, it seems impertinent to interpose a religious
sentiment. It is a confusion of purpose to mutter out praises from a
mouth that waters. The heats of epicurism put out the gentle flame of
devotion. The incense which rises round is pagan, and the belly-god
intercepts it for his own. The very excess of the provision beyond the
needs, takes away all sense of proportion between the end and means.
The giver is veiled by his gifts. You are startled at the injustice
of returning thanks--for what?--for having too much, while so many
starve. It is to praise the Gods amiss.
I have observed this awkwardness felt, scarce consciously perhaps,
by the good man who says the grace. I have seen it in clergymen and
others--a sort of shame--a sense of the co-presence of circumstances
which unhallow the blessing. After a devotional tone put on for a few
seconds, how rapidly the speaker will fall into his common voice,
helping himself or his neighbour, as if to get rid of some uneasy
sensation of hypocrisy. Not that the good man was a hypocrite, or was
not most conscientious in the discharge of the duty; but he felt in
his inmost mind the incompatibility of the scene and the viands before
him with the exercise of a calm and rational gratitude.
I hear somebody exclaim,--Would you have Christians sit down at table,
like hogs to their troughs, without remembering the Giver?--no--I
would have them sit down as Christians, remembering the Giver,
and less like hogs. Or if their appetites must run riot, and they
must pamper themselves with delicacies for which east and west are
ransacked, I would have them postpone their benediction to a fitter
season, when appetite is laid; when the still small voice can be
heard, and the reason of the grace returns--with temperate diet and
restricted dishes. Gluttony and surfeiting are no proper occasions for
thanksgiving. When Jeshurun waxed fat, we read that he kicked. Virgil
knew the harpy-nature better, when he put into the mouth of Celasno
any thing but a blessing. We may be gratefully sensible of the
deliciousness of some kinds of food beyond others, though that is a
meaner and inferior gratitude: but the proper object of the grace is
sustenance, not relishes; daily bread, not delicacies; the means of
life, and not the means of pampering the carcass. With what frame or
composure, I wonder, can a city chaplain pronounce his benediction
at some great Hall feast, when he knows that his last concluding
pious word--and that, in all probability, the sacred name which he
preaches--is but the signal for so many impatient harpies to commence
their foul orgies, with as little sense of true thankfulness (which
is temperance) as those Virgilian fowl! It is well if the good man
himself does not feel his devotions a little clouded, those foggy
sensuous steams mingling with and polluting the pure altar sacrifice.
The severest satire upon full tables and surfeits is the banquet which
Satan, in the Paradise Regained, provides for a temptation in the
wilderness:
A table richly spread in regal mode,
With dishes piled, and meats of noblest sort
And savour; beasts of chase, or fowl of game,
In pastry built, or from the spit, or boiled,
Gris-amber-steamed; all fish from sea or shore,
Freshet or purling brook, for which was drained
Pontus, and Lucrine bay, and Afric coast.
The Tempter, I warrant you, thought these cates would go down without
the recommendatory preface of a benediction. They are like to be short
graces where the devil plays the host.--I am afraid the poet wants his
usual decorum in this place. Was he thinking of the old Roman luxury,
or of a gaudy day at Cambridge? This was a temptation fitter for a
Heliogabalus. The whole banquet is too civic and culinary, and the
accompaniments altogether a profanation of that deep, abstracted, holy
scene. The mighty artillery of sauces, which the cook-fiend conjures
up, is out of proportion to the simple wants and plain hunger of the
guest. He that disturbed him in his dreams, from his dreams might have
been taught better. To the temperate fantasies of the famished Son of
God, what sort of feasts presented themselves?--He dreamed indeed,
--As appetite is wont to dream,
Of meats and drinks, nature's refreshment sweet.
But what meats?--
Him thought, he by the brook of Cherith stood,
And saw the ravens with their horny beaks
Food to Elijah bringing, even and morn;
Though ravenous, taught to abstain from what they brought:
He saw the prophet also how he fled
Into the desert, and how there he slept
Under a juniper; then how awaked
He found his supper on the coals prepared,
And by the angel was bid rise and eat,
And ate the second time after repose,
The strength whereof sufficed him forty days:
Sometimes, that with Elijah he partook,
Or as a guest with Daniel at his pulse.
Nothing in Milton is finelier fancied than these temperate dreams of
the divine Hungerer. To which of these two visionary banquets, think
you, would the introduction of what is called the grace have been most
fitting and pertinent?
Theoretically I am no enemy to graces; but practically I own that
(before meat especially) they seem to involve something awkward and
unseasonable. Our appetites, of one or another kind, are excellent
spurs to our reason, which might otherwise but feebly set about the
great ends of preserving and continuing the species. They are fit
blessings to be contemplated at a distance with a becoming gratitude;
but the moment of appetite (the judicious reader will apprehend me)
is, perhaps, the least fit season for that exercise. The Quakers who
go about their business, of every description, with more calmness
than we, have more title to the use of these benedictory prefaces. I
have always admired their silent grace, and the more because I have
observed their applications to the meat and drink following to be
less passionate and sensual than ours. They are neither gluttons nor
wine-bibbers as a people. They eat, as a horse bolts his chopt hay,
with indifference, calmness, and cleanly circumstances. They neither
grease nor slop themselves. When I see a citizen in his bib and
tucker, I cannot imagine it a surplice.
I am no Quaker at my food. I confess I am not indifferent to the
kinds of it. Those unctuous morsels of deer's flesh were not made to
be received with dispassionate services. I hate a man who swallows
it, affecting not to know what he is eating. I suspect his taste in
higher matters. I shrink instinctively from one who professes to
like minced veal. There is a physiognomical character in the tastes
for food. C---- holds that a man cannot have a pure mind who refuses
apple-dumplings. I am not certain but he is right. With the decay of
my first innocence, I confess a less and less relish daily for those
innocuous cates. The whole vegetable tribe have lost their gust with
me. Only I stick to asparagus, which still seems to inspire gentle
thoughts. I am impatient and querulous under culinary disappointments,
as to come home at the dinner hour, for instance, expecting some
savoury mess, and to find one quite tasteless and sapidless. Butter
ill melted--that commonest of kitchen failures--puts me beside my
tenour.--The author of the Rambler used to make inarticulate animal
noises over a favourite food. Was this the music quite proper to
be preceded by the grace? or would the pious man have done better
to postpone his devotions to a season when the blessing plight be
contemplated with less perturbation? I quarrel with no man's tastes,
nor would set my thin face against those excellent things, in their
way, jollity and feasting. But as these exercises, however laudable,
have little in them of grace or gracefulness, a man should be sure,
before he ventures so to grace them, that while he is pretending his
devotions otherwhere, he is not secretly kissing his hand to some
great fish--his Dagon--with a special consecration of no ark but the
fat tureen before him. Graces are the sweet preluding strains to the
banquets of angels and children; to the roots and severer repasts
of the Chartreuse; to the slender, but not slenderly acknowledged,
refection of the poor and humble man: but at the heaped-up boards of
the pampered and the luxurious they become of dissonant mood, less
timed and tuned to the occasion, methinks, than the noise of those
better befitting organs would be, which children hear tales of, at
Hog's Norton. We sit too long at our meals, or are too curious in
the study of them, or too disordered in our application to them, or
engross too great a portion of those good things (which should be
common) to our share, to be able with any grace to say grace. To
be thankful for what we grasp exceeding our proportion is to add
hypocrisy to injustice. A lurking sense of this truth is what makes
the performance of this duty so cold and spiritless a service at most
tables. In houses where the grace is as indispensable as the napkin,
who has not seen that never settled question arise, as to _who shall
say it_; while the good man of the house and the visitor clergyman, or
some other guest belike of next authority from years or gravity, shall
be bandying about the office between them as a matter of compliment,
each of them not unwilling to shift the awkward burthen of an
equivocal duty from his own shoulders?
I once drank tea in company with two Methodist divines of different
persuasions, whom it was my fortune to introduce to each other for the
first time that evening. Before the first cup was handed round, one of
these reverend gentlemen put it to the other, with all due solemnity,
whether he chose to _say any thing_. It seems it is the custom with
some sectaries to put up a short prayer before this meal also. His
reverend brother did not at first quite apprehend him, but upon an
explanation, with little less importance he made answer, that it was
not a custom known in his church: in which courteous evasion the other
acquiescing for good manner's sake, or in compliance with a weak
brother, the supplementary or tea-grace was waived altogether. With
what spirit might not Lucian have painted two priests, of _his_
religion, playing into each other's hands the compliment of performing
or omitting a sacrifice,--the hungry God meantime, doubtful of his
incense, with expectant nostrils hovering over the two flamens, and
(as between two stools) going away in the end without his supper.
A short form upon these occasions is felt to want reverence; a long
one, I am afraid, cannot escape the charge of impertinence. I do
not quite approve of the epigrammatic conciseness with which that
equivocal wag (but my pleasant school-fellow) C.V.L., when importuned
for a grace, used to inquire, first slyly leering down the table, "Is
there no clergyman here?"--significantly adding, "thank G----." Nor do
I think our old form at school quite pertinent, where we were used to
preface our bald bread and cheese suppers with a preamble, connecting
with that humble blessing a recognition of benefits the most awful
and overwhelming to the imagination which religion has to offer. _Non
tunc illis erat locus._ I remember we were put to it to reconcile the
phrase "good creatures," upon which the blessing rested, with the
fare set before us, wilfully understanding that expression in a low
and animal sense,--till some one recalled a legend, which told how
in the golden days of Christ's, the young Hospitallers were wont to
have smoking joints of roast meat upon their nightly boards, till
some pious benefactor, commiserating the decencies, rather than the
palates, of the children, commuted our flesh for garments, and gave
us--_horresco referens_--trowsers instead of mutton.
MY FIRST PLAY
At the north end of Cross-court there yet stands a portal, of some
architectural pretensions, though reduced to humble use, serving at
present for an entrance to a printing-office. This old door-way, if
you are young, reader, you may not know was the identical pit entrance
to old Drury--Garrick's Drury--all of it that is left. I never pass it
without shaking some forty years from off my shoulders, recurring
to the evening when I passed through it to see _my first play_. The
afternoon had been wet, and the condition of our going (the elder
folks and myself) was, that the rain should cease. With what a beating
heart did I watch from the window the puddles, from the stillness of
which I was taught to prognosticate the desired cessation! I seem to
remember the last spurt, and the glee with which I ran to announce it.
We went with orders, which my godfather F. had sent us. He kept the
oil shop (now Davies's) at the corner of Featherstone-building,
in Holborn. F. was a tall grave person, lofty in speech, and had
pretensions above his rank. He associated in those days with John
Palmer, the comedian, whose gait and bearing he seemed to copy; if
John (which is quite as likely) did not rather borrow somewhat of
his manner from my godfather. He was also known to, and visited by,
Sheridan. It was to his house in Holborn that young Brinsley brought
his first wife on her elopement with him from a boarding-school at
Bath--the beautiful Maria Linley. My parents were present (over a
quadrille table) when he arrived in the evening with his harmonious
charge.--From either of these connexions it may be inferred that
my godfather could command an order for the then Drury-lane
theatre at pleasure--and, indeed, a pretty liberal issue of those
cheap billets, in Brinsley's easy autograph, I have heard him say
was the sole remuneration which he had received for many years'
nightly illumination of the orchestra and various avenues of that
theatre--and he was content it should be so. The honour of Sheridan's
familiarity--or supposed familiarity--was better to my godfather than
money.
F. was the most gentlemanly of oilmen; grandiloquent, yet courteous.
His delivery of the commonest matters of fact was Ciceronian. He had
two Latin words almost constantly in his mouth (how odd sounds Latin
from an oilman's lips!), which my better knowledge since has enabled
me to correct. In strict pronunciation they should have been sounded
_vice versa_--but in those young years they impressed me with more awe
than they would now do, read aright from Seneca or Varro--in his own
peculiar pronunciation, monosyllabically elaborated, or Anglicized,
into something like _verse verse_. By an imposing manner, and the help
of these distorted syllables, he climbed (but that was little) to the
highest parochial honours which St. Andrew's has to bestow.
He is dead--and thus much I thought due to his memory, both for
my first orders (little wondrous talismans!--slight keys, and
insignificant to outward sight, but opening to me more than Arabian
paradises!) and moreover, that by his testamentary beneficence I came
into possession of the only landed property which I could ever call
my own--situate near the road-way village of pleasant Puckeridge, in
Hertfordshire. When I journeyed down to take possession, and planted
foot on my own ground, the stately habits of the donor descended upon
me, and I strode (shall I confess the vanity?) with larger paces over
my allotment of three quarters of an acre, with its commodious mansion
in the midst, with the feeling of an English freeholder that all
betwixt sky and centre was my own. The estate has passed into more
prudent hands, and nothing but an agrarian can restore it.
In those days were pit orders. Beshrew the uncomfortable manager who
abolished them!--with one of these we went. I remember the waiting at
the door--not that which is left--but between that and an inner door
in shelter--O when shall I be such an expectant again!--with the cry
of nonpareils, an indispensable play-house accompaniment in those
days. As near as I can recollect, the fashionable pronunciation of
the theatrical fruiteresses then was, "Chase some oranges, chase
some numparels, chase a bill of the play;"--chase _pro_ chuse. But
when we got in, and I beheld the green curtain that veiled a heaven
to my imagination, which was soon to be disclosed--the breathless
anticipations I endured! I had seen something like it in the plate
prefixed to Troilus and Cressida, in Rowe's Shakspeare--the tent scene
with Diomede--and a sight of that plate can always bring back in a
measure the feeling of that evening.--The boxes at that time, full
of well-dressed women of quality, projected over the pit; and the
pilasters reaching down were adorned with a glistering substance
(I know not what) under glass (as it seemed), resembling--a homely
fancy--but I judged it to be sugar-candy--yet, to my raised
imagination, divested of its homelier qualities, it appeared a
glorified candy!--The orchestra lights at length arose, those
"fair Auroras!" Once the bell sounded. It was to ring out yet once
again--and, incapable of the anticipation, I reposed my shut eyes in
a sort of resignation upon the maternal lap. It rang the second time.
The curtain drew up--I was not past six years old--and the play was
Artaxerxes!
I had dabbled a little in the Universal History--the ancient part of
it--and here was the court of Persia. It was being admitted to a sight
of the past. I took no proper interest in the action going on, for
I understood not its import--but I heard the word Darius, and I was
in the midst of Daniel. All feeling was absorbed in vision. Gorgeous
vests, gardens, palaces, princesses, passed before me. I knew not
players. I was in Persepolis for the time; and the burning idol
of their devotion almost converted me into a worshipper. I was
awe-struck, and believed those significations to be something more
than elemental fires. It was all enchantment and a dream. No such
pleasure has since visited me but in dreams.--Harlequin's Invasion
followed; where, I remember, the transformation of the magistrates
into reverend beldams seemed to me a piece of grave historic justice,
and the tailor carrying his own head to be as sober a verity as the
legend of St. Denys.
The next play to which I was taken was the Lady of the Manor, of
which, with the exception of some scenery, very faint traces are left
in my memory. It was followed by a pantomime, called Lun's Ghost--a
satiric touch, I apprehend, upon Rich, not long since dead--but to my
apprehension (too sincere for satire), Lun was as remote a piece of
antiquity as Lud--the father, of a line of Harlequins--transmitting
his dagger of lath (the wooden sceptre) through countless ages. I saw
the primeval Motley come from his silent tomb in a ghastly vest of
white patch-work, like the apparition of a dead rainbow. So Harlequins
(thought I) look when they are dead.
My third play followed in quick succession. It was the Way of the
World. I think I must have sat at it as grave as a judge; for, I
remember, the hysteric affectations of good Lady Wishfort affected me
like some solemn tragic passion. Robinson Crusoe followed; in which
Crusoe, man Friday, and the parrot, were as good and authentic as in
the story.--The clownery and pantaloonery of these pantomimes have
clean passed out of my head. I believe, I no more laughed at them,
than at the same age I should have been disposed to laugh at the
grotesque Gothic heads (seeming to me then replete with devout
meaning) that gape, and grin, in stone around the inside of the old
Round Church (my church) of the Templars.
I saw these plays in the season 1781-2, when I was from six to seven
years old. After the intervention of six or seven other years (for
at school all play-going was inhibited) I again entered the doors
of a theatre. That old Artaxerxes evening had never done ringing in
my fancy. I expected the same feelings to come again with the same
occasion. But we differ from ourselves less at sixty and sixteen,
than the latter does from six. In that interval what had I not lost!
At the first period I knew nothing, understood nothing, discriminated
nothing. I felt all, loved all, wondered all--
Was nourished, I could not tell how--
I had left the temple a devotee, and was returned a rationalist. The
same things were there materially; but the emblem, the reference,
was gone!--The green curtain was no longer a veil, drawn between two
worlds, the unfolding of which was to bring back past ages, to present
"a royal ghost,"--but a certain quantity of green baize, which was
to separate the audience for a given time from certain of their
fellow-men who were to come forward and pretend those parts. The
lights--the orchestra lights--came up a clumsy machinery. The first
ring, and the second ring, was now but a trick of the prompter's
bell--which had been, like the note of the cuckoo, a phantom of a
voice, no hand seen or guessed at which ministered to its warning.
The actors were men and women painted. I thought the fault was in
them; but it was in myself, and the alteration which those many
centuries--of six short twelve-months--had wrought in me.--Perhaps
it was fortunate for me that the play of the evening was but an
indifferent comedy, as it gave me time to crop some unreasonable
expectations, which might have interfered with the genuine emotions
with which I was soon after enabled to enter upon the first appearance
to me of Mrs. Siddons in Isabella. Comparison and retrospection soon
yielded to the present attraction of the scene; and the theatre became
to me, upon a new stock, the most delightful of recreations.
DREAM-CHILDREN
A REVERIE
Children love to listen to stories about their elders, when _they_
were children; to stretch their imagination to the conception of a
traditionary great-uncle, or grandame, whom they never saw. It was in
this spirit that my little ones crept about me the other evening to
hear about their great-grandmother Field, who lived in a great house
in Norfolk (a hundred times bigger than that in which they and papa
lived) which had been the scene--so at least it was generally believed
in that part of the country--of the tragic incidents which they had
lately become familiar with from the ballad of the Children in the
Wood. Certain it is that the whole story of the children and their
cruel uncle was to be seen fairly carved out in wood upon the
chimney-piece of the great hall, the whole story down to the Robin
Redbreasts, till a foolish rich person pulled it down to set up a
marble one of modern invention in its stead, with no story upon it.
Here Alice put out one of her dear mother's looks, too tender to be
called upbraiding. Then I went on to say, how religious and how good
their great-grandmother Field was, how beloved and respected by every
body, though she was not indeed the mistress of this great house, but
had only the charge of it (and yet in some respects she might be said
to be the mistress of it too) committed to her by the owner, who
preferred living in a newer and more fashionable mansion which he had
purchased somewhere in the adjoining county; but still she lived in it
in a manner as if it had been her own, and kept up the dignity of the
great house in a sort while she lived, which afterwards came to decay,
and was nearly pulled down, and all its old ornaments stripped and
carried away to the owner's other house, where they were set up, and
looked as awkward as if some one were to carry away the old tombs they
had seen lately at the Abbey, and stick them up in Lady C.'s tawdry
gilt drawing-room. Here John smiled, as much as to say, "that would
be foolish indeed." And then I told how, when she came to die, her
funeral was attended by a concourse of all the poor, and some of the
gentry too, of the neighbourhood for many miles round, to show their
respect for her memory, because she had been such a good and religious
woman; so good indeed that she knew all the Psaltery by heart, ay,
and a great part of the Testament besides. Here little Alice spread
her hands. Then I told what a tall, upright, graceful person their
great-grandmother Field once was; and how in her youth she was
esteemed the best dancer--here Alice's little right foot played an
involuntary movement, till, upon my looking grave, it desisted--the
best dancer, I was saying, in the county, till a cruel disease, called
a cancer, came, and bowed her down with pain; but it could never bend
her good spirits, or make them stoop, but they were still upright,
because she was so good and religious. Then I told how she was used
to sleep by herself in a lone chamber of the great lone house; and
how she believed that an apparition of two infants was to be seen
at midnight gliding up and down the great staircase near where she
slept, but she said, "those innocents would do her no harm;" and how
frightened I used to be, though in those days I had my maid to sleep
with me, because I was never half so good or religious as she--and
yet I never saw the infants. Here John expanded all his eye-brows and
tried to look courageous. Then I told how good she was to all her
grand-children, having us to the great-house in the holydays, where I
in particular used to spend many hours by myself, in gazing upon the
old busts of the Twelve Caesars, that had been Emperors of Rome, till
the old marble heads would seem to live again, or I to be turned into
marble with them; how I never could be tired with roaming about that
huge mansion, with its vast empty rooms, with their worn-out hangings,
fluttering tapestry, and carved oaken pannels, with the gilding almost
rubbed out--sometimes in the spacious old-fashioned gardens, which I
had almost to myself, unless when now and then a solitary gardening
man would cross me--and how the nectarines and peaches hung upon the
walls, without my ever offering to pluck them, because they were
forbidden fruit, unless now and then,--and because I had more pleasure
in strolling about among the old melancholy-looking yew trees, or the
firs, and picking up the red berries, and the fir apples, which were
good for nothing but to look at--or in lying about upon the fresh
grass, with all the fine garden smells around me--or basking in the
orangery, till I could almost fancy myself ripening too along with the
oranges and the limes in that grateful warmth--or in watching the dace
that darted to and fro in the fish-pond, at the bottom of the garden,
with here and there a great sulky pike hanging midway down the water
in silent state, as if it mocked at their impertinent friskings,--I
had more pleasure in these busy-idle diversions than in all the sweet
flavours of peaches, nectarines, oranges, and such like common baits
of children. Here John slyly deposited back upon the plate a bunch
of grapes, which, not unobserved by Alice, he had meditated dividing
with her, and both seemed willing to relinquish them for the present
as irrelevant. Then in somewhat a more heightened tone, I told how,
though their great-grandmother Field loved all her grand-children,
yet in an especial manner she might be said to love their uncle, John
L----, because he was so handsome and spirited a youth, and a king to
the rest of us; and, instead of moping about in solitary corners, like
some of us, he would mount the most mettlesome horse he could get,
when but an imp no bigger than themselves, and make it carry him half
over the county in a morning, and join the hunters when there were any
out--and yet he loved the old great house and gardens too, but had
too much spirit to be always pent up within their boundaries--and how
their uncle grew up to man's estate as brave as he was handsome, to
the admiration of every body, but of their great-grandmother Field
most especially; and how he used to carry me upon his back when I was
a lame-footed boy--for he was a good bit older than me--many a mile
when I could not walk for pain;--and how in after life he became
lame-footed too, and I did not always (I fear) make allowances enough
for him when he was impatient, and in pain, nor remember sufficiently
how considerate he had been to me when I was lame-footed; and how
when he died, though he had not been dead an hour, it seemed as if he
had died a great while ago, such a distance there is betwixt life and
death; and how I bore his death as I thought pretty well at first, but
afterwards it haunted and haunted me; and though I did not cry or take
it to heart as some do, and as I think he would have done if I had
died, yet I missed him all day long, and knew not till then how much
I had loved him. I missed his kindness, and I missed his crossness,
and wished him to be alive again, to be quarrelling with him (for
we quarreled sometimes), rather than not have him again, and was as
uneasy without him, as he their poor uncle must have been when the
doctor took off his limb. Here the children fell a crying, and asked
if their little mourning which they had on was not for uncle John,
and they looked up, and prayed me not to go on about their uncle, but
to tell them some stories about their pretty dead mother. Then I told
how for seven long years, in hope sometimes, sometimes in despair,
yet persisting ever, I courted the fair Alice W--n; and, as much as
children could understand, I explained to them what coyness, and
difficulty, and denial meant in maidens--when suddenly, turning to
Alice, the soul of the first Alice looked out at her eyes with such a
reality of re-presentment, that I became in doubt which of them stood
there before me, or whose that bright hair was; and while I stood
gazing, both the children gradually grew fainter to my view, receding,
and still receding till nothing at last but two mournful features
were seen in the uttermost distance, which, without speech, strangely
impressed upon me the effects of speech; "We are not of Alice, nor
of thee, nor are we children at all. The children of Alice called
Bartrum father. We are nothing; less than nothing, and dreams. We
are only what might have been, and must wait upon the tedious shores
of Lethe millions of ages before we have existence, and a name"--and
immediately awaking, I found myself quietly seated in my bachelor
arm-chair, where I had fallen asleep, with the faithful Bridget
unchanged by my side--but John L. (or James Elia) was gone for ever.
DISTANT CORRESPONDENTS
IN A LETTER TO B.F. ESQ. AT SYDNEY, NEW SOUTH WALES
My dear F.--When I think how welcome the sight of a letter from the
world where you were born must be to you in that strange one to which
you have been transplanted, I feel some compunctious visitings at
my long silence. But, indeed, it is no easy effort to set about a
correspondence at our distance. The weary world of waters between us
oppresses the imagination. It is difficult to conceive how a scrawl
of mine should ever stretch across it. It is a sort of presumption
to expect that one's thoughts should live so far. It is like writing
for posterity; and reminds me of one of Mrs. Rowe's superscriptions,
"Alcander to Strephon, in the shades." Cowley's Post-Angel is no more
than would be expedient in such an intercourse. One drops a packet at
Lombard-street, and in twenty-four hours a friend in Cumberland gets
it as fresh as if it came in ice. It is only like whispering through a
long trumpet. But suppose a tube let down from the moon, with yourself
at one end, and _the man_ at the other; it would be some balk to the
spirit of conversation, if you knew that the dialogue exchanged with
that interesting theosophist would take two or three revolutions of a
higher luminary in its passage. Yet for aught I know, you may be some
parasangs nigher that primitive idea--Plato's man--than we in England
here have the honour to reckon ourselves.
Epistolary matter usually compriseth three topics; news, sentiment,
and puns. In the latter, I include all non-serious subjects; or
subjects serious in themselves, but treated after my fashion,
non-seriously.--And first, for news. In them the most desirable
circumstance, I suppose, is that they shall be true. But what security
can I have that what I now send you for truth shall not before you
get it unaccountably turn into a lie? For instance, our mutual friend
P. is at this present writing--_my Now_--in good health, and enjoys
a fair share of worldly reputation. You are glad to hear it. This is
natural and friendly. But at this present reading--_your Now_--he may
possibly be in the Bench, or going to be hanged, which in reason ought
to abate something of your transport (_i.e._ at hearing he was well,
&c.), or at least considerably to modify it. I am going to the play
this evening, to have a laugh with Munden. You have no theatre, I
think you told me, in your land of d----d realities. You naturally
lick your lips, and envy me my felicity. Think but a moment, and you
will correct the hateful emotion. Why, it is Sunday morning with
you, and 1823. This confusion of tenses, this grand solecism of _two
presents_, is in a degree common to all postage. But if I sent you
word to Bath or the Devises, that I was expecting the aforesaid treat
this evening, though at the moment you received the intelligence my
full feast of fun would be over, yet there would be for a day or two
after, as you would well know, a smack, a relish left upon my mental
palate, which would give rational encouragement for you to foster a
portion at least of the disagreeable passion, which it was in part my
intention to produce. But ten months hence your envy or your sympathy
would be as useless as a passion spent upon the dead. Not only does
truth, in these long intervals, un-essence herself, but (what is
harder) one cannot venture a crude fiction for the fear that it may
ripen into a truth upon the voyage. What a wild improbable banter I
put upon you, some three years since ---- of Will Weatherall having
married a servant-maid! I remember gravely consulting you how we
were to receive her--for Will's wife was in no case to be rejected;
and your no less serious replication in the matter; how tenderly you
advised an abstemious introduction of literary topics before the lady,
with a caution not to be too forward in bringing on the carpet matters
more within the sphere of her intelligence; your deliberate judgment,
or rather wise suspension of sentence, how far jacks, and spits, and
mops, could with propriety be introduced as subjects; whether the
conscious avoiding of all such matters in discourse would not have a
worse look than the taking of them casually in our way; in what manner
we should carry ourselves to our maid Becky, Mrs. William Weatherall
being by; whether we should show more delicacy, and a truer sense of
respect for Will's wife, by treating Becky with our customary chiding
before her, or by an unusual deferential civility paid to Becky as
to a person of great worth, but thrown by the caprice of fate into a
humble station. There were difficulties, I remember, on both sides,
which you did me the favour to state with the precision of a lawyer,
united to the tenderness of a friend. I laughed in my sleeve at your
solemn pleadings, when lo! while I was valuing myself upon this
flam put upon you in New South Wales, the devil in England, jealous
possibly of any lie-children not his own, or working after my copy,
has actually instigated our friend (not three days since) to the
commission of a matrimony, which I had only conjured up for your
diversion. William Weatherall has married Mrs. Cotterel's maid. But to
take it in its truest sense, you will see, my dear F., that news from
me must become history to you; which I neither profess to write, nor
indeed care much for reading. No person, under a diviner, can with any
prospect of veracity conduct a correspondence at such an arm's length.
Two prophets, indeed, might thus interchange intelligence with effect;
the epoch of the writer (Habbakuk) falling in with the true present
time of the receiver (Daniel); but then we are no prophets.
Then as to sentiment. It fares little better with that. This kind
of dish, above all, requires to be served up hot; or sent off in
water-plates, that your friend may have it almost as warm as yourself.
If it have time to cool, it is the most tasteless of all cold meats.
I have often smiled at a conceit of the late Lord C. It seems that
travelling somewhere about Geneva, he came to some pretty green spot,
or nook, where a willow, or something, hung so fantastically and
invitingly over a stream--was it?--or a rock?--no matter--but the
stillness and the repose, after a weary journey 'tis likely, in a
languid moment of his lordship's hot restless life, so took his fancy,
that he could imagine no place so proper, in the event of his death,
to lay his bones in. This was all very natural and excusable as a
sentiment, and shows his character in a very pleasing light. But when
from a passing sentiment it came to be an act; and when, by a positive
testamentary disposal, his remains were actually carried all that way
from England; who was there, some desperate sentimentalists excepted,
that did not ask the question, Why could not his lordship have found
a spot as solitary, a nook as romantic, a tree as green and pendent,
with a stream as emblematic to his purpose, in Surrey, in Dorset, or
in Devon? Conceive the sentiment boarded up, freighted, entered at the
Custom House (startling the tide-waiters with the novelty), hoisted
into a ship. Conceive it pawed about and handled between the rude
jests of tarpaulin ruffians--a thing of its delicate texture--the
salt bilge wetting it till it became as vapid as a damaged lustring.
Suppose it in material danger (mariners have some superstition about
sentiments) of being tossed over in a fresh gale to some propitiatory
shark (spirit of Saint Gothard, save us from a quietus so foreign
to the deviser's purpose!) but it has happily evaded a fishy
consummation. Trace it then to its lucky landing--at Lyons shall
we say?--I have not the map before me--jostled upon four men's
shoulders--baiting at this town--stopping to refresh at t'other
village--waiting a passport here, a license there; the sanction of the
magistracy in this district, the concurrence of the ecclesiastics in
that canton; till at length it arrives at its destination, tired out
and jaded, from a brisk sentiment, into a feature of silly pride or
tawdry senseless affectation. How few sentiments, my dear F., I am
afraid we can set down, in the sailor's phrase, as quite sea-worthy.
Lastly, as to the agreeable levities, which, though contemptible
in bulk, are the twinkling corpuscula which should irradiate a
right friendly epistle--your puns and small jests are, I apprehend,
extremely circumscribed in their sphere of action. They are so far
from a capacity of being packed up and sent beyond sea, they will
scarce endure to be transported by hand from this room to the next.
Their vigour is as the instant of their birth. Their nutriment
for their brief existence is the intellectual atmosphere of the
bystanders: or this last, is the fine slime of Nilus--the _melior
Lutis_,--whose maternal recipiency is as necessary as the _sol pater_
to their equivocal generation. A pun hath a hearty kind of present
ear-kissing smack with it; you can no more transmit it in its pristine
flavour, than you can send a kiss.--Have you not tried in some
instances to palm off a yesterday's pun upon a gentleman, and has
it answered? Not but it was new to his hearing, but it did not seem
to come new from you. It did not hitch in. It was like picking up
at a village ale-house a two days old newspaper. You have not seen
it before, but you resent the stale thing as an affront. This sort
of merchandise above all requires a quick return. A pun, and its
recognitory laugh, must be co-instantaneous. The one is the brisk
lightning, the other the fierce thunder. A moment's interval, and the
link is snapped. A pun is reflected from a friend's face as from a
mirror. Who would consult his sweet visnomy, if the polished surface
were two or three minutes (not to speak of twelve-months, my dear F.)
in giving back its copy?
I cannot image to myself where about you are. When I try to fix it,
Peter Wilkins's island comes across me. Sometimes you seem to be in
the _Hades_ of _Thieves_. I see Diogenes prying among you with his
perpetual fruitless lantern. What must you be willing by this time to
give for the sight of an honest man! You must almost have forgotten
how _we_ look. And tell me, what your Sydneyites do? are they th**v*ng
all day long? Merciful heaven! what property can stand against such
a depredation! The kangaroos--your Aborigines--do they keep their
primitive simplicity un-Europe-tainted, with those little short
fore-puds, looking like a lesson framed by nature to the pickpocket!
Marry, for diving into fobs they are rather lamely provided _a
priori_; but if the hue and cry were once up, they would show as fair
a pair of hind-shifters as the expertest loco-motor in the colony.--We
hear the most improbable tales at this distance. Pray, is it true that
the young Spartans among you are born with six fingers, which spoils
their scanning?--It must look very odd; but use reconciles. For their
scansion, it is less to be regretted, for if they take it into their
heads to be poets, it is odds but they turn out, the greater part of
them, vile plagiarists.--Is there much difference to see to between
the son of a th**f, and the grandson? or where does the taint stop? Do
you bleach in three or in four generations?--I have many questions to
put, but ten Delphic voyages can be made in a shorter time than it
will take to satisfy my scruples.--Do you grow your own hemp?--What is
your staple trade, exclusive of the national profession, I mean? Your
lock-smiths, I take it, are some of your great capitalists.
I am insensibly chatting to you as familiarly as when we used
to exchange good-morrows out of our old contiguous windows, in
pump-famed Hare-court in the Temple. Why did you ever leave that quiet
corner?--Why did I?--with its complement of four poor elms, from whose
smoke-dyed barks, the theme of jesting ruralists, I picked my first
lady-birds! My heart is as dry as that spring sometimes proves in
a thirsty August, when I revert to the space that is between us; a
length of passage enough to render obsolete the phrases of our English
letters before they can reach you. But while I talk, I think you hear
me,--thoughts dallying with vain surmise--
Aye me! while thee the seas and sounding shores
Hold far away.
Come back, before I am grown into a very old man, so as you shall
hardly know me. Come, before Bridget walks on crutches. Girls whom you
left children have become sage matrons, while you are tarrying there.
The blooming Miss W----r (you remember Sally W----r) called upon us
yesterday, an aged crone. Folks, whom you knew, die off every year.
Formerly, I thought that death was wearing out,--I stood ramparted
about with so many healthy friends. The departure of J.W., two springs
back corrected my delusion. Since then the old divorcer has been busy.
If you do not make haste to return, there will be little left to greet
you, of me, or mine.
THE PRAISE OF CHIMNEY-SWEEPERS
I like to meet a sweep--understand me--not a grown sweeper--old
chimney-sweepers are by no means attractive--but one of those tender
novices, blooming through their first nigritude, the maternal washings
not quite effaced from the cheek--such as come forth with the dawn, or
somewhat earlier, with their little professional notes sounding like
the _peep peep_ of a young sparrow; or liker to the matin lark should
I pronounce them, in their aerial ascents not seldom anticipating the
sun-rise?
I have a kindly yearning towards these dim specks--poor
blots--innocent blacknesses--
I reverence these young Africans of our own growth--these almost
clergy imps, who sport their cloth without assumption; and from
their little pulpits (the tops of chimneys), in the nipping air of a
December morning, preach a lesson of patience to mankind.
When a child, what a mysterious pleasure it was to witness their
operation! to see a chit no bigger than one's-self enter, one knew not
by what process, into what seemed the _fauces Averni_--to pursue him
in imagination, as he went sounding on through so many dark stifling
caverns, horrid shades!--to shudder with the idea that "now, surely,
he must be lost for ever!"--to revive at hearing his feeble shout of
discovered day-light--and then (O fulness of delight) running out of
doors, to come just in time to see the sable phenomenon emerge in
safety, the brandished weapon of his art victorious like some flag
waved over a conquered citadel! I seem to remember having been told,
that a bad sweep was once left in a stack with his brush, to indicate
which way the wind blew. It was an awful spectacle certainly; not much
unlike the old stage direction in Macbeth, where the "Apparition of a
child crowned with a tree in his hand rises."
Reader, if thou meetest one of these small gentry in thy early
rambles, it is good to give him a penny. It is better to give him
two-pence. If it be starving weather, and to the proper troubles of
his hard occupation, a pair of kibed heels (no unusual accompaniment)
be superadded, the demand on thy humanity will surely rise to a
tester.
There is a composition, the ground-work of which I have understood to
be the sweet wood 'yclept sassafras. This wood boiled down to a kind
of tea, and tempered with an infusion of milk and sugar, hath to some
tastes a delicacy beyond the China luxury. I know not how thy palate
may relish it; for myself, with every deference to the judicious Mr.
Read, who hath time out of mind kept open a shop (the only one he
avers in London) for the vending of this "wholesome and pleasant
beverage, on the south side of Fleet-street, as thou approachest
Bridge-street--_the only Salopian house_,"--I have never yet
adventured to dip my own particular lip in a basin of his commended
ingredients--a cautious premonition to the olfactories constantly
whispering to me, that my stomach must infallibly, with all due
courtesy, decline it. Yet I have seen palates, otherwise not
uninstructed in dietetical elegances, sup it up with avidity.
I know not by what particular conformation of the organ it happens,
but I have always found that this composition is surprisingly
gratifying to the palate of a young chimney-sweeper--whether the oily
particles (sassafras is slightly oleaginous) do attenuate and soften
the fuliginous concretions, which are sometimes found (in dissections)
to adhere to the roof of the mouth in these unfledged practitioners;
or whether Nature, sensible that she had mingled too much of bitter
wood in the lot of these raw victims, caused to grow out of the earth
her sassafras for a sweet lenitive--but so it is, that no possible
taste or odour to the senses of a young chimney-sweeper can convey a
delicate excitement comparable to this mixture. Being penniless, they
will yet hang their black heads over the ascending steam, to gratify
one sense if possible, seemingly no less pleased than those domestic
animals--cats--when they purr over a new-found sprig of valerian.
There is something more in these sympathies than philosophy can
inculcate.
Now albeit Mr. Read boasteth, not without reason, that his is the
_only Salopian house;_ yet be it known to thee, reader--if thou art
one who keepest what are called good hours, thou art haply ignorant
of the fact--he hath a race of industrious imitators, who from
stalls, and under open sky, dispense the same savoury mess to humbler
customers, at that dead time of the dawn, when (as extremes meet) the
rake, reeling home from his midnight cups, and the hard-handed artisan
leaving his bed to resume the premature labours of the day, jostle,
not unfrequently to the manifest disconcerting of the former, for the
honours of the pavement. It is the time when, in summer, between the
expired and the not yet relumined kitchen-fires, the kennels of our
fair metropolis give forth their least satisfactory odours. The rake,
who wisheth to dissipate his o'er-night vapours in more grateful
coffee, curses the ungenial fume, as he passeth; but the artisan stops
to taste, and blesses the fragrant breakfast.
This is _Saloop_--the precocious herb-woman's darling--the delight of
the early gardener, who transports his smoking cabbages by break of
day from Hammersmith to Covent-garden's famed piazzas--the delight,
and, oh I fear, too often the envy, of the unpennied sweep. Him
shouldest thou haply encounter, with his dim visage pendent over the
grateful steam, regale him with a sumptuous basin (it will cost thee
but three half-pennies) and a slice of delicate bread and butter (an
added halfpenny)--so may thy culinary fires, eased of the o'er-charged
secretions from thy worse-placed hospitalities, curl up a lighter
volume to the welkin--so may the descending soot never taint thy
costly well-ingredienced soups--nor the odious cry, quickreaching from
street to street, of the _fired chimney_, invite the rattling engines
from ten adjacent parishes, to disturb for a casual scintillation thy
peace and pocket!
I am by nature extremely susceptible of street affronts; the jeers
and taunts of the populace; the low-bred triumph they display over
the casual trip, or splashed stocking, of a gentleman. Yet can I
endure the jocularity of a young sweep with something more than
forgiveness.--In the last winter but one, pacing along Cheapside with
my accustomed precipitation when I walk westward, a treacherous slide
brought me upon my back in an instant. I scrambled up with pain and
shame enough--yet outwardly trying to face it down, as if nothing had
happened--when the roguish grin of one of these young wits encountered
me. There he stood, pointing me out with his dusky finger to the
mob, and to a poor woman (I suppose his mother) in particular, till
the tears for the exquisiteness of the fun (so he thought it) worked
themselves out at the corners of his poor red eyes, red from many a
previous weeping, and soot-inflamed, yet twinkling through all with
such a joy, snatched out of desolation, that Hogarth--but Hogarth has
got him already (how could he miss him?) in the March to Finchley,
grinning at the pye-man--there he stood, as he stands in the picture,
irremovable, as if the jest was to last for ever--with such a maximum
of glee, and minimum of mischief, in his mirth--for the grin of a
genuine sweep hath absolutely no malice in it--that I could have
been content, if the honour of a gentleman might endure it, to have
remained his butt and his mockery till midnight.
I am by theory obdurate to the seductiveness of what are called a fine
set of teeth. Every pair of rosy lips (the ladies must pardon me) is
a casket, presumably holding such jewels; but, methinks, they should
take leave to "air" them as frugally as possible. The fine lady, or
fine gentleman, who show me their teeth, show me bones. Yet must
I confess, that from the mouth of a true sweep a display (even to
ostentation) of those white and shining ossifications, strikes me as
an agreeable anomaly in manners, and an allowable piece of foppery. It
is, as when
A sable cloud
Turns forth her silver lining on the night.
It is like some remnant of gentry not quite extinct; a badge of
better days; a hint of nobility:--and, doubtless, under the obscuring
darkness and double night of their forlorn disguisement, oftentimes
lurketh good blood, and gentle conditions, derived from lost ancestry,
and a lapsed pedigree. The premature apprenticements of these tender
victims give but too much encouragement, I fear, to clandestine, and
almost infantile abductions; the seeds of civility and true courtesy,
so often discernible in these young grafts (not otherwise to be
accounted for) plainly hint at some forced adoptions; many noble
Rachels mourning for their children, even in our days, countenance the
fact; the tales of fairy-spiriting may shadow a lamentable verity, and
the recovery of the young Montagu be but a solitary instance of, good
fortune, out of many irreparable and hopeless _defiliations_.
In one of the state-beds at Arundel Castle, a few years since--under a
ducal canopy--(that seat of the Howards is an object of curiosity to
visitors, chiefly for its beds, in which the late duke was especially
a connoisseur)--encircled with curtains of delicatest crimson, with
starry coronets inwoven--folded between a pair of sheets whiter and
softer than the lap where Venus lulled Ascanius--was discovered by
chance, after all methods of search had failed, at noon-day, fast
asleep, a lost chimney-sweeper. The little creature, having somehow
confounded his passage among the intricacies of those lordly chimneys,
by some unknown aperture had alighted upon this magnificent chamber;
and, tired with his tedious explorations, was unable to resist the
delicious invitement to repose, which he there saw exhibited; so,
creeping between the sheets very quietly, laid his black head upon the
pillow, and slept like a young Howard.
Such is the account given to the visitors at the Castle.--But I cannot
help seeming to perceive a confirmation of what I have just hinted
at in this story. A high instinct was at work in the case, or I am
mistaken. Is it probable that a poor child of that description, with
whatever weariness he might be visited, would have ventured, under
such a penalty, as he would be taught to expect, to uncover the sheets
of a Duke's bed, and deliberately to lay himself down between them,
when the rug, or the carpet, presented an obvious couch, still far
above his pretensions--is this probable, I would ask, if the great
power of nature, which I contend for, had not been manifested within
him, prompting to the adventure? Doubtless this young nobleman (for
such my mind misgives me that he must be) was allured by some memory,
not amounting to full consciousness, of his condition in infancy,
when he was used to be lapt by his mother, or his nurse, in just such
sheets as he there found, into which he was now but creeping back as
into his proper _incunabula_, and resting-place.--By no other theory,
than by this sentiment of a pre-existent state (as I may call it), can
I explain a deed so venturous, and, indeed, upon any other system, so
indecorous, in this tender, but unseasonable, sleeper.
My pleasant friend JEM WHITE was so impressed with a belief of
metamorphoses like this frequently taking place, that in some sort to
reverse the wrongs of fortune in these poor changelings, he instituted
an annual feast of chimney-sweepers, at which it was his pleasure
to officiate as host and waiter. It was a solemn supper held in
Smithfield, upon the yearly return of the fair of St. Bartholomew.
Cards were issued a week before to the master-sweeps in and about the
metropolis, confining the invitation to their younger fry. Now and
then an elderly stripling would get in among us, and be good-naturedly
winked at; but our main body were infantry. One unfortunate wight,
indeed, who, relying upon his dusky suit, had intruded himself into
our party, but by tokens was providentially discovered in time to be
no chimney-sweeper (all is not soot which looks so), was quoited out
of the presence with universal indignation, as not having on the
wedding garment; but in general the greatest harmony prevailed. The
place chosen was a convenient spot among the pens, at the north side
of the fair, not so far distant as to be impervious to the agreeable
hubbub of that vanity; but remote enough not to be obvious to the
interruption of every gaping spectator in it. The guests assembled
about seven. In those little temporary parlours three tables were
spread with napery, not so fine as substantial, and at every board a
comely hostess presided with her pan of hissing sausages. The nostrils
of the young rogues dilated at the savour. JAMES WHITE, as head
waiter, had charge of the first table; and myself, with our trusty
companion BIGOD, ordinarily ministered to the other two. There was
clambering and jostling, you may be sure, who should get at the first
table--for Rochester in his maddest days could not have done the
humours of the scene with more spirit than my friend. After some
general expression of thanks for the honour the company had done him,
his inaugural ceremony was to clasp the greasy waist of old dame
Ursula (the fattest of the three), that stood frying and fretting,
half-blessing, half-cursing "the gentleman," and imprint upon her
chaste lips a tender salute, whereat the universal host would set up a
shout that tore the concave, while hundreds of grinning teeth startled
the night with their brightness. O it was a pleasure to see the
sable younkers lick in the unctuous meat, with _his_ more unctuous
sayings--how he would fit the tit bits to the puny mouths, reserving
the lengthier links for the seniors--how he would intercept a morsel
even in the jaws of some young desperado, declaring it "must to
the pan again to be browned, for it was not fit for a gentleman's
eating"--how he would recommend this slice of white bread, or
that piece of kissing-crust, to a tender juvenile, advising them
all to have a care of cracking their teeth, which were their best
patrimony,--how genteelly he would deal about the small ale, as if it
were wine, naming the brewer, and protesting, if it were not good,
he should lose their custom; with a special recommendation to wipe
the lip before drinking. Then we had our toasts--"The King,"--the
"Cloth,"--which, whether they understood or not, was equally diverting
and flattering;--and for a crowning sentiment, which never failed,
"May the Brush supersede the Laurel!" All these, and fifty other
fancies, which were rather felt than comprehended by his guests,
would he utter, standing upon tables, and prefacing every sentiment
with a "Gentlemen, give me leave to propose so and so," which was a
prodigious comfort to those young orphans; every now and then stuffing
into his mouth (for it did not do to be squeamish on these occasions)
indiscriminate pieces of those reeking sausages, which pleased them
mightily, and was the savouriest part, you may believe, of the
entertainment.
Golden lads and lasses must.
As chimney-sweepers, come to dust--
JAMES WHITE is extinct, and with him these suppers have long ceased.
He carried away with him half the fun of the world when he died--of
my world at least. His old clients look for him among the pens; and,
missing him, reproach the altered feast of St. Bartholomew, and the
glory of Smithfield departed for ever.
A COMPLAINT OF THE DECAY OF BEGGARS IN THE METROPOLIS
The all-sweeping besom of societarian reformation--your only
modern Alcides' club to rid the time of its abuses--is uplift with
many-handed sway to extirpate the last fluttering tatters of the
bugbear MENDICITY from the metropolis. Scrips, wallets, bags--staves,
dogs, and crutches--the whole mendicant fraternity with all their
baggage are fast posting out of the purlieus of this eleventh
persecution. From the crowded crossing, from the corners of streets
and turnings of allies, the parting Genius of Beggary is "with sighing
sent."
I do not approve of this wholesale going to work, this impertinent
crusado, or _bellum ad exterminationem_, proclaimed against a species.
Much good might be sucked from these Beggars.
They were the oldest and the honourablest form of pauperism. Their
appeals were to our common nature; less revolting to an ingenuous mind
than to be a suppliant to the particular humours or caprice of any
fellow-creature, or set of fellow-creatures, parochial or societarian.
Theirs were the only rates uninvidious in the levy, ungrudged in the
assessment.
There was a dignity springing from the very depth of their desolation;
as to be naked is to be so much nearer to the being a man, than to go
in livery.
The greatest spirits have felt this in their reverses; and when
Dionysius from king turned schoolmaster, do we feel any thing towards
him but contempt? Could Vandyke have made a picture of him, swaying
a ferula for a sceptre, which would have affected our minds with the
same heroic pity, the same compassionate admiration, with which we
regard his Belisarius begging for an _obolum_? Would the moral have
been more graceful, more pathetic?
The Blind Beggar in the legend--the father of pretty Bessy--whose
story doggrel rhymes and ale-house signs cannot so degrade or
attenuate, but that some sparks of a lustrous spirit will shine
through the disguisements--this noble Earl of Cornwall (as indeed he
was) and memorable sport of fortune, fleeing from the unjust sentence
of his liege lord, stript of all, and seated on the flowering green
of Bethnal, with his more fresh and springing daughter by his side,
illumining his rags and his beggary--would the child and parent have
cut a better figure, doing the honours of a counter, or expiating
their fallen condition upon the three-foot eminence of some
sempstering shop-board?
In tale or history your Beggar is ever the just antipode to your King.
The poets and romancical writers (as dear Margaret Newcastle would
call them) when they would most sharply and feelingly paint a reverse
of fortune, never stop till they have brought down their hero in good
earnest to rags and the wallet. The depth of the descent illustrates
the height he falls from. There is no medium which can be presented
to the imagination without offence. There is no breaking the fall.
Lear, thrown from his palace, must divest him of his garments, till
he answer "mere nature;" and Cresseid, fallen from a prince's love,
must extend her pale arms, pale with other whiteness than of beauty,
supplicating lazar alms with bell and clap-dish.
The Lucian wits knew this very well; and, with a converse policy, when
they would express scorn of greatness without the pity, they show us
an Alexander in the shades cobbling shoes, or a Semiramis getting up
foul linen.
How would it sound in song, that a great monarch had declined
his affections upon the daughter of a baker! yet do we feel the
imagination at all violated when we read the "true ballad," where King
Cophetua wooes the beggar maid?
Pauperism, pauper, poor man, are expressions of pity, but pity alloyed
with contempt. No one properly contemns a beggar. Poverty is a
comparative thing, and each degree of it is mocked by its "neighbour
grice." Its poor rents and comings-in are soon summed up and told.
Its pretences to property are almost ludicrous. Its pitiful attempts
to save excite a smile. Every scornful companion can weigh his
trifle-bigger purse against it. Poor man reproaches poor man in the
streets with impolitic mention of his condition, his own being a
shade better, while the rich pass by and jeer at both. No rascally
comparative insults a Beggar, or thinks of weighing purses with him.
He is not in the scale of comparison. He is not under the measure of
property. He confessedly hath none, any more than a dog or a sheep. No
one twitteth him with ostentation above his means. No one accuses him
of pride, or upbraideth him with mock humility. None jostle with him
for the wall, or pick quarrels for precedency. No wealthy neighbour
seeketh to eject him from his tenement. No man sues him. No man goes
to law with him. If I were not the independent gentleman that I am,
rather than I would be a retainer to the great, a led captain, or a
poor relation, I would choose, out of the delicacy and true greatness
of my mind, to be a Beggar.
Rags, which are the reproach of poverty, are the Beggar's robes, and
graceful _insignia_ of his profession, his tenure, his full dress, the
suit in which he is expected to show himself in public. He is never
out of the fashion, or limpeth awkwardly behind it. He is not required
to put on court mourning. He weareth all colours, fearing none. His
costume hath undergone less change than the Quaker's. He is the only
man in the universe who is not obliged to study appearances. The ups
and downs of the world concern him no longer. He alone continueth
in one stay. The price of stock or land affecteth him not. The
fluctuations of agricultural or commercial prosperity touch him not,
or at worst but change his customers. He is not expected to become
bail or surety for any one. No man troubleth him with questioning his
religion or politics. He is the only free man in the universe. The
Mendicants of this great city were so many of her sights, her lions. I
can no more spare them than I could the Cries of London. No corner of
a street is complete without them. They are as indispensable as the
Ballad Singer; and in their picturesque attire as ornamental as the
Signs of old London. They were the standing morals, emblems, mementos,
dial-mottos, the spital sermons, the books for children, the salutary
checks and pauses to the high and rushing tide of greasy citizenry--
--Look
Upon that poor and broken bankrupt there.
Above all, those old blind Tobits that used to line the wall of
Lincoln's Inn Garden, before modern fastidiousness had expelled them,
casting up their ruined orbs to catch a ray of pity, and (if possible)
of light, with their faithful Dog Guide at their feet,--whither are
they fled? or into what corners, blind as themselves, have they been
driven, out of the wholesome air and sun-warmth? immersed between
four walls, in what withering poor-house do they endure the penalty
of double darkness, where the chink of the dropt half-penny no more
consoles their forlorn bereavement, far from the sound of the cheerful
and hope-stirring tread of the passenger? Where hang their useless
staves? and who will farm their dogs?--Have the overseers of St. L----
caused them to be shot? or were they tied up in sacks, and dropt into
the Thames, at the suggestion of B----, the mild rector of ----?
Well fare the soul of unfastidious Vincent Bourne, most classical, and
at the same time, most English, of the Latinists!--who has treated
of this human and quadrupedal alliance, this dog and man friendship,
in the sweetest of his poems, the _Epitaphium in Canem_, or, _Dog's
Epitaph_. Reader, peruse it; and say, if customary sights, which could
call up such gentle poetry as this, were of a nature to do more
harm or good to the moral sense of the passengers through the daily
thoroughfares of a vast and busy metropolis.
Pauperis hic Iri requiesco Lyciscus, herilis,
Dum vixi, tutela vigil columenque senectae,
Dux caeco fidus: nec, me ducente, solebat,
Praetenso hinc atque hinc baculo, per iniqua locorum
Incertam explorare viam; sed fila secutus,
Quae dubios regerent passus, vestigia tuta
Fixit inoffenso gressu; gelidumque sedile
In nudo nactus saxo, qua praetereuntium
Unda frequens confluxit, ibi miserisque tenebras
Lamentis, noctemque oculis ploravit obortam.
Ploravit nec frustra; obolum dedit alter et alter,
Queis corda et mentem indiderat natura benignam.
Ad latus interea jacui sopitus herile,
Vel mediis vigil in somnis; ad herilia jussa
Auresque atque animum arrectus, seu frustula amice
Porrexit sociasque dapes, seu longa diei
Taedia perpessus, reditum sub nocte parabat.
Hi mores, haec vita fuit, dum fata sinebant,
Dum neque languebam morbis, nec inerte senecta;
Quae tandem obrepsit, veterique satellite caecum
Orbavit dominum: prisci sed gratia facti
Ne tola intereat, longos deleta per annos,
Exiguum hunc Irus tumulum de cespite fecit,
Etsi inopis, non ingratae, munuscula dextrae;
Carmine signavitque brevi, dominumque canemque
Quod memoret, fidumque canem dominumque benignum.
* * * * *
Poor Irus' faithful wolf-dog here I lie,
That wont to tend my old blind master's steps,
His guide and guard: nor, while my service lasted,
Had he occasion for that staff, with which
He now goes picking out his path in fear
Over the highways and crossings; but would plant,
Safe in the conduct of my friendly string,
A firm foot forward still, till he had reach'd
His poor seat on some stone, nigh where the tide
Of passers by in thickest confluence flow'd:
To whom with loud and passionate laments
From morn to eve his dark estate he wail'd.
Nor wail'd to all in vain: some here and there,
The well-disposed and good, their pennies gave.
I meantime at his feet obsequious slept;
Not all-asleep in sleep, but heart and ear
Prick'd up at his least motion; to receive
At his kind hand ray customary crums,
And common portion in his feast of scraps;
Or when night warn'd us homeward, tired and spent
With our long day and tedious beggary.
These were my manners, this my way of life,
Till age and slow disease me overtook,
And sever'd from my sightless master's side.
But lest the grace of so good deeds should die.
Through tract of years in mute oblivion lost,
This slender tomb of turf hath Irus reared,
Cheap monument of no ungrudging hand,
And with short verse inscribed it, to attest,
In long and lasting union to attest,
The virtues of the Beggar and his Dog.
These dim eyes have in vain explored for some months past a well-known
figure, or part of the figure, of a man, who used to glide his comely
upper half over the pavements of London, wheeling along with most
ingenious celerity upon a machine of wood; a spectacle to natives,
to foreigners, and to children. He was of a robust make, with a
florid sailor-like complexion, and his head was bare to the storm and
sunshine. He was a natural curiosity, a speculation to the scientific,
a prodigy to the simple. The infant would stare at the mighty man
brought down to his own level. The common <DW36> would despise his
own pusillanimity, viewing the hale stoutness, and hearty heart,
of this half-limbed giant. Few but must have noticed him; for the
accident, which brought him low, took place during the riots of 1780,
and he has been a groundling so long. He seemed earth-born, an Antaeus,
and to suck in fresh vigour from the soil which he neighboured. He
was a grand fragment; as good as an Elgin marble. The nature, which
should have recruited his reft legs and thighs, was not lost, but only
retired into his upper parts, and he was half a Hercules. I heard a
tremendous voice thundering and growling, as before an earthquake,
and, casting down my eyes, it was this mandrake reviling a steed that
had started at his portentous appearance. He seemed to want but his
just stature to have rent the offending quadruped in shivers. He was
as the man-part of a Centaur, from which the horse-half had been
cloven in some dire Lapithan controversy. He moved on, as if he could
have made shift with yet half of the body-portion which was left
him. The _os sublime_ was not wanting; and he threw out yet a jolly
countenance upon the heavens. Forty-and-two years had he driven this
out of door trade, and now that his hair is grizzled in the service,
but his good spirits no way impaired, because he is not content to
exchange his free air and exercise for the restraints of a poor-house,
he is expiating his contumacy in one of those houses (ironically
christened) of Correction.
Was a daily spectacle like this to be deemed a nuisance, which called
for legal interference to remove? or not rather a salutary and a
touching object, to the passers-by in a great city? Among her shows,
her museums, and supplies for ever-gaping curiosity (and what else but
an accumulation of sights--endless sights--_is_ a great city; or for
what else is it desirable?) was there not room for one _Lusus_ (not
_Naturae_, indeed, but) _Accidentium_? What if in forty-and-two years'
going about, the man had scraped together enough to give a portion
to his child (as the rumour ran) of a few hundreds--whom had he
injured?--whom had he imposed upon? The contributors had enjoyed their
_sight_ for their pennies. What if after being exposed all day to the
heats, the rains, and the frosts of heaven--shuffling his ungainly
trunk along in an elaborate and painful motion--he was enabled to
retire at night to enjoy himself at a club of his fellow <DW36>s over
a dish of hot meat and vegetables, as the charge was gravely brought
against him by a clergyman deposing before a House of Commons'
Committee--was _this_, or was his truly paternal consideration, which
(if a fact) deserved a statue rather than a whipping-post, and is
inconsistent at least with the exaggeration of nocturnal orgies which
he has been slandered with--a reason that he should be deprived of his
chosen, harmless, nay edifying, way of life, and be committed in hoary
age for a sturdy vagabond?--
There was a Yorick once, whom it would not have shamed to have sate
down at the <DW36>s' feast, and to have thrown in his benediction,
ay, and his mite too, for a companionable symbol. "Age, thou hast lost
thy breed."--
Half of these stories about the prodigious fortunes made by begging
are (I verily believe) misers' calumnies. One was much talked of in
the public papers some time since, and the usual charitable inferences
deduced. A clerk in the Bank was surprised with the announcement of
a five hundred pound legacy left him by a person whose name he was a
stranger to. It seems that in his daily morning walks from Peckham
(or some village thereabouts) where he lived, to his office, it had
been his practice for the last twenty years to drop his half-penny
duly into the hat of some blind Bartimeus, that sate begging alms
by the way-side in the Borough. The good old beggar recognised his
daily benefactor by the voice only; and, when he died, left all the
amassings of his alms (that had been half a century perhaps in the
accumulating) to his old Bank friend. Was this a story to purse up
people's hearts, and pennies, against giving an alms to the blind?--or
not rather a beautiful moral of well-directed charity on the one part,
and noble gratitude upon the other?
I sometimes wish I had been that Bank clerk.
I seem to remember a poor old grateful kind of creature, blinking, and
looking up with his no eyes in the sun--Is it possible I could have
steeled my purse against him?
Perhaps I had no small change.
Reader, do not be frightened at the hard words, imposition,
imposture--_give, and ask no questions_. Cast thy bread upon the
waters. Some have unawares (like this Bank clerk) entertained angels.
Shut not thy purse-strings always against painted distress. Act a
charity sometimes. When a poor creature (outwardly and visibly such)
comes before thee, do not stay to inquire whether the "seven small
children," in whose name he implores thy assistance, have a veritable
existence. Rake not into the bowels of unwelcome truth, to save
a halfpenny. It is good to believe him. If he be not all that he
pretendeth, _give_, and under a personate father of a family, think
(if thou pleasest) that thou hast relieved an indigent bachelor. When
they come with their counterfeit looks, and mumping tones, think them
players. You pay your money to see a comedian feign these things,
which, concerning these poor people, thou canst not certainly tell
whether they are feigned or not.
A DISSERTATION UPON ROAST PIG
Mankind, says a Chinese manuscript, which my friend M. was obliging
enough to read and explain to me, for the first seventy thousand ages
ate their meat raw, clawing or biting it from the living animal, just
as they do in Abyssinia to this day. This period is not obscurely
hinted at by their great Confucius in the second chapter of his
Mundane Mutations, where he designates a kind of golden age by the
term Cho-fang, literally the Cooks' holiday. The manuscript goes on
to say, that the art of roasting, or rather broiling (which I take
to be the elder brother) was accidentally discovered in the manner
following. The swine-herd, Ho-ti, having gone out into the woods one
morning, as his manner was, to collect mast for his hogs, left his
cottage in the care of his eldest son Bo-bo, a great lubberly boy, who
being fond of playing with fire, as younkers of his age commonly are,
let some sparks escape into a bundle of straw, which kindling quickly,
spread the conflagration over every part of their poor mansion,
till it was reduced to ashes. Together with the cottage (a sorry
antediluvian make-shift of a building, you may think it), what was of
much more importance, a fine litter of new-farrowed pigs, no less than
nine in number, perished. China pigs have been esteemed a luxury all
over the East from the remotest periods that we read of. Bo-bo was in
the utmost consternation, as you may think, not so much for the sake
of the tenement, which his father and he could easily build up again
with a few dry branches, and the labour of an hour or two, at any
time, as for the loss of the pigs. While he was thinking what he
should say to his father, and wringing his hands over the smoking
remnants of one of those untimely sufferers, an odour assailed his
nostrils, unlike any scent which he had before experienced. What
could it proceed from?--not from the burnt cottage--he had smelt that
smell before--indeed this was by no means the first accident of the
kind which had occurred through the negligence of this unlucky young
fire-brand. Much less did it resemble that of any known herb, weed,
or flower. A premonitory moistening at the same time overflowed his
nether lip. He knew not what to think. He next stooped down to feel
the pig, if there were any signs of life in it. He burnt his fingers,
and to cool them he applied them in his booby fashion to his mouth.
Some of the crums of the scorched skin had come away with his fingers,
and for the first time in his life (in the world's life indeed, for
before him no man had known it) he tasted--_crackling_! Again he felt
and fumbled at the pig. It did not burn him so much now, still he
licked his fingers from a sort of habit. The truth at length broke
into his slow understanding, that it was the pig that smelt so, and
the pig that tasted so delicious; and, surrendering himself up to the
newborn pleasure, he fell to tearing up whole handfuls of the scorched
skin with the flesh next it, and was cramming it down his throat in
his beastly fashion, when his sire entered amid the smoking rafters,
armed with retributory cudgel, and finding how affairs stood, began to
rain blows upon the young rogue's shoulders, as thick as hail-stones,
which Bo-bo heeded not any more than if they had been flies. The
tickling pleasure, which he experienced in his lower regions, had
rendered him quite callous to any inconveniences he might feel in
those remote quarters. His father might lay on, but he could not beat
him from his pig, till he had fairly made an end of it, when, becoming
a little more sensible of his situation, something like the following
dialogue ensued.
"You graceless whelp, what have you got there devouring? Is it not
enough that you have burnt me down three houses with your dog's
tricks, and be hanged to you, but you must be eating fire, and I know
not what--what have you got there, I say?"
"O father, the pig, the pig, do come and taste how nice the burnt pig
eats."
The ears of Ho-ti tingled with horror. He cursed his son, and he
cursed himself that ever he should beget a son that should eat burnt
pig.
Bo-bo, whose scent was wonderfully sharpened since moming, soon raked
out another pig, and fairly rending it asunder, thrust the lesser
half by main force into the fists of Ho-ti, still shouting out "Eat,
eat, eat the burnt pig, father, only taste--O Lord,"--with such like
barbarous ejaculations, cramming all the while as if he would choke.
Ho-ti trembled every joint while he grasped the abominable thing,
wavering whether he should not put his son to death for an unnatural
young monster, when the crackling scorching his fingers, as it had
done his son's, and applying the same remedy to them, he in his turn
tasted some of its flavour, which, make what sour mouths he would for
a pretence, proved not altogether displeasing to him. In conclusion
(for the manuscript here is a little tedious) both father and son
fairly sat down to the mess, and never left off till they had
despatched all that remained of the litter.
Bo-bo was strictly enjoined not to let the secret escape, for the
neighbours would certainly have stoned them for a couple of abominable
wretches, who could think of improving upon the good meat which
God had sent them. Nevertheless, strange stories got about. It was
observed that Ho-ti's cottage was burnt down now more frequently than
ever. Nothing but fires from this time forward. Some would break out
in broad day, others in the night-time. As often as the sow farrowed,
so sure was the house of Ho-ti to be in a blaze; and Ho-ti himself,
which was the more remarkable, instead of chastising his son, seemed
to grow more indulgent to him than ever. At length they were watched,
the terrible mystery discovered, and father and son summoned to take
their trial at Pekin, then an inconsiderable assize town. Evidence was
given, the obnoxious food itself produced in court, and verdict about
to be pronounced, when the foreman of the jury begged that some of the
burnt pig, of which the culprits stood accused, might be handed into
the box. He handled it, and they all handled it, and burning their
fingers, as Bo-bo and his father had done before them, and nature
prompting to each of them the same remedy, against the face of all
the facts, and the clearest charge which judge had ever given,--to
the surprise of the whole court, townsfolk, strangers, reporters, and
all present--without leaving the box, or any manner of consultation
whatever, they brought in a simultaneous verdict of Not Guilty.
The judge, who was a shrewd fellow, winked at the manifest iniquity
of the decision: and, when the court was dismissed, went privily, and
bought up all the pigs that could be had for love or money. In a few
days his Lordship's town house was observed to be on fire. The thing
took wing, and now there was nothing to be seen but fires in every
direction. Fuel and pigs grew enormously dear all over the district.
The insurance offices one and all shut up shop. People built slighter
and slighter every day, until it was feared that the very science of
architecture would in no long time be lost to the world. Thus this
custom of firing houses continued, till in process of time, says my
manuscript, a sage arose, like our Locke, who made a discovery, that
the flesh of swine, or indeed of any other animal, might be cooked
(_burnt_, as they called it) without the necessity of consuming a
whole house to dress it. Then first began the rude form of a gridiron.
Roasting by the string, or spit, came in a century or two later,
I forget in whose dynasty. By such slow degrees, concludes the
manuscript, do the most useful, and seemingly the most obvious arts,
make their way among mankind.--
Without placing too implicit faith in the account above given, it must
be agreed, that if a worthy pretext for so dangerous an experiment as
setting houses on fire (especially in these days) could be assigned in
favour of any culinary object, that pretext and excuse might be found
in ROAST PIG.
Of all the delicacies in the whole _mundus edibilis_, I will maintain
it to be the most delicate--_princeps obsoniorum_.
I speak not of your grown porkers--things between pig and pork--those
hobbydehoys--but a young and tender suckling--under a moon
old--guiltless as yet of the sty--with no original speck of the
_amor immunditiae_, the hereditary failing of the first parent, yet
manifest--his voice as yet not broken, but something between a
childish treble, and a grumble--the mild forerunner, or _praeludium_,
of a grunt.
_He must be roasted._ I am not ignorant that our ancestors ate them
seethed, or boiled--but what a sacrifice of the exterior tegument!
There is no flavour comparable, I will contend, to that of the crisp,
tawny, well-watched, not over-roasted, _crackling_, as it is well
called--the very teeth are invited to their share of the pleasure
at this banquet in overcoming the coy, brittle resistance--with the
adhesive oleaginous--O call it not fat--but an indefinable sweetness
growing up to it--the tender blossoming of fat--fat cropped in the
bud--taken in the shoot--in the first innocence--the cream and
quintessence of the child-pig's yet pure food--the lean, no lean, but
a kind of animal manna--or, rather, fat and lean (if it must be so) so
blended and running into each other, that both together make but one
ambrosian result, or common substance.
Behold him, while he is doing--it seemeth rather a refreshing warmth,
than a scorching heat, that he is so passive to. How equably he
twirleth round the string!--Now he is just done. To see the extreme
sensibility of that tender age, he hath wept out his pretty
eyes--radiant jellies--shooting stars--
See him in the dish, his second cradle, how meek he lieth!--wouldst
thou have had this innocent grow up to the grossness and indocility
which too often accompany maturer swinehood? Ten to one he would
have proved a glutton, a sloven, an obstinate, disagreeable
animal--wallowing in all manner of filthy conversation--from these
sins he is happily snatched away--
Ere sin could blight, or sorrow fade,
Death came with timely care--
his memory is odoriferous--no clown curseth, while his stomach half
rejecteth, the rank bacon--no coalheaver bolteth him in reeking
sausages--he hath a fair sepulchre in the grateful stomach of the
judicious epicure--and for such a tomb might be content to die.
He is the best of Sapors. Pine-apple is great. She is indeed almost
too transcendent--a delight, if not sinful, yet so like to sinning,
that really a tender-conscienced person would do well to pause--too
ravishing for mortal taste, she woundeth and excoriateth the lips
that approach her--like lovers' kisses, she biteth--she is a pleasure
bordering on pain from the fierceness and insanity of her relish--but
she stoppeth at the palate--she meddleth not with the appetite--and
the coarsest hunger might barter her consistently for a mutton chop.
Pig--let me speak his praise--is no less provocative of the appetite,
than he is satisfactory to the criticalness of the censorious palate.
The strong man may batten on him, and the weakling refuseth not his
mild juices.
Unlike to mankind's mixed characters, a bundle of virtues and vices,
inexplicably intertwisted, and not to be unravelled without hazard, he
is--good throughout. No part of him is better or worse than another.
He helpeth, as far as his little means extend, all around. He is the
least envious of banquets. He is all neighbours' fare.
I am one of those, who freely and ungrudgingly impart a share of the
good things of this life which fall to their lot (few as mine are in
this kind) to a friend. I protest I take as great an interest in my
friend's pleasures, his relishes, and proper satisfactions, as in mine
own. "Presents," I often say, "endear Absents." Hares, pheasants,
partridges, snipes, barn-door chicken (those "tame villatic fowl"),
capons, plovers, brawn, barrels of oysters, I dispense as freely as
I receive them. I love to taste them, as it were, upon the tongue
of my friend. But a stop must be put somewhere. One would not, like
Lear, "give every thing." I make my stand upon pig. Methinks it is an
ingratitude to the Giver of all good flavours, to extra-domiciliate,
or send out of the house, slightingly, (under pretext of friendship,
or I know not what) a blessing so particularly adapted, predestined, I
may say, to my individual palate--It argues an insensibility.
I remember a touch of conscience in this kind at school. My good
old aunt, who never parted from me at the end of a holiday without
stuffing a sweet-meat, or some nice thing, into my pocket, had
dismissed me one evening with a smoking plum-cake, fresh from the
oven. In my way to school (it was over London bridge) a grey-headed
old beggar saluted me (I have no doubt at this time of day that he was
a counterfeit). I had no pence to console him with, and in the vanity
of self-denial, and the very coxcombry of charity, school-boy-like,
I made him a present of--the whole cake! I walked on a little,
buoyed up, as one is on such occasions, with a sweet soothing of
self-satisfaction; but before I had got to the end of the bridge,
my better feelings returned, and I burst into tears, thinking how
ungrateful I had been to my good aunt, to go and give her good gift
away to a stranger, that I had never seen before, and who might be a
bad man for aught I knew; and then I thought of the pleasure my aunt
would be taking in thinking that I--I myself, and not another--would
eat her nice cake--and what should I say to her the next time I saw
her--how naughty I was to part with her pretty present--and the odour
of that spicy cake came back upon my recollection, and the pleasure
and the curiosity I had taken in seeing her make it, and her joy
when she sent it to the oven, and how disappointed she would feel
that I had never had a bit of it in my mouth at last--and I blamed
my impertinent spirit of alms-giving, and out-of-place hypocrisy of
goodness, and above all I wished never to see the face again of that
insidious, good-for-nothing, old grey impostor.
Our ancestors were nice in their method of sacrificing these tender
victims. We read of pigs whipt to death with something of a shock,
as we hear of any other obsolete custom. The age of discipline is
gone by, or it would be curious to inquire (in a philosophical light
merely) what effect this process might have towards intenerating and
dulcifying a substance, naturally so mild and dulcet as the flesh
of young, pigs. It looks like refining a violet. Yet we should be
cautious, while we condemn the inhumanity, how we censure the wisdom
of the practice. It might impart a gusto--
I remember an hypothesis, argued upon by the young students, when I
was at St. Omer's, and maintained with much learning and pleasantry on
both sides, "Whether, supposing that the flavour of a pig who obtained
his death by whipping (_per flagellationem extremam_) superadded a
pleasure upon the palate of a man more intense than any possible
suffering we can conceive in the animal, is man justified in using
that method of putting the animal to death?" I forget the decision.
His sauce should be considered. Decidedly, a few bread crums, done up
with his liver and brains, and a dash of mild sage. But, banish, dear
Mrs. Cook, I beseech you, the whole onion tribe. Barbecue your whole
hogs to your palate, steep them in shalots, stuff them out with
plantations of the rank and guilty garlic; you cannot poison them, or
make them stronger than they are--but consider, he is a weakling--a
flower.
A BACHELOR'S COMPLAINT OF THE BEHAVIOUR OF MARRIED PEOPLE
As a single man, I have spent a good deal of my time in noting down
the infirmities of Married People, to console myself for those
superior pleasures, which they tell me I have lost by remaining as I
am.
I cannot say that the quarrels of men and their wives ever made any
great impression upon me, or had much tendency to strengthen me in
those anti-social resolutions, which I took up long ago upon more
substantial considerations. What oftenest offends me at the houses
of married persons where I visit, is an error of quite a different
description;--it is that they are too loving.
Not too loving neither: that does not explain my meaning. Besides,
why should that offend me? The very act of separating themselves from
the rest of the world, to have the fuller enjoyment of each other's
society, implies that they prefer one another to all the world.
But what I complain of is, that they carry this preference so
undisguisedly, they perk it up in the faces of us single people so
shamelessly, you cannot be in their company a moment without being
made to feel, by some indirect hint or open avowal, that _you_ are not
the object of this preference. Now there are some things which give
no offence, while implied or taken for granted merely; but expressed,
there is much offence in them. If a man were to accost the first
homely-featured or plain-dressed young woman of his acquaintance, and
tell her bluntly, that she was not handsome or rich enough for him,
and he could not marry her, he would deserve to be kicked for his ill
manners; yet no less is implied in the fact, that having access and
opportunity of putting the question to her, he has never yet thought
fit to do it. The young woman understands this as clearly as if it
were put into words; but no reasonable young woman would think of
making this the ground of a quarrel. Just as little right have a
married couple to tell me by speeches, and looks that are scarce less
plain than speeches, that I am not the happy man,--the lady's choice.
It is enough that I know I am not: I do not want this perpetual
reminding.
The display of superior knowledge or riches may be made sufficiently
mortifying; but these admit of a palliative. The knowledge which is
brought out to insult me, may accidentally improve me; and in the rich
man's houses and pictures,--his parks and gardens, I have a temporary
usufruct at least. But the display of married happiness has none of
these palliatives: it is throughout pure, unrecompensed, unqualified
insult.
Marriage by its best title is a monopoly, and not of the least
invidious sort. It is the cunning of most possessors of any exclusive
privilege to keep their advantage as much out of sight as possible,
that their less favoured neighbours, seeing little of the benefit,
may the less be disposed to question the right. But these married
monopolists thrust the most obnoxious part of their patent into our
faces.
Nothing is to me more distasteful than that entire complacency and
satisfaction which beam in the countenances of a new-married couple,
in that of the lady particularly: it tells you, that her lot is
disposed of in this world: that _you_ can have no hopes of her.
It is true, I have none; nor wishes either, perhaps: but this is
one of those truths which ought, as I said before, to be taken for
granted, not expressed. The excessive airs which those people give
themselves, founded on the ignorance of us unmarried people, would be
more offensive if they were less irrational. We will allow them to
understand the mysteries belonging to their own craft better than we
who have not had the happiness to be made free of the company: but
their arrogance is not content within these limits. If a single person
presume to offer his opinion in their presence, though upon the most
indifferent subject, he is immediately silenced as an incompetent
person. Nay, a young married lady of my acquaintance, who, the best
of the jest was, had not changed her condition above a fortnight
before, in a question on which I had the misfortune to differ from
her, respecting the properest mode of breeding oysters for the London
market, had the assurance to ask with a sneer, how such an old
Bachelor as I could pretend to know any thing about such matters.
But what I have spoken of hitherto is nothing to the airs which these
creatures give themselves when they come, as they generally do,
to have children. When I consider how little of a rarity children
are,--that every street and blind alley swarms with them,--that the
poorest people commonly have them in most abundance,--that there
are few marriages that are not blest with at least one of these
bargains,--how often they turn out ill, and defeat the fond hopes
of their parents, taking to vicious courses, which end in poverty,
disgrace, the gallows, &c.--I cannot for my life tell what cause
for pride there can possibly be in having them. If they were young
phoenixes, indeed, that were born but one in a year, there might be a
pretext. But when they are so common--
I do not advert to the insolent merit which they assume with their
husbands on these occasions. Let them look to that. But why _we_, who
are not their natural-born subjects, should be expected to bring our
spices, myrrh, and incense,--our tribute and homage of admiration,--I
do not see.
"Like as the arrows in the hand of the giant, even so are the young
children:" so says the excellent office in our Prayer-book appointed
for the churching of women. "Happy is the man that hath his quiver
full of them:" So say I; but then don't let him discharge his
quiver upon us that are weaponless;--let them be arrows, but not to
gall and stick us. I have generally observed that these arrows are
double-headed: they have two forks, to be sure to hit with one or the
other. As for instance, when you come into a house which is full of
children, if you happen to take no notice of them (you are thinking
of something else, perhaps, and turn a deaf ear to their innocent
caresses), you are set down as untractable, morose, a hater of
children. On the other hand, if you find them more than usually
engaging,--if you are taken with their pretty manners, and set about
in earnest to romp and play with them, some pretext or other is sure
to be found for sending them out of the room: they are too noisy or
boisterous, or Mr. ---- does not like children. With one or other of
these forks the arrow is sure to hit you.
I could forgive their jealousy, and dispense with toying with their
brats, if it gives them any pain; but I think it unreasonable to be
called upon to _love_ them, where I see no occasion,--to love a whole
family, perhaps, eight, nine, or ten, indiscriminately,--to love all
the pretty dears, because children are so engaging.
I know there is a proverb, "Love me, love my dog:" that is not always
so very practicable, particularly if the dog be set upon you to tease
you or snap at you in sport. But a dog, or a lesser thing,--any
inanimate substance, as a keep-sake, a watch or a ring, a tree, or
the place where we last parted when my friend went away upon a long
absence, I can make shift to love, because I love him, and any thing
that reminds me of him; provided it be in its nature indifferent, and
apt to receive whatever hue fancy can give it. But children have a
real character and an essential being of themselves: they are amiable
or unamiable _per se_; I must love or hate them as I see cause for
either 'in their qualities. A child's nature is too serious a thing to
admit of its being regarded as a mere appendage to another being, and
to be loved or hated accordingly: they stand with me upon their own
stock, as much as men and women do. O! but you will say, sure it is
an attractive age,--there is something in the tender years of infancy
that of itself charms us. That is the very reason why I am more nice
about them. I know that a sweet child is the sweetest thing in nature,
not even excepting the delicate creatures which bear them; but the
prettier the kind of a thing is, the more desirable it is that it
should be pretty of its kind. One daisy differs not much from another
in glory; but a violet should look and smell the daintiest.--I was
always rather squeamish in my women and children.
But this is not the worst: one must be admitted into their familiarity
at least, before they can complain of inattention. It implies visits,
and some kind of intercourse. But if the husband be a man with whom
you have lived on a friendly footing before marriage,--if you did not
come in on the wife's side,--if you did not sneak into the house in
her train, but were an old friend in fast habits of intimacy before
their courtship was so much as thought on,--look about you--your
tenure is precarious--before a twelve-month shall roll over your head,
you shall find your old friend gradually grow cool and altered towards
you, and at last seek opportunities of breaking with you. I have
scarce a married friend of my acquaintance, upon whose firm faith I
can rely, whose friendship did not commence _after the period of his
marriage_. With some limitations they can endure that: but that the
good man should have dared to enter into a solemn league of friendship
in which they were not consulted, though it happened before they
knew him,--before they that are now man and wife ever met,--this
is intolerable to them. Every long friendship, every old authentic
intimacy, must be brought into their office to be new stamped with
their currency, as a sovereign Prince calls in the good old money that
was coined in some reign before he was born or thought of, to be new
marked and minted with the stamp of his authority, before he will
let it pass current in the world. You may guess what luck generally
befalls such a rusty piece of metal as I am in these _new mintings_.
Innumerable are the ways which they take to insult and worm you out
of their husband's confidence. Laughing at all you say with a kind of
wonder, as if you were a queer kind of fellow that said good things,
_but an oddity_, is one of the ways;--they have a particular kind of
stare for the purpose;--till at last the husband, who used to defer to
your judgment, and would pass over some excrescences of understanding
and manner for the sake of a general vein of observation (not quite
vulgar) which he perceived in you, begins to suspect whether you are
not altogether a humorist,--a fellow well enough to have consorted
with in his bachelor days, but not quite so proper to be introduced
to ladies. This may be called the staring way; and is that which has
oftenest been put in practice against me.
Then there is the exaggerating way, or the way of irony: that is,
where they find you an object of especial regard with their husband,
who is not so easily to be shaken from the lasting attachment founded
on esteem which he has conceived towards you; by never-qualified
exaggerations to cry up all that you say or do, till the good man,
who understands well enough that it is all done in compliment to him,
grows weary of the debt of gratitude which is due to so much candour,
and by relaxing a little on his part, and taking down a peg or two
in his enthusiasm, sinks at length to that kindly level of moderate
esteem,--that "decent affection and complacent kindness" towards you,
where she herself can join in sympathy with him without much stretch
and violence to her sincerity.
Another way (for the ways they have to accomplish so desirable
a purpose are infinite) is, with a kind of innocent simplicity,
continually to mistake what it was which first made their husband fond
of you. If an esteem for something excellent in your moral character
was that which riveted the chain which she is to break, upon any
imaginary discovery of a want of poignancy in your conversation, she
will cry, "I thought, my dear, you described your friend, Mr. ---- as
a great wit." If, on the other hand, it was for some supposed charm
in your conversation that he first grew to like you, and was content
for this to overlook some trifling irregularities in your moral
deportment, upon the first notice of any of these she as readily
exclaims, "This, my dear, is your good Mr. ----." One good lady whom
I took the liberty of expostulating with for not showing me quite so
much respect as I thought due to her husband's old friend, had the
candour to confess to me that she had often heard Mr. ---- speak
of me before marriage, and that she had conceived a great desire
to be acquainted with me, but that the sight of me had very much
disappointed her expectations; for from her husband's representations
of me, she had formed a notion that she was to see a fine, tall,
officer-like looking man (I use her very words); the very reverse of
which proved to be the truth. This was candid; and I had the civility
not to ask her in return, how she came to pitch upon a standard of
personal accomplishments for her husband's friends which differed so
much from his own; for my friend's dimensions as near as possible
approximate to mine; he standing five feet five in his shoes, in which
I have the advantage of him by about half an inch; and he no more than
myself exhibiting any indications of a martial character in his air or
countenance.
These are some of the mortifications which I have encountered in the
absurd attempt to visit at their houses. To enumerate them all would
be a vain endeavour: I shall therefore just glance at the very common
impropriety of which married ladies are guilty,--of treating us as if
we were their husbands, and _vice versa_. I mean, when they use us
with familiarity, and their husbands with ceremony. _Testacea_, for
instance, kept me the other night two or three hours beyond my usual
time of supping, while she was fretting because Mr. ---- did not come
home, till the oysters were all spoiled, rather than she would be
guilty of the impoliteness of touching one in his absence. This was
reversing the point of good manners: for ceremony is an invention to
take off the uneasy feeling which we derive from knowing ourselves to
be less the object of love and esteem with a fellow-creature than some
other person is. It endeavours to make up, by superior attentions in
little points, for that invidious preference which it is forced to
deny in the greater. Had _Testacea_ kept the oysters back for me, and
withstood her husband's importunities to go to supper, she would have
acted according to the strict rules of propriety. I know no ceremony
that ladies are bound to observe to their husbands, beyond the point
of a modest behaviour and decorum: therefore I must protest against
the vicarious gluttony of _Cerasia_, who at her own table sent away a
dish of Morellas, which I was applying to with great good will, to her
husband at the other end of the table, and recommended a plate of
less extraordinary gooseberries to my unwedded palate in their stead.
Neither can I excuse the wanton affront of ----.
But I am weary of stringing up all my married acquaintance by Roman
denominations. Let them amend and change their manners, or I promise
to record the full-length English of their names, to the terror of all
such desperate offenders in future.
ON SOME OF THE OLD ACTORS
The casual sight of an old Play Bill, which I picked up the other
day--I know not by what chance it was preserved so long--tempts me to
call to mind a few of the Players, who make the principal figure in
it. It presents the cast of parts in the Twelfth Night, at the old
Drury-lane Theatre two-and-thirty years ago. There is something very
touching in these old remembrances. They make us think how we _once_
used to read a Play Bill--not, as now peradventure, singling out a
favorite performer, and casting a negligent eye over the rest; but
spelling out every name, down to the very mutes and servants of
the scene;--when it was a matter of no small moment to us whether
Whitfield, or Packer, took the part of Fabian; when Benson, and
Burton, and Phillimore--names of small account--had an importance,
beyond what we can be content to attribute now to the time's best
actors.--"Orsino, by Mr. Barrymore."--What a full Shakspearian sound
it carries! how fresh to memory arise the image, and the manner, of
the gentle actor!
Those who have only seen Mrs. Jordan within the last ten or fifteen
years, can have no adequate notion of her performance of such parts as
Ophelia; Helena, in All's Well that Ends Well; and Viola in this play.
Her voice had latterly acquired a coarseness, which suited well enough
with her Nells and Hoydens, but in those days it sank, with her steady
melting eye, into the heart. Her joyous parts--in which her memory now
chiefly lives--in her youth were outdone by her plaintive ones. There
is no giving an account how she delivered the disguised story of her
love for Orsino. It was no set speech, that she had foreseen, so as to
weave it into an harmonious period, line necessarily following line,
to make up the music--yet I have heard it so spoken, or rather _read_,
not without its grace and beauty--but, when she had declared her
sister's history to be a "blank," and that she "never told her love,"
there was a pause, as if the story had ended--and then the image of
the "worm in the bud" came up as a new suggestion--and the heightened
image of "Patience" still followed after that, as by some growing (and
not mechanical) process, thought springing up after thought, I would
almost say, as they were watered by her tears. So in those fine
lines--
Write loyal cantos of contemned love--
Hollow your name to the reverberate hills--
there was no preparation made in the foregoing image for that which
was to follow. She used no rhetoric in her passion; or it was nature's
own rhetoric, most legitimate then, when it seemed altogether without
rule or law.
Mrs. Powel (now Mrs. Renard), then in the pride of her beauty, made
an admirable Olivia. She was particularly excellent in her unbending
scenes in conversation with the Clown. I have seen some Olivias--and
those very sensible actresses too--who in these interlocutions have
seemed to set their wits at the jester, and to vie conceits with him
in downright emulation. But she used him for her sport, like what
he was, to trifle a leisure sentence or two with, and then to be
dismissed, and she to be the Great Lady still. She touched the
imperious fantastic humour of the character with nicety. Her fine
spacious person filled the scene.
The part of Malvolio has in my judgment been so often misunderstood,
and the _general merits_ of the actor, who then played it, so unduly
appreciated, that I shall hope for pardon, if I am a little prolix
upon these points.
Of all the actors who flourished in my time--a melancholy phrase
if taken aright, reader--Bensley had most of the swell of soul,
was greatest in the delivery of heroic conceptions, the emotions
consequent upon the presentment of a great idea to the fancy. He had
the true poetical enthusiasm--the rarest faculty among players. None
that I remember possessed even a portion of that fine madness which he
threw out in Hotspur's famous rant about glory, or the transports of
the Venetian incendiary at the vision of the fired city. His voice had
the dissonance, and at times the inspiriting effect of the trumpet.
His gait was uncouth and stiff, but no way embarrassed by affectation;
and the thorough-bred gentleman was uppermost in every movement. He
seized the moment of passion with the greatest truth; like a faithful
clock, never striking before the time; never anticipating or leading
you to anticipate. He was totally destitute of trick and artifice. He
seemed come upon the stage to do the poet's message simply, and he
did it with as genuine fidelity as the nuncios in Homer deliver the
errands of the gods. He let the passion or the sentiment do its own
work without prop or bolstering. He would have scorned to mountebank
it; and betrayed none of that _cleverness_ which is the bane of
serious acting. For this reason, his Iago was the only endurable one
which I remember to have seen. No spectator from his action could
divine more of his artifice than Othello was supposed to do. His
confessions in soliloquy alone put you in possession of the mystery.
There were no by-intimations to make the audience fancy their own
discernment so much greater than that of the Moor--who commonly stands
like a great helpless mark set up for mine Ancient, and a quantity of
barren spectators, to shoot their bolts at. The Iago of Bensley did
not go to work so grossly. There was a triumphant tone about the
character, natural to a general consciousness of power; but none of
that petty vanity which chuckles and cannot contain itself upon any
little successful stroke of its knavery--as is common with your small
villains, and green probationers in mischief. It did not clap or crow
before its time. It was not a man setting his wits at a child, and
winking all the while at other children who are mightily pleased at
being let into the secret; but a consummate villain entrapping a noble
nature into toils, against which no discernment was available, where
the manner was as fathomless as the purpose seemed dark, and without
motive. The part of Malvolio, in the Twelfth Night, was performed by
Bensley, with a richness and a dignity, of which (to judge from some
recent castings of that character) the very tradition must be worn out
from the stage. No manager in those days would have dreamed of giving
it to Mr. Baddeley, or Mr. Parsons: when Bensley was occasionally
absent from the theatre, John Kemble thought it no derogation to
succeed to the part. Malvolio is not essentially ludicrous. He becomes
comic but by accident. He is cold, austere, repelling; but dignified,
consistent, and, for what appears, rather of an over-stretched
morality. Maria describes him as a sort of Puritan; and he might have
worn his gold chain with honour in one of our old round-head families,
in the service of a Lambert, or a Lady Fairfax. But his morality and
his manners are misplaced in Illyria. He is opposed to the proper
_levities_ of the piece, and falls in the unequal contest. Still his
pride, or his gravity, (call it which you will) is inherent, and
native to the man, not mock or affected, which latter only are the
fit objects to excite laughter. His quality is at the best unlovely,
but neither buffoon nor contemptible. His bearing is lofty, a little
above his station, but probably not much above his deserts. We see no
reason why he should not have been brave, honourable, accomplished.
His careless committal of the ring to the ground (which he was
commissioned to restore to Cesario), bespeaks a generosity of birth
and feeling. His dialect on all occasions is that of a gentleman, and
a man of education. We must not confound him with the eternal old, low
steward of comedy. He is master of the household to a great Princess;
a dignity probably conferred upon him for other respects than age or
length of service. Olivia, at the first indication of his supposed
madness, declares that she "would not have him miscarry for half of
her dowry." Does this look as if the character was meant to appear
little or insignificant? Once, indeed, she accuses him to his face--of
what?--of being "sick of self-love,"--but with a gentleness and
considerateness which could not have been, if she had not thought
that this particular infirmity shaded some virtues. His rebuke to the
knight, and his sottish revellers, is sensible and spirited; and when
we take into consideration the unprotected condition of his mistress,
and the strict regard with which her state of real or dissembled
mourning would draw the eyes of the world upon her house-affairs,
Malvolio might feel the honour of the family in some sort in his
keeping; as it appears not that Olivia had any more brothers, or
kinsmen, to look to it--for Sir Toby had dropped all such nice
respects at the buttery hatch. That Malvolio was meant to be
represented as possessing estimable qualities, the expression of the
Duke in his anxiety to have him reconciled, almost infers. "Pursue
him, and entreat him to a peace." Even in his abused state of chains
and darkness, a sort of greatness seems never to desert him. He
argues highly and well with the supposed Sir Topas, and philosophises
gallantly upon his straw.[1] There must have been some shadow of worth
about the man; he must have been something more than a mere vapour--a
thing of straw, or Jack in office--before Fabian and Maria could have
ventured sending him upon a courting-errand to Olivia. There was some
consonancy (as he would say) in the undertaking, or the jest would
have been too bold even for that house of misrule.
Bensley, accordingly, threw over the part an air of Spanish loftiness.
He looked, spake, and moved like an old Castilian. He was starch,
spruce, opinionated, but his superstructure of pride seemed bottomed
upon a sense of worth. There was something in it beyond the coxcomb.
It was big and swelling, but you could not be sure that it was hollow.
You might wish to see it taken down, but you felt that it was upon an
elevation. He was magnificent from the outset; but when the decent
sobrieties of the character began to give way, and the poison of
self-love, in his conceit of the Countess's affection, gradually to
work, you would have thought that the hero of La Mancha in person
stood before you. How he went smiling to himself! with what ineffable
carelessness would he twirl his gold chain! what a dream it was! you
were infected with the illusion, and did not wish that it should be
removed! you had no room for laughter! if an unseasonable reflection
of morality obtruded itself, it was a deep sense of the pitiable
infirmity of man's nature, that can lay him open to such frenzies--but
in truth you rather admired than pitied the lunacy while it
lasted--you felt that an hour of such mistake was worth an age with
the eyes open. Who would not wish to live but for a day in the conceit
of such a lady's love as Olivia? Why, the Duke would have given his
principality but for a quarter of a minute, sleeping or waking, to
have been so deluded. The man seemed to tread upon air, to taste
manna, to walk with his head in the clouds, to mate Hyperion. O! shake
not the castles of his pride--endure yet for a season bright moments
of confidence--"stand still ye watches of the element," that Malvolio
may be still in fancy fair Olivia's lord--but fate and retribution say
no--I hear the mischievous titter of Maria--the witty taunts of Sir
Toby--the still more insupportable triumph of the foolish knight--the
counterfeit Sir Topas is unmasked--and "thus the whirligig of time,"
as the true clown hath it, "brings in his revenges." I confess that I
never saw the catastrophe of this character, while Bensley played it,
without a kind of tragic interest. There was good foolery too. Few now
remember Dodd. What an Aguecheek the stage lost in him! Lovegrove, who
came nearest to the old actors, revived the character some few seasons
ago, and made it sufficiently grotesque; but Dodd was _it_, as it
came out of Nature's hands. It might be said to remain _in puris
naturalibus_. In expressing slowness of apprehension this actor
surpassed all others. You could see the first dawn of an idea stealing
slowly over his countenance, climbing up by little and little, with
a painful process, till it cleared up at last to the fulness of a
twilight conception--its highest meridian. He seemed to keep back
his intellect, as some have had the power to <DW44> their pulsation.
The balloon takes less time in filling, than it took to cover
the expansion of his broad moony face over all its quarters with
expression. A glimmer of understanding would appear in a corner of his
eye, and for lack of fuel go out again. A part of his forehead would
catch a little intelligence, and be a long time in communicating it to
the remainder.
I am ill at dates, but I think it is now better than five and twenty
years ago that walking in the gardens of Gray's Inn--they were then
far finer than they are now--the accursed Verulam Buildings had not
encroached upon all the east side of them, cutting out delicate green
crankles, and shouldering away one of two of the stately alcoves
of the terrace--the survivor stands gaping and relationless as if
it remembered its brother--they are still the best gardens of any
of the Inns of Court, my beloved Temple not forgotten--have the
gravest character, their aspect being altogether reverend and
law-breathing--Bacon has left the impress of his foot upon their
gravel walks--taking my afternoon solace on a summer day upon the
aforesaid terrace, a comely sad personage came towards me, whom, from
his grave air and deportment, I judged to be one of the old Benchers
of the Inn. He had a serious thoughtful forehead, and seemed to be
in meditations of mortality. As I have an instinctive awe of old
Benchers, I was passing him with that sort of subindicative token of
respect which one is apt to demonstrate towards a venerable stranger,
and which rather denotes an inclination to greet him, than any
positive motion of the body to that effect--a species of humility and
will-worship which I observe, nine times out of ten, rather puzzles
than pleases the person it is offered to--when the face turning
full upon me strangely identified itself with that of Dodd. Upon
close inspection I was not mistaken. But could this sad thoughtful
countenance be the same vacant face of folly which I had hailed so
often under circumstances of gaiety; which I had never seen without
a smile, or recognised but as the usher of mirth; that looked out
so formally flat in Foppington, so frothily pert in Tattle, so
impotently busy in Backbite; so blankly divested of all meaning, or
resolutely expressive of none, in Acres, in Fribble, and a thousand
agreeable impertinences? Was this the face--full of thought and
carefulness--that had so often divested itself at will of every trace
of either to give me diversion, to clear my cloudy face for two or
three hours at least of its furrows? Was this the face--manly, sober,
intelligent,--which I had so often despised, made mocks at, made merry
with? The remembrance of the freedoms which I had taken with it came
upon me with a reproach of insult. I could have asked it pardon. I
thought it looked upon me with a sense of injury. There is something
strange as well as sad in seeing actors--your pleasant fellows
particularly--subjected to and suffering the common lot--their
fortunes, their casualties, their deaths, seem to belong to the scene,
their actions to be amenable to poetic justice only. We can hardly
connect them with more awful responsibilities. The death of this fine
actor took place shortly after this meeting. He had quitted the stage
some months; and, as I learned afterwards, had been in the habit of
resorting daily to these gardens almost to the day of his decease. In
these serious walks probably he was divesting himself of many scenic
and some real vanities--weaning himself from the frivolities of the
lesser and the greater theatre--doing gentle penance for a life of no
very reprehensible fooleries,--taking off by degrees the buffoon mask
which he might feel he had worn too long--and rehearsing for a more
solemn cast of part. Dying he "put on the weeds of Dominic."[2]
If few can remember Dodd, many yet living will not easily forget the
pleasant creature, who in those days enacted the part of the Clown
to Dodd's Sir Andrew.--Richard, or rather Dicky Suett--for so in
his life-time he delighted to be called, and time hath ratified the
appellation--lieth buried on the north side of the cemetery of Holy
Paul, to whose service his nonage and tender years were dedicated.
There are who do yet remember him at that period--his pipe clear and
harmonious. He would often speak of his chorister days, when he was
"cherub Dicky."
What clipped his wings, or made it expedient that he should exchange
the holy for the profane state; whether he had lost his good voice
(his best recommendation to that office), like Sir John, "with
hallooing and singing of anthems;" or whether he was adjudged to lack
something, even in those early years, of the gravity indispensable to
an occupation which professeth to "commerce with the skies"--I could
never rightly learn; but we find him, after the probation of a
twelvemonth or so, reverting to a secular condition, and become one
of us.
I think he was not altogether of that timber, out of which cathedral
seats and sounding boards are hewed. But if a glad heart--kind and
therefore glad--be any part of sanctity, then might the robe of
Motley, with which he invested himself with so much humility after
his deprivation, and which he wore so long with so much blameless
satisfaction to himself and to the public, be accepted for a
surplice--his white stole, and _albe_.
The first fruits of his secularization was an engagement upon the
boards of Old Drury, at which theatre he commenced, as I have been
told, with adopting the manner of Parsons in old men's characters. At
the period in which most of us knew him, he was no more an imitator
than he was in any true sense himself imitable.
He was the Robin Good-Fellow of the stage. He came in to trouble all
things with a welcome perplexity, himself no whit troubled for the
matter. He was known, like Puck, by his note--_Ha! Ha! Ha!_--sometimes
deepening to _Ho! Ho! Ho!_ with an irresistible accession, derived
perhaps remotely from his ecclesiastical education, foreign to
his prototype of,--_O La!_ Thousands of hearts yet respond to the
chuckling _O La!_ of Dicky Suett, brought back to their remembrance by
the faithful transcript of his friend Mathews's mimicry. The "force of
nature could no further go." He drolled upon the stock of these two
syllables richer than the cuckoo.
Care, that troubles all the world, was forgotten in his composition.
Had he had but two grains (nay, half a grain) of it, he could never
have supported himself upon those two spider's strings, which served
him (in the latter part of his unmixed existence) as legs. A doubt
or a scruple must have made him totter, a sigh have puffed him down;
the weight of a frown had staggered him, a wrinkle made him lose his
balance. But on he went, scrambling upon those airy stilts of his,
with Robin Good-Fellow, "thorough brake, thorough briar," reckless of
a scratched face or a torn doublet.
Shakspeare foresaw him, when he framed his fools and jesters. They
have all the true Suett stamp, a loose and shambling gait, a slippery
tongue, this last the ready midwife to a without-pain-delivered jest;
in words, light as air, venting truths deep as the centre; with idlest
rhymes tagging conceit when busiest, singing with Lear in the tempest,
or Sir Toby at the buttery-hatch.
Jack Bannister and he had the fortune to be more of personal
favourites with the town than any actors before or after. The
difference, I take it, was this:--Jack was more _beloved_ for his
sweet, good-natured, moral pretensions. Dicky was more _liked_ for
his sweet, good-natured, no pretensions at all. Your whole conscience
stirred with Bannister's performance of Walter in the Children in the
Wood--but Dicky seemed like a thing, as Shakspeare says of Love, too
young to know what conscience is. He put us into Vesta's days. Evil
fled before him--not as from Jack, as from an antagonist,--but because
it could not touch him, any more than a cannon-ball a fly. He was
delivered from the burthen of that death; and, when Death came
himself, not in metaphor, to fetch Dicky, it is recorded of him by
Robert Palmer, who kindly watched his exit, that he received the
last stroke, neither varying his accustomed tranquillity, nor tune,
with the simple exclamation, worthy to have been recorded in his
epitaph--_O La! O La! Bobby!_
The elder Palmer (of stage-treading celebrity) commonly played Sir
Toby in those days; but there is a solidity of wit in the jests of
that half-Falstaff which he did not quite fill out. He was as much too
showy as Moody (who sometimes took the part) was dry and sottish. In
sock or buskin there was an air of swaggering gentility about Jack
Palmer. He was a _gentleman_ with a slight infusion of _the footman_.
His brother Bob (of recenter memory) who was his shadow in every thing
while he lived, and dwindled into less than a shadow afterwards--was
a _gentleman_ with a little stronger infusion of the _latter
ingredient_; that was all. It is amazing how a little of the more or
less makes a difference in these things. When you saw Bobby in the
Duke's Servant,[3] you said, what a pity such a pretty fellow was only
a servant. When you saw Jack figuring in Captain Absolute, you thought
you could trace his promotion to some lady of quality who fancied
the handsome fellow in his topknot, and had bought him a commission.
Therefore Jack in Dick Amlet was insuperable.
Jack had two voices,--both plausible, hypocritical, and insinuating;
but his secondary or supplemental voice still more decisively
histrionic than his common one. It was reserved for the spectator; and
the dramatis personas were supposed to know nothing at all about it.
The _lies_ of young Wilding, and the _sentiments_ in Joseph Surface,
were thus marked out in a sort of italics to the audience. This secret
correspondence with the company before the curtain (which is the
bane and death of tragedy) has an extremely happy effect in some
kinds of comedy, in the more highly artificial comedy of Congreve
or of Sheridan especially, where the absolute sense of reality (so
indispensable to scenes of interest) is not required, or would rather
interfere to diminish your pleasure. The fact is, you do not believe
in such characters as Surface--the villain of artificial comedy--even
while you read or see them. If you did, they would shock and not
divert you. When Ben, in Love for Love, returns from sea, the
following exquisite dialogue occurs at his first meeting with his
father--
_Sir Sampson._ Thou hast been many a weary league, Ben, since I saw
thee.
_Ben._ Ey, ey, been! Been far enough, an that be all.--Well, father,
and how do all at home? how does brother Dick, and brother Val?
_Sir Sampson._ Dick! body o' me, Dick has been dead these two years. I
writ you word when you were at Leghorn.
_Ben._ Mess, that's true; Marry, I had forgot. Dick's dead, as you
say--Well, and how?--I have a many questions to ask you--
Here is an instance of insensibility which in real life would be
revolting, or rather in real life could not have co-existed with the
warm-hearted temperament of the character. But when you read it in the
spirit with which such playful selections and specious combinations
rather than strict _metaphrases_ of nature should be taken, or when
you saw Bannister play it, it neither did, nor does wound the moral
sense at all. For what is Ben--the pleasant sailor which Bannister
gives us--but a piece of satire--a creation of Congreve's fancy--a
dreamy combination of all the accidents of a sailor's character--his
contempt of money--his credulity to women--with that necessary
estrangement from home which it is just within the verge of
credibility to suppose _might_ produce such an hallucination as is
here described. We never think the worse of Ben for it, or feel it as
a stain upon his character. But when an actor comes, and instead
of the delightful phantom--the creature dear to half-belief--which
Bannister exhibited--displays before our eyes a downright concretion
of a Wapping sailor--a jolly warm-hearted Jack Tar--and nothing
else--when instead of investing it with a delicious confusedness of
the head, and a veering undirected goodness of purpose--he gives to it
a downright daylight understanding, and a full consciousness of its
actions; thrusting forward the sensibilities of the character with a
pretence as if it stood upon nothing else, and was to be judged by
them alone--we feel the discord of the thing; the scene is disturbed;
a real man has got in among the dramatis personae, and puts them out.
We want the sailor turned out. We feel that his true place is not
behind the curtain but in the first or second gallery.
[Footnote 1:_Clown_. What is the opinion of Pythagoras concerning wild
fowl?
_Mal_. That the soul of our grandam might haply inhabit a bird.
_Clown_. What thinkest thou of his opinion?
_Mal_. I think nobly of the soul, and no way approve of his opinion.]
[Footnote 2: Dodd was a man of reading, and left at his death a choice
collection of old English literature. I should judge him to have been
a man of wit. I know one instance of an impromptu which no length of
study could have bettered. My merry friend, Jem White, had seen him
one evening in Aguecheek, and recognising Dodd the next day in Fleet
Street, was irresistibly impelled to take off his hat and salute him
as the identical Knight of the preceding evening with a "Save you,
_Sir Andrew_." Dodd, not at all disconcerted at this unusual address
from a stranger, with a courteous half-rebuking wave of the hand, put
him off with an "Away, _Fool_."]
[Footnote 3: High Life Below Stairs.]
ON THE ARTIFICIAL COMEDY OF THE LAST CENTURY
The artificial Comedy, or Comedy of manners, is quite extinct on our
stage. Congreve and Farquhar show their heads once in seven years
only, to be exploded and put down instantly. The times cannot bear
them. Is it for a few wild speeches, an occasional license of
dialogue? I think not altogether. The business of their dramatic
characters will not stand the moral test. We screw every thing up to
that. Idle gallantry in a fiction, a dream, the passing pageant of
an evening, startles us in the same way as the alarming indications
of profligacy in a son or ward in real life should startle a parent
or guardian. We have no such middle emotions as dramatic interests
left. We see a stage libertine playing his loose pranks of two hours'
duration, and of no after consequence, with the severe eyes which
inspect real vices with their bearings upon two worlds. We are
spectators to a plot or intrigue (not reducible in life to the point
of strict morality) and take it all for truth. We substitute a real
for a dramatic person, and judge him accordingly. We try him in our
courts, from which there is no appeal to the _dramatis personae_, his
peers. We have been spoiled with--not sentimental comedy--but a tyrant
far more pernicious to our pleasures which has succeeded to it, the
exclusive and all devouring drama of common life; where the moral
point is every thing; where, instead of the fictitious half-believed
personages of the stage (the phantoms of old comedy) we recognise
ourselves, our brothers, aunts, kinsfolk, allies, patrons,
enemies,--the same as in life,--with an interest in what is going on
so hearty and substantial, that we cannot afford our moral judgment,
in its deepest and most vital results, to compromise or slumber for
a moment. What is _there_ transacting, by no modification is made
to affect us in any other manner than the same events or characters
would do in our relationships of life. We carry our fire-side concerns
to the theatre with us. We do not go thither, like our ancestors,
to escape from the pressure of reality, so much as to confirm our
experience of it; to make assurance double, and take a bond of fate.
We must live our toilsome lives twice over, as it was the mournful
privilege of Ulysses to descend twice to the shades. All that neutral
ground of character, which stood between vice and virtue; or which in
fact was indifferent to neither, where neither properly was called in
question; that happy breathing-place from the burthen of a perpetual
moral questioning--the sanctuary and quiet Alsatia of hunted
casuistry--is broken up and disfranchised, as injurious to the
interests of society. The privileges of the place are taken away
by law. We dare not dally with images, or names, of wrong. We bark
like foolish dogs at shadows. We dread infection from the scenic
representation of disorder; and fear a painted pustule. In our anxiety
that our morality should not take cold, we wrap it up in a great
blanket surtout of precaution against the breeze and sunshine.
I confess for myself that (with no great delinquencies to answer
for) I am glad for a season to take an airing beyond the diocese of
the strict conscience,--not to live always in the precincts of the
law-courts,--but now and then, for a dream-while or so, to imagine a
world with no meddling restrictions--to get into recesses, whither the
hunter cannot follow me--
--Secret shades
Of woody Ida's inmost grove,
While yet there was no fear of Jove--
I come back to my cage and my restraint the fresher and more healthy
for it. I wear my shackles more contentedly for having respired
the breath of an imaginary freedom. I do not know how it is with
others, but I feel the better always for the perusal of one of
Congreve's--nay, why should I not add even of Wycherley's--comedies. I
am the gayer at least for it; and I could never connect those sports
of a witty fancy in any shape with any result to be drawn from them to
imitation in real life. They are a world of themselves almost as much
as fairy-land. Take one of their characters, male or female (with
few exceptions they are alike), and place it in a modern play, and
my virtuous indignation shall rise against the profligate wretch as
warmly as the Catos of the pit could desire; because in a modern play
I am to judge of the right and the wrong. The standard of _police_
is the measure of _political justice_. The atmosphere will blight
it, it cannot live here. It has got into a moral world, where it has
no business, from which it must needs fall headlong; as dizzy, and
incapable of making a stand, as a Swedenborgian bad spirit that has
wandered unawares into the sphere of one of his Good Men, or Angels.
But in its own world do we feel the creature is so very bad?--The
Fainalls and the Mirabels, the Dorimants and the Lady Touchwoods, in
their own sphere, do not offend my moral sense; in fact they do not
appeal to it at all. They seem engaged in their proper element. They
break through no laws, or conscientious restraints. They know of none.
They have got out of Christendom into the land--what shall I call
it?--of cuckoldry--the Utopia of gallantry, where pleasure is duty,
and the manners perfect freedom. It is altogether a speculative scene
of things, which has no reference whatever to the world that is. No
good person can be justly offended as a spectator, because no good
person suffers on the stage. Judged morally, every character in
in these plays--the few exceptions only are _mistakes_--is alike
essentially vain and worthless. The great art of Congreve is
especially shown in this, that he has entirely excluded from his
scenes,--some little generosities in the part of Angelica perhaps
excepted,--not only any thing like a faultless character, but any
pretensions to goodness or good feelings whatsoever. Whether he did
this designedly, or instinctively, the effect is as happy, as the
design (if design) was bold. I used to wonder at the strange power
which his Way of the World in particular possesses of interesting you
all along in the pursuits of characters, for whom you absolutely care
nothing--for you neither hate nor love his personages--and I think it
is owing to this very indifference for any, that you endure the whole.
He has spread a privation of moral light, I will call it, rather
than by the ugly name of palpable darkness, over his creations; and
his shadows flit before you without distinction or preference. Had
he introduced a good character, a single gush of moral feeling, a
revulsion of the judgment to actual life and actual duties, the
impertinent Goshen would have only lighted to the discovery of
deformities, which now are none, because we think them none.
Translated into real life, the characters of his, and his friend
Wycherley's dramas, are profligates and strumpets,--the business of
their brief existence, the undivided pursuit of lawless gallantry. No
other spring of action, or possible motive of conduct, is recognised;
principles which, universally acted upon, must reduce this frame of
things to a chaos. But we do them wrong in so translating them. No
such effects are produced in _their_ world. When we are among them, we
are amongst a chaotic people. We are not to judge them by our usages.
No reverend institutions are insulted by their proceedings,--for
they have none among them. No peace of families is violated,--for
no family ties exist among them. No purity of the marriage bed is
stained,--for none is supposed to have a being. No deep affections
are disquieted,--no holy wedlock bands are snapped asunder,--for
affection's depth and wedded faith are not of the growth of that soil.
There is neither right nor wrong,--gratitude or its opposite,--claim
or duty,--paternity or sonship. Of what consequence is it to virtue,
or how is she at all concerned about it, whether Sir Simon, or
Dapperwit, steal away Miss Martha; or who is the father of Lord
Froth's, or Sir Paul Pliant's children.
The whole is a passing pageant, where we should sit as unconcerned at
the issues, for life or death, as at a battle of the frogs and mice.
But, like Don Quixote, we take part against the puppets, and quite
as impertinently. We dare not contemplate an Atlantis, a scheme, out
of which our coxcombical moral sense is for a little transitory ease
excluded. We have not the courage to imagine a state of things for
which there is neither reward nor punishment. We cling to the painful
necessities of shame and blame. We would indict our very dreams.
Amidst the mortifying circumstances attendant upon growing old, it
is something to have seen the School for Scandal in its glory. This
comedy grew out of Congreve and Wycherley, but gathered some allays of
the sentimental comedy which followed theirs. It is impossible that it
should be now _acted_, though it continues, at long intervals, to be
announced in the bills. Its hero, when Palmer played it at least, was
Joseph Surface. When I remember the gay boldness, the graceful solemn
plausibility, the measured step, the insinuating voice--to express it
in a word--the downright _acted_ villany of the part, so different
from the pressure of conscious actual wickedness,--the hypocritical
assumption of hypocrisy,--which made Jack so deservedly a favourite
in that character, I must needs conclude the present generation of
play-goers more virtuous than myself, or more dense. I freely confess
that he divided the palm with me with his better brother; that, in
fact, I liked him quite as well. Not but there are passages,--like
that, for instance, where Joseph is made to refuse a pittance to a
poor relation,--incongruities which Sheridan was forced upon by the
attempt to join the artificial with the sentimental comedy, either
of which must destroy the other--but over these obstructions Jack's
manner floated him so lightly, that a refusal from him no more shocked
you, than the easy compliance of Charles gave you in reality any
pleasure; you got over the paltry question as quickly as you could, to
get back into the regions of pure comedy, where no cold moral reigns.
The highly artificial manner of Palmer in this character counteracted
every disagreeable impression which you might have received from the
contrast, supposing them real, between the two brothers. You did not
believe in Joseph with the same faith with which you believed in
Charles. The latter was a pleasant reality, the former a no less
pleasant poetical foil to it. The comedy, I have said, is incongruous;
a mixture of Congreve with sentimental incompatibilities: the gaiety
upon the whole is buoyant; but it required the consummate art of
Palmer to reconcile the discordant elements.
A player with Jack's talents, if we had one now, would not dare to do
the part in the same manner. He would instinctively avoid every
turn which might tend to unrealise, and so to make the character
fascinating. He must take his cue from his spectators, who would
expect a bad man and a good man as rigidly opposed to each other as
the death-beds of those geniuses are contrasted in the prints, which
I am sorry to say have disappeared from the windows of my old friend
Carrington Bowles, of St. Paul's Church-yard memory--(an exhibition
as venerable as the adjacent cathedral, and almost coeval) of the bad
and good man at the hour of death; where the ghastly apprehensions
of the former,--and truly the grim phantom with his reality of a
toasting fork is not to be despised,--so finely contrast with the
meek complacent kissing of the rod,--taking it in like honey and
butter,--with which the latter submits to the scythe of the gentle
bleeder, Time, who wields his lancet with the apprehensive finger of
a popular young ladies' surgeon. What flesh, like loving grass, would
not covet to meet half-way the stroke of such a delicate mower?--John
Palmer was twice an actor in this exquisite part. He was playing to
you all the while that he was playing upon Sir Peter and his lady. You
had the first intimation of a sentiment before it was on his lips.
His altered voice was meant to you, and you were to suppose that his
fictitious co-flutterers on the stage perceived nothing at all of it.
What was it to you if that half-reality, the husband, was over-reached
by the puppetry--or the thin thing (Lady Teazle's reputation) was
persuaded it was dying of a plethory? The fortunes of Othello and
Desdemona were not concerned in it. Poor Jack has past from the stage
in good time, that he did not live to this our age of seriousness.
The pleasant old Teazle _King_, too, is gone in good time. His
manner would scarce have past current in our day. We must love or
hate--acquit or condemn--censure or pity--exert our detestable
coxcombry of moral judgment upon every thing. Joseph Surface, to go
down now, must be a downright revolting villain--no compromise--his
first appearance must shock and give horror--his specious
plausibilities, which the pleasurable faculties of our fathers
welcomed with such hearty greetings, knowing that no harm (dramatic
harm even) could come, or was meant to come of them, must inspire a
cold and killing aversion. Charles (the real canting person of the
scene--for the hypocrisy of Joseph has its ulterior legitimate ends,
but his brother's professions of a good heart centre in downright
self-satisfaction) must be _loved_ and Joseph _hated_. To balance one
disagreeable reality with another, Sir Peter Teazle must be no longer
the comic idea of a fretful old bachelor bridegroom, whose teasings
(while King acted it) were evidently as much played off at you, as
they were meant to concern any body on the stage,--he must be a real
person, capable in law of sustaining an injury--a person towards whom
duties are to be acknowledged--the genuine crim-con antagonist of the
villanous seducer Joseph. To realise him more, his sufferings under
his unfortunate match must have the downright pungency of life--must
(or should) make you not mirthful but uncomfortable, just as the same
predicament would move you in a neighbour or old friend. The delicious
scenes which give the play its name and zest, must affect you in
the same serious manner as if you heard the reputation of a dear
female friend attacked in your real presence. Crabtree, and Sir
Benjamin--those poor snakes that live but in the sunshine of your
mirth--must be rippened by this hot-bed process of realization
into asps or amphisbaenas; and Mrs. Candour--O! frightful! become a
hooded serpent. Oh who that remembers Parsons and Dodd--the wasp and
butterfly of the School for Scandal--in those two characters; and
charming natural Miss Pope, the perfect gentlewoman as distinguished
from the fine lady of comedy, in this latter part--would forego
the true scenic delight--the escape from life--the oblivion of
consequences--the holiday barring out of the pedant Reflection--those
Saturnalia of two or three brief hours, well won from the world--to
sit instead at one of our modern plays--to have his coward conscience
(that forsooth must not be left for a moment) stimulated with
perpetual appeals--dulled rather, and blunted, as a faculty without
repose must be--and his moral vanity pampered with images of notional
justice, notional beneficence, lives saved without the spectators'
risk, and fortunes given away that cost the author nothing?
No piece was, perhaps, ever so completely cast in all its parts as
this _manager's comedy_. Miss Farren had succeeded to Mrs. Abingdon
in Lady Teazle; and Smith, the original Charles, had retired, when I
first saw it. The rest of the characters, with very slight exceptions,
remained. I remember it was then the fashion to cry down John Kemble,
who took the part of Charles after Smith; but, I thought, very
unjustly. Smith, I fancy, was more airy, and took the eye with a
certain gaiety of person. He brought with him no sombre recollections
of tragedy. He had not to expiate the fault of having pleased
beforehand in lofty declamation. He had no sins of Hamlet or of
Richard to atone for. His failure in these parts was a passport to
success in one of so opposite a tendency. But, as far as I could
judge, the weighty sense of Kemble made up for more personal
incapacity than he had to answer for. His harshest tones in this part
came steeped and dulcified in good humour. He made his defects a
grace. His exact declamatory manner, as he managed it, only served
to convey the points of his dialogue with more precision. It seemed
to head the shafts to carry them deeper. Not one of his sparkling
sentences was lost. I remember minutely how he delivered each in
succession, and cannot by any effort imagine how any of them could be
altered for the better. No man could deliver brilliant dialogue--the
dialogue of Congreve or of Wycherley--because none understood it--half
so well as John Kemble. His Valentine, in Love for Love, was, to my
recollection, faultless. He flagged sometimes in the intervals of
tragic passion. He would slumber over the level parts of an heroic
character. His Macbeth has been known to nod. But he always seemed
to me to be particularly alive to pointed and witty dialogue. The
relaxing levities of tragedy have not been touched by any since
him--the playful court-bred spirit in which he condescended to the
players in Hamlet--the sportive relief which he threw into the darker
shades of Richard--disappeared with him. He had his sluggish moods,
his torpors--but they were the halting-stones and resting-places of
his tragedy-politic savings, and fetches of the breath--husbandry of
the lungs, where nature pointed him to be an economist--rather, I
think, than errors of the judgment. They were, at worst, less painful
than the eternal tormenting unappeasable vigilance, the "lidless
dragon eyes," of present fashionable tragedy.
ON THE ACTING OF MUNDEN
Not many nights ago I had come home from seeing this extraordinary
performer in Cockletop; and when I retired to my pillow, his whimsical
image still stuck by me, in a manner as to threaten sleep. In vain
I tried to divest myself of it, by conjuring up the most opposite
associations. I resolved to be serious. I raised up the gravest topics
of life; private misery, public calamity. All would not do.
--There the antic sate
Mocking our state--
his queer visnomy--his bewildering costume--all the strange things
which he had raked together--his serpentine rod, swagging about in his
pocket--Cleopatra's tear, and the rest of his relics--O'Keefe's wild
farce, and _his_ wilder commentary--till the passion of laughter, like
grief in excess, relieved itself by its own weight, inviting the sleep
which in the first instance it had driven away.
But I was not to escape so easily. No sooner did I fall into slumbers,
than the same image, only more perplexing, assailed me in the shape
of dreams. Not one Munden, but five hundred, were dancing before me,
like the faces which, whether you will or no, come when you have been
taking opium--all the strange combinations, which this strangest of
all strange mortals ever shot his proper countenance into, from the
day he came commissioned to dry up the tears of the town for the loss
of the now almost forgotten Edwin. O for the power of the pencil
to have fixed them when I awoke! A season or two since there was
exhibited a Hogarth gallery. I do not see why there should not be a
Munden gallery. In richness and variety the latter would not fall far
short of the former.
There is one face of Farley, one face of Knight, one (but what a one
it is!) of Liston; but Munden has none that you can properly pin down,
and call _his_. When you think he has exhausted his battery of looks,
in unaccountable warfare with your gravity, suddenly he sprouts out an
entirely new set of features, like Hydra. He is not one, but legion.
Not so much a comedian, as a company. If his name could be multiplied
like his countenance, it might fill a play-bill. He, and he alone,
literally _makes faces_: applied to any other person, the phrase is a
mere figure, denoting certain modifications of the human countenance.
Out of some invisible wardrobe he dips for faces, as his friend
Suett used for wigs, and fetches them out as easily. I should not be
surprised to see him some day put out the head of a river horse; or
come forth a pewitt, or lapwing, some feathered metamorphosis.
I have seen this gifted actor, in Sir Christopher Curry--in Old
Dornton--diffuse a glow of sentiment which has made the pulse of a
crowded theatre beat like that of one man; when he has come in aid of
the pulpit, doing good to the moral heart of a people. I have seen
some faint approaches to this sort of excellence in other players.
But in the grand grotesque of farce, Munden stands out as single and
unaccompanied as Hogarth. Hogarth, strange to tell, had no followers.
The school of Munden began, and must end with himself.
Can any man _wonder_, like him? can any man _see ghosts_, like
him? or _fight with his own shadow_--"SESSA"--as he does in that
strangely-neglected thing, the Cobbler of Preston--where his
alternations from the Cobbler to the Magnifico, and from the Magnifico
to the Cobbler, keep the brain of the spectator in as wild a ferment,
as if some Arabian Night were being acted before him. Who like him
can throw, or ever attempted to throw, a preternatural interest over
the commonest daily-life objects? A table, or a joint stool, in his
conception, rises into a dignity equivalent to Cassiopeia's chair. It
is invested with constellatory importance. You could not speak of it
with more deference, if it were mounted into the firmament. A beggar
in the hands of Michael Angelo, says Fuseli, rose the Patriarch of
Poverty. So the gusto of Munden antiquates and ennobles what it
touches. His pots and his ladles are as grand and primal as the
seething-pots and hooks seen in old prophetic vision. A tub of butter,
contemplated by him, amounts to a Platonic idea. He understands a leg
of mutton in its quiddity. He stands wondering, amid the common-place
materials of life, like primaeval man with the sun and stars about him.
THE LAST ESSAYS OF ELIA
(_From the 1st Edition_, 1833)
PREFACE
BY A FRIEND OF THE LATE ELIA
This poor gentleman, who for some months past had been in a declining
way, hath at length paid his final tribute to nature.
To say truth, it is time he were gone. The humour of the thing, if
there was ever much in it, was pretty well exhausted; and a two years'
and a half existence has been a tolerable duration for a phantom.
I am now at liberty to confess, that much which I have heard objected
to my late friend's writings was well-founded. Crude they are, I grant
you--a sort of unlicked, incondite things--villainously pranked in an
affected array of antique modes and phrases. They had not been _his_,
if they had been other than such; and better it is, that a writer
should be natural in a self-pleasing quaintness, than to affect a
naturalness (so called) that should be strange to him. Egotistical
they have been pronounced by some who did not know, that what he tells
us, as of himself, was often true only (historically) of another; as
in a former Essay (to save many instances)--where under the _first
person_ (his favourite figure) he shadows forth the forlorn estate
of a country-boy placed at a London school, far from his friends and
connections--in direct opposition to his own early history. If it
be egotism to imply and twine with his own identity the griefs and
affections of another--making himself many, or reducing many unto
himself--then is the skilful novelist, who all along brings in his
hero, or heroine, speaking of themselves, the greatest egotist of all;
who yet has never, therefore, been accused of that narrowness. And how
shall the intenser dramatist escape being faulty, who doubtless, under
cover of passion uttered by another, oftentimes gives blameless vent
to his most inward feelings, and expresses his own story modestly?
My late friend was in many respects a singular character. Those who
did not like him, hated him; and some, who once liked him, afterwards
became his bitterest haters. The truth is, he gave himself too little
concern what he uttered, and in whose presence. He observed neither
time nor place, and would e'en out with what came uppermost. With the
severe religionist he would pass for a free-thinker; while the other
faction set him down for a bigot, or persuaded themselves that he
belied his sentiments. Few understood him; and I am not certain that
at all times he quite understood himself. He too much affected that
dangerous figure--irony. He sowed doubtful speeches, and reaped
plain, unequivocal hatred.--He would interrupt the gravest discussion
with some light jest; and yet, perhaps, not quite irrelevant in ears
that could understand it. Your long and much talkers hated him. The
informal habit of his mind, joined to an inveterate impediment of
speech, forbade him to be an orator; and he seemed determined that,
no one else should play that part when he was present. He was _petit_
and ordinary in his person and appearance. I have seen him sometimes
in what is called good company, but where he has been a stranger, sit
silent, and be suspected for an odd fellow; till some unlucky occasion
provoking it, he would stutter out some senseless pun (not altogether
senseless perhaps, if rightly taken), which has stamped his character
for the evening. It was hit or miss with him; but nine times out of
ten, he contrived by this device to send away a whole company his
enemies. His conceptions rose kindlier than his utterance, and his
happiest _impromptus_ had the appearance of effort. He has been
accused of trying to be witty, when in truth he was but struggling
to give his poor thoughts articulation. He chose his companions for
some individuality of character which they manifested.--Hence, not
many persons of science, and few professed _literati_, were of his
councils. They were, for the most part, persons of an uncertain
fortune; and, as to such people commonly nothing is more obnoxious
than a gentleman of settled (though moderate) income, he passed with
most of them for a great miser. To my knowledge this was a mistake.
His _intimados_, to confess a truth, were in the world's eye a ragged
regiment. He found them floating on the surface of society; and the
colour, or something else, in the weed pleased him. The burrs stuck
to him--but they were gbod and loving burrs for all that. He never
greatly cared for the society of what are called good people. If any
of these were scandalised (and offences were sure to arise), he could
not help it. When he has been remonstrated with for not making more
concessions to the feelings of good people, he would retort by asking,
what one point did these good people ever concede to him? He was
temperate in his meals and diversions, but always kept a little on
this side of abstemiousness. Only in the use of the Indian weed he
might be thought a little excessive. He took it, he would say, as
a solvent of speech. Marry--as the friendly vapour ascended, how
his prattle would curl up sometimes with it! the ligaments, which
tongue-tied him, were loosened, and the stammerer proceeded a statist!
I do not know whether I ought to bemoan or rejoice that my old friend
is departed. His jests were beginning to grow obsolete, and his
stories to be found out. He felt the approaches of age; and while he
pretended to cling to life, you saw how slender were the ties left to
bind him. Discoursing with him latterly on this subject, he expressed
himself with a pettishness, which I thought unworthy of him. In our
walks about his suburban retreat (as he called it) at Shacklewell,
some children belonging to a school of industry had met us, and bowed
and curtseyed, as he thought, in an especial manner to _him_. "They
take me for a visiting governor," he muttered earnestly. He had
a horror, which he carried to a foible, of looking like anything
important and parochial. He thought that he approached nearer to that
stamp daily.. He had a general aversion from being treated like a
grave or respectable character, and kept a wary eye upon the advances
of age that should so entitle him. He herded always, while it was
possible, with people younger than himself. He did not conform to the
march of time, but was dragged along in the procession. His manners
lagged behind his years. He was too much of the boy-man. The _toga
virilis_ never sate gracefully on his shoulders. The impressions
of infancy had burnt into him, and he resented the impertinence of
manhood. These were weaknesses; but such as they were, they are a key
to explicate some of his writings.
BLAKESMOOR IN H-----SHIRE
I do not know a pleasure more affecting than to range at will
over the deserted apartments of some fine old family mansion. The
traces of extinct grandeur admit of a better passion than envy: and
contemplations on the great and good, whom we fancy in succession
to have been its inhabitants, weave for us illusions, incompatible
with the bustle of modern occupancy, and vanities of foolish present
aristocracy. The same difference of feeling, I think, attends us
between entering an empty and a crowded church. In the latter it is
chance but some present human frailty--an act of inattention on the
part of some of the auditory--or a trait of affectation, or worse,
vain-glory, on that of the preacher--puts us by our best thoughts,
disharmonising the place and the occasion. But would'st thou know the
beauty of holiness?--go alone on some week-day, borrowing the keys of
good Master Sexton, traverse the cool aisles of some country church:
think of the piety that has kneeled there--the congregations, old
and young, that have found consolation there--the meek pastor--the
docile parishioner. With no disturbing emotions, no cross conflicting
comparisons, drink in the tranquillity of the place, till thou thyself
become as fixed and motionless as the marble effigies that kneel and
weep around thee.
Journeying northward lately, I could not resist going some few miles
out of my road to look upon the remains of an old great house with
which I had been impressed in this way in infancy. I was apprised that
the owner of it had lately pulled it down; still I had a vague notion
that it could not all have perished, that so much solidity with
magnificence could not have been crushed all at once into the mere
dust and rubbish which I found it.
The work of ruin had proceeded with a swift hand indeed, and the
demolition of a few weeks had reduced it to--an antiquity.
I was astonished at the indistinction of everything. Where had stood
the great gates? What bounded the court-yard? Whereabout did the
out-houses commence? a few bricks only lay as representatives of that
which was so stately and so spacious.
Death does not shrink up his human victim at this rate. The burnt
ashes of a man weigh more in their proportion.
Had I seen these brick-and-mortar knaves at their process of
destruction, at the plucking of every pannel I should have felt the
varlets at my heart. I should have cried out to them to spare a plank
at least out of the cheerful store-room, in whose hot window-seat I
used to sit and read Cowley, with the grass-plat before, and the hum
and flappings of that one solitary wasp that ever haunted it about
me--it is in mine ears now, as oft as summer returns; or a pannel of
the yellow room.
Why, every plank and pannel of that house for me had magic in it.
The tapestried bed-rooms--tapestry so much better than painting--not
adorning merely, but peopling the wainscots--at which childhood ever
and anon would steal a look, shifting its coverlid (replaced as
quickly) to exercise its tender courage in a momentary eye-encounter
with those stern bright visages, staring reciprocally--all Ovid on the
walls, in colours vivider than his descriptions. Actaeon in mid sprout,
with the unappeasable prudery of Diana; and the still more provoking,
and almost culinary coolness of Dan Phoebus, eel-fashion, deliberately
divesting of Marsyas.
Then, that haunted room--in which old Mrs. Battle died--whereinto I
have crept, but always in the day-time, with a passion of fear; and
a sneaking curiosity, terror-tainted, to hold communication with the
past.--_How shall they build it up again?_
It was an old deserted place, yet not so long deserted but that
traces of the splendour of past inmates were everywhere apparent.
Its furniture was still standing--even to the tarnished gilt leather
battledores, and crumbling feathers of shuttlecocks in the nursery,
which told that children had once played there. But I was a lonely
child, and had the range at will of every apartment, knew every nook
and corner, wondered and worshipped everywhere.
The solitude of childhood is not so much the mother of thought, as
it is the feeder of love, and silence, and admiration, So strange a
passion for the place possessed me in those years, that, though there
lay--I shame to say how few roods distant from the mansion--half hid
by trees, what I judged some romantic lake, such was the spell which
bound me to the house, and such my carefulness not to pass its strict
and proper precincts, that the idle waters lay unexplored for me; and
not till late in life, curiosity prevailing over elder devotion, I
found, to my astonishment, a pretty brawling brook had been the Lacus
Incognitus of my infancy. Variegated views, extensive prospects--and
those at no great distance from the house--I was told of such--what
were they to me, being out of the boundaries of my Eden?--So far from
a wish to roam, I would have drawn, methought, still closer the fences
of my chosen prison; and have been hemmed in by a yet securer cincture
of those excluding garden walls. I could have exclaimed with that
garden-loving poet--
Bind me, ye woodbines, in your 'twines,
Curl me about, ye gadding vines;
And oh so close your circles lace,
That I may never leave this place;
But, lest your fetters prove too weak,
Ere I your silken bondage break,
Do you, O brambles, chain me too,
And, courteous briars, nail me through!
I was here as in a lonely temple. Snug firesides--the low-built
roof--parlours ten feet by ten--frugal boards, and all the homeliness
of home--these were the condition of my birth--the wholesome soil
which I was planted in. Yet, without impeachment to their tenderest
lessons, I am not sorry to have had glances of something beyond;
and to have taken, if but a peep, in childhood, at the contrasting
accidents of a great fortune.
To have the feeling of gentility, it is not necessary to have been
born gentle. The pride of ancestry may be had on cheaper terms than
to be obliged to an importunate race of ancestors; and the coatless
antiquary in his unemblazoned cell, revolving the long line of a
Mowbray's or De Clifford's pedigree, at those sounding names may warm
himself into as gay a vanity as those who do inherit them. The claims
of birth are ideal merely, and what herald shall go about to strip me
of an idea? Is it trenchant to their swords? can it be hacked off as a
spur can? or torn away like a tarnished garter?
What, else, were the families of the great to us? what pleasure should
we take in their tedious genealogies, or their capitulatory brass
monuments? What to us the uninterrupted current of their bloods,
if our own did not answer within us to a cognate and correspondent
elevation?
Or wherefore, else, O tattered and diminished 'Scutcheon that hung
upon the time-worn walls of thy princely stairs, BLAKESMOOR! have
I in childhood so oft stood poring upon thy mystic characters--thy
emblematic supporters, with their prophetic "Resurgam"--till, every
dreg of peasantry purging off, I received into myself Very Gentility?
Thou wert first in my morning eyes; and of nights, hast detained my
steps from bedward, till it was but a step from gazing at thee to
dreaming on thee.
This is the only true gentry by adoption; the veritable change of
blood, and not, as empirics have fabled, by transfusion.
Who it was by dying that had earned the splendid trophy, I know not,
I inquired not; but its fading rags, and colours cobweb-stained, told
that its subject was of two centuries back.
And what if my ancestor at that date was some Damoetas--feeding
flocks, not his own, upon the hills of Lincoln--did I in less
earnest vindicate to myself the family trappings of this once proud
AEgon?--repaying by a backward triumph the insults he might possibly
have heaped in his life-time upon my poor pastoral progenitor.
If it were presumption so to speculate, the present owners of the
mansion had least reason to complain. They had long forsaken the
old house of their fathers for a newer trifle; and I was left to
appropriate to myself what images I could pick up, to raise my fancy,
or to soothe my vanity.
I was the true descendant of those old W----s; and not the present
family of that name, who had fled the old waste places.
Mine was that gallery of good old family portraits, which as I have
gone over, giving them in fancy my own family name, one--and then
another--would seem to smile, reaching forward from the canvas, to
recognise the new relationship; while the rest looked grave, as
it seemed, at the vacancy in their dwelling, and thoughts of fled
posterity.
That Beauty with the cool blue pastoral drapery, and a lamb--that hung
next the great bay window--with the bright yellow H----shire hair, and
eye of watchet hue--so like my Alice!--I am persuaded she was a true
Elia--Mildred Elia, I take it.
Mine too, BLAKESMOOR, was thy noble Marble Hall, with its mosaic
pavements, and its Twelve Caesars--stately busts in marble--ranged
round: of whose countenances, young reader of faces as I was, the
frowning beauty of Nero, I remember, had most of my wonder; but the
mild Galba had my love. There they stood in the coldness of death, yet
freshness of immortality.
Mine too, thy lofty Justice Hall, with its one chair of authority,
high-backed and wickered, once the terror of luckless poacher, or
self-forgetful maiden--so common since, that bats have roosted in it.
Mine too--whose else?--thy costly fruit-garden, with its sun-baked
southern wall; the ampler pleasure-garden, rising backwards from the
house in triple terraces, with flower-pots now of palest lead, save
that a speck here and there, saved from the elements, bespeak their
pristine state to have been gilt and glittering; the verdant quarters
backwarder still; and, stretching still beyond, in old formality,
thy firry wilderness, the haunt of the squirrel, and the day-long
murmuring woodpigeon, with that antique image in the centre, God or
Goddess I wist not; but child of Athens or old Rome paid never a
sincerer worship to Pan or to Sylvanus in their native groves, than I
to that fragmental mystery.
Was it for this, that I kissed my childish hands too fervently in your
idol worship, walks and windings of BLAKESMOOR! for this, or what sin
of mine, has the plough passed over your pleasant places? I sometimes
think that as men, when they die, do not die all, so of their
extinguished habitations there may be a hope--a germ to be revivified.
POOR RELATIONS
A poor relation--is the most irrelevant thing in nature,--a piece of
impertinent correspondency,--an odious approximation,--a haunting
conscience,--a preposterous shadow, lengthening in the noontide of
your prosperity,--an unwelcome remembrancer,--a perpetually recurring
mortification,--a drain on your purse,--a more intolerable dun upon
your pride,--a drawback upon success,--a rebuke to your rising,--a
stain in your blood,--a blot on your scutcheon,--a rent in your
garment,--a death's head at your banquet,--Agathocles' pot,--a
Mordecai in your gate,--a Lazarus at your door,--a lion in your
path,--a frog in your chamber,--a fly in your ointment,--a mote in
your eye,--a triumph to your enemy, an apology to your friends,--the
one thing not needful,--the hail in harvest,--the ounce of sour in a
pound of sweet.
He is known by his knock. Your heart telleth you "That is Mr.
----." A rap, between familiarity and respect; that demands, and,
at the same time, seems to despair of, entertainment. He entereth
smiling, and--embarrassed. He holdeth out his hand to you to shake,
and--draweth it back again. He casually looketh in about dinner
time--when the table is full. He offereth to go away, seeing you
have company--but is induced to stay. He filleth a chair, and your
visitor's two children are accommodated at a side table. He never
cometh upon open days, when your wife says with some complacency,
"My dear, perhaps Mr. ---- will drop in to-day." He remembereth
birth-days--and professeth he is fortunate to have stumbled upon one.
He declareth against fish, the turbot being small--yet suffereth
himself to be importuned into a slice against his first resolution.
He sticketh by the port--yet will be prevailed upon to empty the
remainder glass of claret, if a stranger press it upon him. He is
a puzzle to the servants, who are fearful of being too obsequious,
or not civil enough, to him. The guests think "they have seen him
before." Every one speculateth upon his condition; and the most part
take him to be--a tide-waiter. He calleth you by your Christian
name, to imply that his other is the same with your own. He is too
familiar by half, yet you wish he had less diffidence. With half the
familiarity he might pass for a casual dependent; with more boldness
he would be in no danger of being taken for what he is. He is too
humble for a friend, yet taketh on him more state than befits a
client. He is a worse guest than a country tenant, inasmuch as he
bringeth up no rent--yet 'tis odds, from his garb and demeanour, that
your guests take him for one. He is asked to make one at the whist
table; refuseth on the score of poverty, and--resents being left
out. When the company break up, he proffereth to go for a coach--and
lets the servant go. He recollects your grandfather; and will thrust
in some mean, and quite unimportant anecdote of--the family. He
knew it when it was not quite so flourishing as "he is blest in
seeing it now." He reviveth past situations, to institute what
he calleth--favourable comparisons. With a reflecting sort of
congratulation, he will inquire the price of your furniture; and
insults you with a special commendation of your window-curtains. He
is of opinion that the urn is the more elegant shape, but, after all,
there was something more comfortable about the old tea-kettle--which
you must remember. He dare say you must find a great convenience in
having a carriage of your own, and appealeth to your lady if it is not
so. Inquireth if you have had your arms done on vellum yet; and did
not know till lately, that such-and-such had been the crest of the
family. His memory is unseasonable; his compliments perverse; his talk
a trouble; his stay pertinacious; and when he goeth away, you dismiss
his chair into a corner, as precipitately as possible, and feel fairly
rid of two nuisances.
There is a worse evil under the sun, and that is--a female Poor
Relation. You may do something with the other; you may pass him off
tolerably well; but your indigent she-relative is hopeless. "He is
an old humourist," you may say, "and affects to go threadbare. His
circumstances are better than folks would take them to be. You are
fond of having a Character at your table, and truly he is one." But
in the indications of female poverty there can be no disguise. No
woman dresses below herself from caprice. The truth must out without
shuffling. "She is plainly related to the L----s; or what does she at
their house?" She is, in all probability, your wife's cousin. Nine
times out of ten, at least, this is the case. Her garb is something
between a gentlewoman and a beggar, yet the former evidently
predominates. She is most provokingly humble, and ostentatiously
sensible to her inferiority. He may require to be repressed
sometimes--_aliquando sufflaminandus erat_--but there is no raising
her. You send her soup at dinner, and she begs to be helped--after the
gentlemen. Mr. ---- requests the honour of taking wine with her; she
hesitates between Port and Madeira, and chooses the former--because
he does. She calls the servant _Sir_; and insists on not troubling
him to hold her plate. The housekeeper patronizes her. The children's
governess takes upon her to correct her, when she has mistaken the
piano for a harpsichord.
Richard Amlet, Esq., in the play, is a notable instance of the
disadvantages, to which this chimerical notion of _affinity
constituting a claim to acquaintance_, may subject the spirit of a
gentleman. A little foolish blood is all that is betwixt him and
a lady of great estate. His stars are perpetually crossed by the
malignant maternity of an old woman, who persists in calling him
"her son Dick." But she has wherewithal in the end to recompense his
indignities, and float him again upon the brilliant surface, under
which it had been her seeming business and pleasure all along to sink
him. All men, besides, are not of Dick's temperament. I knew an Amlet
in real life, who, wanting Dick's buoyancy, sank indeed. Poor W----
was of my own standing at Christ's, a fine classic, and a youth of
promise. If he had a blemish, it was too much pride; but its quality
was inoffensive; it was not of that sort which hardens the heart, and
serves to keep inferiors at a distance; it only sought to ward off
derogation from itself. It was the principle of self-respect carried
as far as it could go, without infringing upon that respect, which he
would have every one else equally maintain for himself. He would have
you to think alike with him on this topic. Many a quarrel have I had
with him, when we were rather older boys, and our tallness made us
more obnoxious to observation in the blue clothes, because I would not
thread the alleys and blind ways of the town with him to elude notice,
when we have been out together on a holiday in the streets of this
sneering and prying metropolis. W---- went, sore with these notions,
to Oxford, where the dignity and sweetness of a scholar's life,
meeting with the alloy of a humble introduction, wrought in him a
passionate devotion to the place, with a profound aversion from the
society. The servitor's gown (worse than his school array) clung to
him with Nessian venom. He thought himself ridiculous in a garb, under
which Latimer must have walked erect; and in which Hooker, in his
young days, possibly flaunted in a vein of no discommendable vanity.
In the depth of college shades, or in his lonely chamber, the poor
student shrunk from observation. He found shelter among books, which
insult not; and studies, that ask no questions of a youth's finances.
He was lord of his library, and seldom cared for looking out beyond
his domains. The healing influence of studious pursuits was upon him,
to soothe and to abstract. He was almost a healthy man; when the
waywardness of his fate broke out against him with a second and worse
malignity. The father of W---- had hitherto exercised the humble
profession of house-painter at N----, near Oxford. A supposed interest
with some of the heads of the colleges had now induced him to take
up his abode in that city, with the hope of being employed upon some
public works which were talked of. From that moment I read in the
countenance of the young man, the determination which at length tore
him from academical pursuits for ever. To a person unacquainted with
our Universities, the distance between the gownsmen and the townsmen,
as they are called--the trading part of the latter especially--is
carried to an excess that would appear harsh and incredible. The
temperament of W----'s father was diametrically the reverse of his
own. Old W---- was a little, busy, cringing tradesman, who, with his
son upon his arm, would stand bowing and scraping, cap in hand, to
any-thing that wore the semblance of a gown--insensible to the winks
and opener remonstrances of the young man, to whose chamber-fellow, or
equal in standing, perhaps, he was thus obsequiously and gratuitously
ducking. Such a state of things could not last. W---- must change
the air of Oxford or be suffocated. He chose the former; and let the
sturdy moralist, who strains the point of the filial duties as high
as they can bear, censure the dereliction; he cannot estimate the
struggle. I stood with W----, the last afternoon I ever saw him, under
the eaves of his paternal dwelling. It was in the fine lane leading
from the High-street to the back of ***** college, where W---- kept
his rooms. He seemed thoughtful, and more reconciled. I ventured to
rally him--finding him in a better mood--upon a representation of the
Artist Evangelist, which the old man, whose affairs were beginning to
flourish, had caused to be set up in a splendid sort of frame over his
really handsome shop, either as a token of prosperity, or badge of
gratitude to his saint. W---- looked up at the Luke, and, like Satan,
"knew his mounted sign--and fled." A letter on his father's table
the next morning, announced that he had accepted a commission in a
regiment about to embark for Portugal. He was among the first who
perished before the walls of St. Sebastian.
I do not know how, upon a subject which I began with treating half
seriously, I should have fallen upon a recital so eminently painful;
but this theme of poor relationship is replete with so much matter for
tragic as well as comic associations, that it is difficult to keep
the account distinct without blending. The earliest impressions which
I received on this matter, are certainly not attended with anything
painful, or very humiliating, in the recalling. At my father's table
(no very splendid one) was to be found, every Saturday, the mysterious
figure of an aged gentleman, clothed in neat black, of a sad yet
comely appearance. His deportment was of the essence of gravity; his
words few or none; and I was not to make a noise in his presence. I
had little inclination to have done so--for my cue was to admire in
silence. A particular elbow chair was appropriated to him, which was
in no case to be violated. A peculiar sort of sweet pudding, which
appeared on no other occasion, distinguished the days of his coming.
I used to think him a prodigiously rich man. All I could make out of
him was, that he and my father had been schoolfellows a world ago at
Lincoln, and that he came from the Mint. The Mint I knew to be a place
where all the money was coined--and I thought he was the owner of
all that money. Awful ideas of the Tower twined themselves about his
presence. He seemed above human infirmities and passions. A sort
of melancholy grandeur invested him. From some inexplicable doom I
fancied him obliged to go about in an eternal suit of mourning; a
captive--a stately being, let out of the Tower on Saturdays. Often
have I wondered at the temerity of my father, who, in spite of an
habitual general respect which we all in common manifested towards
him, would venture now and then to stand up against him in some
argument, touching their youthful days. The houses of the ancient
city of Lincoln are divided (as most of my readers know) between the
dwellers on the hill, and in the valley. This marked distinction
formed an obvious division between the boys who lived above (however
brought together in a common school) and the boys whose paternal
residence was on the plain; a sufficient cause of hostility in
the code of these young Grotiuses. My father had been a leading
Mountaineer; and would still maintain the general superiority, in
skill and hardihood, of the _Above Boys_ (his own faction) over the
_Below Boys_ (so were they called), of which party his contemporary
had been a chieftain. Many and hot were the skirmishes on this
topic--the only one upon which the old gentleman was ever brought
out--and bad blood bred; even sometimes almost to the recommencement
(so I expected) of actual hostilities. But my father, who scorned to
insist upon advantages, generally contrived to turn the conversation
upon some adroit by-commendation of the old Minster; in the general
preference of which, before all other cathedrals in the island, the
dweller on the hill, and the plain-born, could meet on a conciliating
level, and lay down their less important differences. Once only I saw
the old gentleman really ruffled, and I remembered with anguish the
thought that came over me: "Perhaps he will never come here again."
He had been pressed to take another plate of the viand, which I have
already mentioned as the indispensable concomitant of his visits. He
had refused, with a resistance amounting to rigour--when my aunt,
an old Lincolnian, but who had something of this, in common with
my cousin Bridget, that she would sometimes press civility out of
season--uttered the following memorable application--"Do take another
slice, Mr. Billet, for you do not get pudding every day." The old
gentleman said nothing at the time--but he took occasion in the course
of the evening, when some argument had intervened between them, to
utter with an emphasis which chilled the company, and which chills me
now as I write it--"Woman, you are superannuated." John Billet did not
survive long, after the digesting of this affront; but he survived
long enough to assure me that peace was actually restored! and, if I
remember aright, another pudding was discreetly substituted in the
place of that which had occasioned the offence. He died at the Mint
(Anno 1781) where he had long held, what he accounted, a comfortable
independence; and with five pounds, fourteen shillings, and a penny,
which were found in his escrutoire after his decease, left the world,
blessing God that he had enough to bury him, and that he had never
been obliged to any man for a sixpence. This was--a Poor Relation.
STAGE ILLUSION
A play is said to be well or ill acted in proportion to the scenical
illusion produced. Whether such illusion can in any case be perfect,
is not the question. The nearest approach to it, we are told, is, when
the actor appears wholly unconscious of the presence of spectators.
In tragedy--in all which is to affect the feelings--this undivided
attention to his stage business, seems indispensable. Yet it is, in
fact, dispensed with every day by our cleverest tragedians; and while
these references to an audience, in the shape of rant or sentiment,
are not too frequent or palpable, a sufficient quantity of illusion
for the purposes of dramatic interest may be said to be produced in
spite of them. But, tragedy apart, it may be inquired whether, in
certain characters in comedy, especially those which are a little
extravagant, or which involve some notion repugnant to the moral
sense, it is not a proof of the highest skill in the comedian when,
without absolutely appealing to an audience, he keeps up a tacit
understanding with them; and makes them, unconsciously to themselves,
a party in the scene. The utmost nicety is required in the mode of
doing this; but we speak only of the great artists in the profession.
The most mortifying infirmity in human nature, to feel in ourselves,
or to contemplate in another, is, perhaps, cowardice. To see a coward
_done to the life_ upon a stage would produce anything but mirth.
Yet we most of us remember Jack Bannister's cowards. Could any thing
be more agreeable, more pleasant? We loved the rogues. How was
this effected but by the exquisite art of the actor in a perpetual
sub-insinuation to us, the spectators, even in the extremity of the
shaking fit, that he was not half such a coward as we took him for? We
saw all the common symptoms of the malady upon him; the quivering lip,
the cowering knees, the teeth chattering; and could have sworn "that
man was frightened." But we forgot all the while--or kept it almost a
secret to ourselves--that he never once lost his self-possession; that
he let out by a thousand droll looks and gestures--meant at _us_, and
not at all supposed to be visible to his fellows in the scene, that
his confidence in his own resources had never once deserted him. Was
this a genuine picture of a coward? or not rather a likeness, which
the clever artist contrived to palm upon us instead of an original;
while we secretly connived at the delusion for the purpose of greater
pleasure, than a more genuine counterfeiting of the imbecility,
helplessness, and utter self-desertion, which we know to be
concomitants of cowardice in real life, could have given us?
Why are misers so hateful in the world, and so endurable on the stage,
but because the skilful actor, by a sort of sub-reference, rather than
direct appeal to us, disarms the character of a great deal of its
odiousness, by seeming to engage _our_ compassion for the insecure
tenure by which he holds his money bags and parchments? By this subtle
vent half of the hatefulness of the character--the self-closeness
with which in real life it coils itself up from the sympathies of
men--evaporates. The miser becomes sympathetic; _i.e._ is no genuine
miser. Here again a diverting likeness is substituted for a very
disagreeable reality.
Spleen, irritability--the pitiable infirmities of old men, which
produce only pain to behold in the realities, counterfeited upon a
stage, divert not altogether for the comic appendages to them, but in
part from an inner conviction that they are _being acted_ before us;
that a likeness only is going on, and not the thing itself. They
please by being done under the life, or beside it; not _to the life_.
When Gatty acts an old man, is he angry indeed? or only a pleasant
counterfeit, just enough of a likeness to recognise, without pressing
upon us the uneasy sense of reality?
Comedians, paradoxical as it may seem, may be too natural. It was the
case with a late actor. Nothing could be more earnest or true than the
manner of Mr. Emery; this told excellently in his Tyke, and characters
of a tragic cast. But when he carried the same rigid exclusiveness of
attention to the stage business, and wilful blindness and oblivion of
everything before the curtain into his comedy, it produced a harsh and
dissonant effect. He was out of keeping with the rest of the _Personae
Dramatis_. There was as little link between him and them as betwixt
himself and the audience. He was a third estate, dry, repulsive, and
unsocial to all. Individually considered, his execution was masterly.
But comedy is not this unbending thing; for this reason, that the same
degree of credibility is not required of it as to serious scenes. The
degrees of credibility demanded to the two things may be illustrated
by the different sort of truth which we expect when a man tells us a
mournful or a merry story. If we suspect the former of falsehood in
any one tittle, we reject it altogether. Our tears refuse to flow at a
suspected imposition. But the teller of a mirthful tale has latitude
allowed him. We are content with less than absolute truth. 'Tis the
same with dramatic illusion. We confess we love in comedy to see an
audience naturalised behind the scenes, taken in into the interest
of the drama, welcomed as by-standers however. There is something
ungracious in a comic actor holding himself aloof from all
participation or concern with those who are come to be diverted by
him. Macbeth must see the dagger, and no ear but his own be told of
it; but an old fool in farce may think he _sees something_, and by
conscious words and looks express it, as plainly as he can speak, to
pit, box, and gallery. When an impertinent in tragedy, an Osric, for
instance, breaks in upon the serious passions of the scene, we approve
of the contempt with which he is treated. But when the pleasant
impertinent of comedy, in a piece purely meant to give delight, and
raise mirth out of whimsical perplexities, worries the studious man
with taking up his leisure, or making his house his home, the same
sort of contempt expressed (however _natural_) would destroy the
balance of delight in the spectators. To make the intrusion comic,
the actor who plays the annoyed man must a little desert nature; he
must, in short, be thinking of the audience, and express only so much
dissatisfaction and peevishness as is consistent with the pleasure of
comedy. In other words, his perplexity must seem half put on. If he
repel the intruder with the sober set face of a man in earnest, and
more especially if he deliver his expostulations in a tone which in
the world must necessarily provoke a duel; his real-life manner will
destroy the whimsical and purely dramatic existence of the other
character (which to render it comic demands an antagonist comicality
on the part of the character opposed to it), and convert what was
meant for mirth, rather than belief, into a downright piece of
impertinence indeed, which would raise no diversion in us, but rather
stir pain, to see inflicted in earnest upon any unworthy person. A
very judicious actor (in most of his parts) seems to have fallen into
an error of this sort in his playing with Mr. Wrench in the farce of
Free and Easy.
Many instances would be tedious; these may suffice to show that comic
acting at least does not always demand from the performer that strict
abstraction from all reference to an audience, which is exacted of
it; but that in some cases a sort of compromise may take place, and
all the purposes of dramatic delight be attained by a judicious
understanding, not too openly announced, between the ladies and
gentlemen--on both sides of the curtain.
TO THE SHADE OF ELLISTON
Joyousest of once embodied spirits, whither at length hast thou flown?
to what genial region are we permitted to conjecture that thou has
flitted.
Art thou sowing thy WILD OATS yet (the harvest time was still to come
with thee) upon casual sands of Avernus? or art thou enacting ROVER
(as we would gladlier think) by wandering Elysian streams?
This mortal frame, while thou didst play thy brief antics amongst us,
was in truth any thing but a prison to thee, as the vain Platonist
dreams of this _body_ to be no better than a county gaol, forsooth, or
some house of durance vile, whereof the five senses are the fetters.
Thou knewest better than to be in a hurry to cast off those gyves; and
had notice to quit, I fear, before thou wert quite ready to abandon
this fleshly tenement. It was thy Pleasure House, thy Palace of Dainty
Devices; thy Louvre, or thy White Hall.
What new mysterious lodgings dost thou tenant now? or when may we
expect thy aerial house-warming?
Tartarus we know, and we have read of the Blessed Shades; now cannot I
intelligibly fancy thee in either.
Is it too much to hazard a conjecture, that (as the school-men
admitted a receptacle apart for Patriarchs and un-chrisom Babes) there
may exist--not far perchance from that storehouse of all vanities,
which Milton saw in visions--a LIMBO somewhere for PLAYERS? and that
Up thither like aerial vapours fly
Both all Stage things, and all that in Stage things
Built their fond hopes of glory, or lasting fame?
All the unaccomplish'd works of Authors' hands,
Abortive, monstrous, or unkindly mix'd,
Damn'd upon earth, fleet thither--
Play, Opera, Farce, with all their trumpery--
There, by the neighbouring moon (by some not improperly supposed
thy Regent Planet upon earth) mayst thou not still be acting thy
managerial pranks, great disembodied Lessee? but Lessee still, and
still a Manager.
In Green Rooms, impervious to mortal eye, the muse beholds thee
wielding posthumous empire.
Thin ghosts of Figurantes (never plump on earth) circle thee in
endlessly, and still their song is _Fye on sinful Phantasy_.
Magnificent were thy capriccios on this globe of earth, ROBERT WILLIAM
ELLISTON! for as yet we know not thy new name in heaven.
It irks me to think, that, stript of thy regalities, thou shouldst
ferry over, a poor forked shade, in crazy Stygian wherry. Methinks I
hear the old boatman, paddling by the weedy wharf, with raucid voice,
bawling "SCULLS, SCULLS:" to which, with waving hand, and majestic
action, thou deignest no reply, other than in two curt monosyllables,
"No: OARS."
But the laws of Pluto's kingdom know small difference between king,
and cobbler; manager, and call-boy; and, if haply your dates of life
were conterminant, you are quietly taking your passage, cheek by
cheek (O ignoble levelling of Death) with the shade of some recently
departed candle-snuffer.
But mercy! what strippings, what tearing off of histrionic robes,
and private vanities! what denudations to the bone, before the surly
Ferryman will admit you to set a foot within his battered lighter!
Crowns, sceptres; shield, sword, and truncheon; thy own coronation
robes (for thou hast brought the whole property man's wardrobe with
thee, enough to sink a navy); the judge's ermine; the coxcomb's wig;
the snuff-box _a la Foppington_--all must overboard, he positively
swears--and that ancient mariner brooks no denial; for, since the
tiresome monodrame of the old Thracian Harper, Charon, it is to be
believed, hath shown small taste for theatricals.
Aye, now 'tis done. You are just boat weight; _pura et puta anima_.
But bless me, how _little_ you look!
So shall we all look--kings, and keysars--stript for the last voyage.
But the murky rogue pushes off. Adieu, pleasant, and thrice pleasant
shade! with my parting thanks for many a heavy hour of life lightened
by thy harmless extravaganzas, public or domestic.
Rhadamanthus, who tries the lighter causes below, leaving to his
two brethren the heavy calendars--honest Rhadamanth, always partial
to players, weighing their parti- existence here upon
earth,--making account of the few foibles, that may have shaded thy
_real life_ as we call it, (though, substantially, scarcely less a
vapour than thy idlest vagaries upon the boards of Drury,) as but of
so many echoes, natural repercussions, and results to be expected from
the assumed extravagancies of thy _secondary_ or _mock life_, nightly
upon a stage--after a lenient castigation, with rods lighter than
of those Medusean ringlets, but just enough to "whip the offending
Adam out of thee"--shall courteously dismiss thee at the right
hand gate--the O.P. side of Hades--that conducts to masques, and
merry-makings, in the Theatre Royal of Proserpine.
PLAUDITO, ET VALETO
ELLISTONIANA
My acquaintance with the pleasant creature, whose loss we all deplore,
was but slight.
My first introduction to E., which afterwards ripened into an
acquaintance a little on this side of intimacy, was over a counter
of the Leamington Spa Library, then newly entered upon by a branch
of his family. E., whom nothing misbecame--to auspicate, I suppose,
the filial concern, and set it a going with a lustre--was serving in
person two damsels fair, who had come into the shop ostensibly to
inquire for some new publication, but in reality to have a sight of
the illustrious shopman, hoping some conference. With what an air did
he reach down the volume, dispassionately giving his opinion upon the
worth of the work in question, and launching out into a dissertation
on its comparative merits with those of certain publications of a
similar stamp, its rivals! his enchanted customers fairly hanging on
his lips, subdued to their authoritative sentence. So have I seen a
gentleman in comedy _acting_ the shopman. So Lovelace sold his gloves
in King Street. I admired the histrionic art, by which he contrived to
carry clean away every notion of disgrace, from the occupation he had
so generously submitted to; and from that hour I judged him, with no
after repentance, to be a person, with whom it would be a felicity to
be more acquainted.
To descant upon his merits as a Comedian would be superfluous. With
his blended private and professional habits alone I have to do;
that harmonious fusion of the manners of the player into those of
every day life, which brought the stage boards into streets, and
dining-parlours, and kept up the play when the play was ended.--"I
like Wrench," a friend was saying to him one day, "because he is the
same natural, easy creature, _on_ the stage, that he is _off_." "My
case exactly," retorted Elliston--with a charming forgetfulness,
that the converse of a proposition does not always lead to the same
conclusion--"I am the same person _off_ the stage that I am _on_." The
inference, at first sight, seems identical; but examine it a little,
and it confesses only, that the one performer was never, and the other
always, _acting_.
And in truth this was the charm of Elliston's private deportment.
You had a spirited performance always going on before your eyes,
with nothing to pay. As where a monarch takes up his casual abode for
a night, the poorest hovel which he honours by his sleeping in it,
becomes _ipso facto_ for that time a palace; so where-ever Elliston
walked, sate, or stood still, there was the theatre. He carried about
with him his pit, boxes, and galleries, and set up his portable
playhouse at corners of streets, and in the market-places. Upon
flintiest pavements he trod the boards still; and if his theme chanced
to be passionate, the green baize carpet of tragedy spontaneously rose
beneath his feet. Now this was hearty, and showed a love for his art.
So Apelles _always_ painted--in thought. So G.D. _always_ poetises.
I hate a lukewarm artist. I have known actors--and some of them of
Elliston's own stamp--who shall have agreeably been amusing you in
the part of a rake or a coxcomb, through the two or three hours of
their dramatic existence; but no sooner does the curtain fall with
its leaden clatter, but a spirit of lead seems to seize on all their
faculties. They emerge sour, morose persons, intolerable to their
families, servants, &c. Another shall have been expanding your heart
with generous deeds and sentiments, till it even beats with yearnings
of universal sympathy; you absolutely long to go home, and do some
good action. The play seems tedious, till you can get fairly out of
the house, and realise your laudable intentions. At length the final
bell rings, and this cordial representative of all that is amiable
in human breasts steps forth--a miser. Elliston was more of a piece.
Did he _play_ Ranger? and did Ranger fill the general bosom of the
town with satisfaction? why should _he_ not be Ranger, and diffuse
the same cordial satisfaction among his private circles? with _his_
temperament, _his_ animal spirits, _his_ good-nature, _his_ follies
perchance, could he do better than identify himself with his
impersonation? Are we to like a pleasant rake, or coxcomb, on the
stage, and give ourselves airs of aversion for the identical character
presented to us in actual life? or what would the performer have
gained by divesting himself of the impersonation? Could the man
Elliston have been essentially different from his part, even if he
had avoided to reflect to us studiously, in private circles, the
airy briskness, the forwardness, and 'scape goat trickeries of his
prototype?
"But there is something not natural in this everlasting _acting_; we
want the real man."
Are you quite sure that it is not the man himself, whom you cannot, or
will not see, under some adventitious trappings, which, nevertheless,
sit not at all inconsistently upon him? What if it is the nature of
some men to be highly artificial? The fault is least reprehensible in
_players_. Cibber was his own Foppington, with almost as much wit as
Vanburgh could add to it.
"My conceit of his person,"--it is Ben Jonson speaking of Lord
Bacon,--"was never increased towards him by his _place_ or _honours_.
But I have, and do reverence him for the _greatness_, that was only
proper to himself; in that he seemed to me ever one of the _greatest_
men, that had been in many ages. In his adversity I ever prayed that
heaven would give him strength; for _greatness_ he could not want."
The quality here commended was scarcely less conspicuous in the
subject of these idle reminiscences, than in my Lord Verulam. Those
who have imagined that an unexpected elevation to the direction of a
great London Theatre, affected the consequence of Elliston, or at all
changed his nature, knew not the essential _greatness_ of the man whom
they disparage. It was my fortune to encounter him near St. Dunstan's
Church (which, with its punctual giants, is now no more than dust
and a shadow), on the morning of his election to that high office.
Grasping my hand with a look of significance, he only uttered,--"Have
you heard the news?"--then with another look following up
the blow, he subjoined, "I am the future Manager of Drury Lane
Theatre."--Breathless as he saw me, he stayed not for congratulation
or reply, but mutely stalked away, leaving me to chew upon his
new-blown dignities at leisure. In fact, nothing could be said to
it. Expressive silence alone could muse his praise. This was in his
_great_ style.
But was he less _great_, (be witness, O ye Powers of Equanimity,
that supported in the ruins of Carthage the consular exile, and
more recently transmuted for a more illustrious exile the barren
constableship of Elba into an image of Imperial France), when, in
melancholy after-years, again, much near the same spot, I met him,
when that sceptre had been wrested from his hand, and his dominion was
curtailed to the petty managership, and part proprietorship, of the
small Olympic, _his Elba?_ He still played nightly upon the boards
of Drury, but in parts alas! allotted to him, not magnificently
distributed by him. Waiving his great loss as nothing, and
magnificently sinking the sense of fallen _material_ grandeur in
the more liberal resentment of depreciations done to his more
lofty _intellectual_ pretensions, "Have you heard" (his customary
exordium)--"have you heard," said he, "how they treat me? they put me
in _comedy_." Thought I--but his finger on his lips forbade any verbal
interruption--"where could they have put you better?" Then, after a
pause--"Where I formerly played Romeo, I now play Mercutio,"--and so
again he stalked away, neither staying, nor caring for, responses.
O, it was a rich scene,--but Sir A---- C----, the best of
story-tellers and surgeons, who mends a lame narrative almost as
well as he sets a fracture, alone could do justice to it--that I was
witness to, in the tarnished room (that had once been green) of that
same little Olympic. There, after his deposition from Imperial Drury,
he substituted a throne. That Olympic Hill was his "highest heaven;"
himself "Jove in his chair." There he sat in state, while before
him, on complaint of prompter, was brought for judgment--how shall
I describe her?--one of those little tawdry things that flirt at
the tails of choruses--a probationer for the town, in either of its
senses--the pertest little drab--a dirty fringe and appendage of the
lamps' smoke--who, it seems, on some disapprobation expressed by a
"highly respectable" audience, had precipitately quitted her station
on the boards, and withdrawn her small talents in disgust.
"And how dare you," said her Manager--assuming a censorial severity
which would have crushed the confidence of a Vestris, and disarmed
that beautiful Rebel herself of her professional caprices--I verily
believe, he thought _her_ standing before him--"how dare you, Madam,
withdraw yourself, without a notice, from your theatrical duties?" "I
was hissed, Sir." "And you have the presumption to decide upon the
taste of the town?" "I don't know that, Sir, but I will never stand
to be hissed," was the subjoinder of young Confidence--when gathering
up his features into one significant mass of wonder, pity, and
expostulatory indignation--in a lesson never to have been lost upon a
creature less forward than she who stood before him--his words were
these: "They have hissed _me_."
'Twas the identical argument _a fortiori_, which the son of Peleus
uses to Lycaon trembling under his lance, to persuade him to take his
destiny with a good grace. "I too am mortal." And it is to be believed
that in both cases the rhetoric missed of its application, for want
of a proper understanding with the faculties of the respective
recipients.
"Quite an Opera pit," he said to me, as he was courteously conducting
me over the benches of his Surrey Theatre, the last retreat, and
recess, of his every-day waning grandeur.
Those who knew Elliston, will know the _manner_ in which he pronounced
the latter sentence of the few words I am about to record. One proud
day to me he took his roast mutton with us in the Temple, to which
I had superadded a preliminary haddock. After a rather plentiful
partaking of the meagre banquet, not unrefreshed with the humbler sort
of liquors, I made a sort of apology for the humility of the fare,
observing that for my own part I never ate but of one dish at dinner.
"I too never eat but one thing at dinner"--was his reply--then after
a pause--"reckoning fish as nothing." The manner was all. It was as
if by one peremptory sentence he had decreed the annihilation of all
the savory esculents, which the pleasant and nutritious-food-giving
Ocean pours forth upon poor humans from her watery bosom. This was
_greatness_, tempered with considerate _tenderness_ to the feelings of
his scanty but welcoming entertainer.
_Great_ wert thou in thy life, Robert William Elliston! and _not
lessened_ in thy death, if report speak truly, which says that
thou didst direct that thy mortal remains should repose under no
inscription but one of pure _Latinity_. Classical was thy bringing
up! and beautiful was the feeling on thy last bed, which, connecting
the man with the boy, took thee back in thy latest exercise
of imagination, to the days when, undreaming of Theatres and
Managerships, thou wert a scholar, and an early ripe one, under the
roofs builded by the munificent and pious Colet. For thee the Pauline
Muses weep. In elegies, that shall silence this crude prose, they
shall celebrate thy praise.
DETACHED THOUGHTS ON BOOKS AND READING
To mind the inside of a book is to entertain one's self with
the forced product of another man's brain. Now I think a man of
quality and breeding may be much amused with the natural sprouts
of his own.
_Lord Foppington in the Relapse._
An ingenious acquaintance of my own was so much struck with this
bright sally of his Lordship, that he has left off reading altogether,
to the great improvement of his originality. At the hazard of
losing some credit on this head, I must confess that I dedicate no
inconsiderable portion of my time to other people's thoughts. I dream
away my life in others' speculations. I love to lose myself in other
men's minds. When I am not walking, I am reading; I cannot sit and
think. Books think for me.
I have no repugnances. Shaftesbury is not too genteel for me, nor
Jonathan Wild too low. I can read any thing which I call a _book_.
There are things in that shape which I cannot allow for such.
In this catalogue of _books which are no books--biblia a-biblia_--I
reckon Court Calendars, Directories, Pocket Books, Draught Boards
bound and lettered at the back, Scientific Treatises, Almanacks,
Statutes at Large; the works of Hume, Gibbon, Robertson, Beattie,
Soame Jenyns, and, generally, all those volumes which "no gentleman's
library should be without:" the Histories of Flavins Josephus (that
learned Jew), and Paley's Moral Philosophy. With these exceptions, I
can read almost any thing. I bless my stars for a taste so catholic,
so unexcluding.
I confess that it moves my spleen to see these _things in books'
clothing_ perched upon shelves, like false saints, usurpers of true
shrines, intruders into the sanctuary, thrusting out the legitimate
occupants. To reach down a well-bound semblance of a volume, and
hope it is some kind-hearted play-book, then, opening what "seem its
leaves," to come bolt upon a withering Population Essay. To expect a
Steele, or a Farquhar, and find--Adam Smith. To view a well-arranged
assortment of blockheaded Encyclopaedias (Anglicanas or Metropolitanas)
set out in an array of Russia, or Morocco, when a tithe of that
good leather would comfortably re-clothe my shivering folios; would
renovate Paracelsus himself, and enable old Raymund Lully to look like
himself again in the world. I never see these impostors, but I long to
strip them, to warm my ragged veterans in their spoils.
To be strong-backed and neat-bound is the desideratum of a volume.
Magnificence comes after. This, when it can be afforded, is not to be
lavished upon all kinds of books indiscriminately. I would not dress
a set of Magazines, for instance, in full suit. The dishabille, or
half-binding (with Russia backs ever) is _our_ costume. A Shakespeare,
or a Milton (unless the first editions), it were mere foppery to trick
out in gay apparel. The possession of them confers no distinction. The
exterior of them (the things themselves being so common), strange to
say, raises no sweet emotions, no tickling sense of property in the
owner. Thomson's Seasons, again, looks best (I maintain it) a little
torn, and dog's-eared. How beautiful to a genuine lover of reading
are the sullied leaves, and worn out appearance, nay, the very
odour (beyond Russia), if we would not forget kind feelings in
fastidiousness, of an old "Circulating Library" Tom Jones, or Vicar
of Wakefield! How they speak of the thousand thumbs, that have turned
over their pages with delight!--of the lone sempstress, whom they may
have cheered (milliner, or harder-working mantua-maker) after her long
day's needle-toil, running far into midnight, when she has snatched an
hour, ill spared from sleep, to steep her cares, as in some Lethean
cup, in spelling out their enchanting contents! Who would have them a
whit less soiled? What better condition could we desire to see them
in?
In some respects the better a book is, the less it demands from
binding. Fielding, Smollet, Sterne, and all that class of perpetually
self-reproductive volumes--Great Nature's Stereotypes--we see them
individually perish with less regret, because we know the copies
of them to be "eterne." But where a book is at once both good and
rare--where the individual is almost the species, and when _that_
perishes,
We know not where is that Promethean torch
That can its light relumine--
such a book, for instance, as the Life of the Duke of Newcastle, by
his Duchess--no casket is rich enough, no casing sufficiently durable,
to honour and keep safe such a jewel.
Not only rare volumes of this description, which seem hopeless ever to
be reprinted; but old editions of writers, such as Sir Philip Sydney,
Bishop Taylor, Milton in his prose-works, Fuller--of whom we _have_
reprints, yet the books themselves, though they go about, and are
talked of here and there, we know, have not endenizened themselves
(nor possibly ever will) in the national heart, so as to become stock
books--it is good to possess these in durable and costly covers. I do
not care for a First Folio of Shakspeare. I rather prefer the common
editions of Rowe and Tonson, without notes, and with _plates_, which,
being so execrably bad, serve as maps, or modest remembrancers, to the
text; and without pretending to any supposable emulation with it, are
so much better than the Shakspeare gallery _engravings_, which _did_.
I have a community of feeling with my countrymen about his Plays, and
I like those editions of him best, which have been oftenest tumbled
about and handled.--On the contrary, I cannot read Beaumont and
Fletcher but in Folio. The Octavo editions are painful to look at. I
have no sympathy with them. If they were as much read as the current
editions of the other poet, I should prefer them in that shape to the
older one. I do not know a more heartless sight than the reprint of
the Anatomy of Melancholy. What need was there of unearthing the bones
of that fantastic old great man, to expose them in a winding-sheet of
the newest fashion to modern censure? what hapless stationer could
dream of Burton ever becoming popular?--The wretched Malone could not
do worse, when he bribed the sexton of Stratford church to let him
white-wash the painted effigy of old Shakspeare, which stood there,
in rude but lively fashion depicted, to the very colour of the cheek,
the eye, the eye-brow, hair, the very dress he used to wear--the only
authentic testimony we had, however imperfect, of these curious parts
and parcels of him. They covered him over with a coat of white paint.
By ----, if I had been a justice of peace for Warwickshire, I would
have clapt both commentator and sexton fast in the stocks, for a pair
of meddling sacrilegious varlets.
I think I see them at their work--these sapient trouble-tombs.
Shall I be thought fantastical, if I confess, that the names of some
of our poets sound sweeter, and have a finer relish to the ear--to
mine, at least--than that of Milton or of Shakspeare? It may be, that
the latter are more staled and rung upon in common discourse. The
sweetest names, and which carry a perfume in the mention, are, Kit
Marlowe, Drayton, Drummond of Hawthornden, and Cowley.
Much depends upon _when_ and _where_ you read a book. In the five or
six impatient minutes, before the dinner is quite ready, who would
think of taking up the Fairy Queen for a stop-gap, or a volume of
Bishop Andrewes' sermons?
Milton almost requires a solemn service of music to be played before
you enter upon him. But he brings his music, to which, who listens,
had need bring docile thoughts, and purged ears.
Winter evenings--the world shut out--with less of ceremony the gentle
Shakspeare enters. At such a season, the Tempest, or his own Winter's
Tale--
These two poets you cannot avoid reading aloud--to yourself, or (as
it chances) to some single person listening. More than one--and it
degenerates into an audience.
Books of quick interest, that hurry on for incidents, are for the eye
to glide over only. It will not do to read them out. I could never
listen to even the better kind of modern novels without extreme
irksomeness.
A newspaper, read out, is intolerable. In some of the Bank offices
it is the custom (to save so much individual time) for one of the
clerks--who is the best scholar--to commence upon the Times, or the
Chronicle, and recite its entire contents aloud _pro bono publico_.
With every advantage of lungs and elocution, the effect is singularly
vapid. In barbers' shops and public-houses a fellow will get up,
and spell out a paragraph, which he communicates as some discovery.
Another follows with _his_ selection. So the entire journal transpires
at length by piece-meal. Seldom-readers are slow readers, and, without
this expedient no one in the company would probably ever travel
through the contents of a whole paper.
Newspapers always excite curiosity. No one ever lays one down without
a feeling of disappointment.
What an eternal time that gentleman in black, at Nando's, keeps the
paper! I am sick of hearing the waiter bawling out incessantly, "the
Chronicle is in hand, Sir."
Coming in to an inn at night--having ordered your supper--what can be
more delightful than to find lying in the window-seat, left there time
out of mind by the carelessness of some former guest--two or three
numbers of the old Town and Country Magazine, with its amusing
_tete-a-tete_ pictures--"The Royal Lover and Lady G----;" "The Melting
Platonic and the old Beau,"--and such like antiquated scandal? Would
you exchange it--at that time, and in that place--for a better book?
Poor Tobin, who latterly fell blind, did not regret it so much for the
weightier kinds of reading--the Paradise Lost, or Comus, he could have
_read_ to him--but he missed the pleasure of skimming over with his
own eye a magazine, or a light pamphlet.
I should not care to be caught in the serious avenues of some
cathedral alone, and reading _Candide_.
I do not remember a more whimsical surprise than having been once
detected--by a familiar damsel--reclined at my ease upon the grass, on
Primrose Hill (her Cythera), reading--_Pamela_. There was nothing in
the book to make a man seriously ashamed at the exposure; but as she
seated herself down by me, and seemed determined to read in company,
I could have wished it had been--any other book. We read on very
sociably for a few pages; and, not finding the author much to her
taste, she got up, and--went away. Gentle casuist, I leave it to thee
to conjecture, whether the blush (for there was one between us) was
the property of the nymph or the swain in this dilemma. From me you
shall never get the secret.
I am not much a friend to out-of-doors reading. I cannot settle my
spirits to it. I knew a Unitarian minister, who was generally to be
seen upon Snow-hill (as yet Skinner's-street _was not_), between the
hours of ten and eleven in the morning, studying a volume of Lardner.
I own this to have been a strain of abstraction beyond my reach. I
used to admire how he sidled along, keeping clear of secular contacts.
An illiterate encounter with a porter's knot, or a bread basket, would
have quickly put to flight all the theology I am master of, and have
left me worse than indifferent to the five points.
There is a class of street-readers, whom I can never contemplate
without affection--the poor gentry, who, not having wherewithal to buy
or hire a book, filch a little learning at the open stalls--the owner,
with his hard eye, casting envious looks at them all the while, and
thinking when they will have done. Venturing tenderly, page after
page, expecting every moment when he shall interpose his interdict,
and yet unable to deny themselves the gratification, they "snatch
a fearful joy." Martin B----, in this way, by daily fragments,
got through two volumes of Clarissa, when the stall-keeper damped
his laudable ambition, by asking him (it was in his younger days)
whether he meant to purchase the work. M. declares, that under no
circumstances of his life did he ever peruse a book with half the
satisfaction which he took in those uneasy snatches. A quaint poetess
of our day has moralised upon this subject in two very touching but
homely stanzas.
I saw a boy with eager eye
Open a book upon a stall,
And read, as he'd devour it all;
Which when the stall-man did espy,
Soon to the boy I heard him call,
"You, Sir, you never buy a book,
Therefore in one you shall not look."
The boy pass'd slowly on, and with a sigh
He wish'd he never had been taught to read,
Then of the old churl's books he should have had no need.
Of sufferings the poor have many,
Which never can the rich annoy:
I soon perceiv'd another boy,
Who look'd as if he'd not had any
Food, for that day at least--enjoy
The sight of cold meat in a tavern larder.
This boy's case, then thought I, is surely harder,
Thus hungry, longing, thus without a penny,
Beholding choice of dainty-dressed meat:
No wonder if he wish he ne'er had learn'd to eat.
THE OLD MARGATE HOY
I am fond of passing my vacations (I believe I have said so before) at
one or other of the Universities. Next to these my choice would fix
me at some woody spot, such as the neighbourhood of Henley affords in
abundance, upon the banks of my beloved Thames. But somehow or other
my cousin contrives to wheedle me once in three or four seasons to a
watering place. Old attachments cling to her in spite of experience.
We have been dull at Worthing one summer, duller at Brighton another,
dullest at Eastbourn a third, and are at this moment doing dreary
penance at--Hastings!--and all because we were happy many years ago
for a brief week at--Margate. That was our first sea-side experiment,
and many circumstances combined to make it the most agreeable holyday
of my life. We had neither of us seen the sea, and we had never been
from home so long together in company.
Can I forget thee, thou old Margate Hoy, with thy weather-beaten,
sun-burnt captain, and his rough accommodations--ill exchanged for the
foppery and fresh-water niceness of the modern steam-packet? To the
winds and waves thou committedst thy goodly freightage, and didst
ask no aid of magic fumes, and spells, and boiling cauldrons. With
the gales of heaven thou wentest swimmingly; or, when it was their
pleasure, stoodest still with sailor-like patience. Thy course was
natural, not forced, as in a hot-bed; nor didst thou go poisoning
the breath of ocean with sulphureous smoke--a great sea-chimaera,
chimneying and furnacing the deep; or liker to that fire-god parching
up Scamander.
Can I forget thy honest, yet slender crew, with their coy reluctant
responses (yet to the suppression of anything like contempt, to the
raw questions, which we of the great city would be ever and anon
putting to them, as to the uses of this or that strange naval
implement?) 'Specially can I forget thee, thou happy medium, thou shade
of refuge between us and them, conciliating interpreter of their skill
to our simplicity, comfortable ambassador between sea and land!--whose
sailor-trowsers did not more convincingly assure thee to be an adopted
denizen of the former, than thy white cap, and whiter apron over them,
with thy neat-fingered practice in thy culinary vocation, bespoke thee
to have been of inland nurture heretofore--a master cook of Eastcheap?
How busily didst thou ply thy multifarious occupation, cook, mariner,
attendant, chamberlain; here, there, like another Ariel, flaming at
once about all parts of the deck, yet with kindlier ministrations--not
to assist the tempest, but, as if touched with a kindred sense of our
infirmities, to soothe the qualms which that untried motion might
haply raise in our crude land-fancies. And when the o'er-washing
billows drove us below deck (for it was far gone in October, and we
had stiff and blowing weather) how did thy officious ministerings,
still catering for our comfort, with cards, and cordials, and thy more
cordial conversation, alleviate the closeness and the confinement of
thy else (truth to say) not very savoury, nor very inviting, little
cabin!
With these additaments to boot, we had on board a fellow-passenger,
whose discourse in verity might have beguiled a longer voyage than we
meditated, and have made mirth and wonder abound as far as the Azores.
He was a dark, Spanish complexioned young man, remarkably handsome,
with an officer-like assurance, and an insuppressible volubility of
assertion. He was, in fact, the greatest liar I had met with then,
or since. He was none of your hesitating, half story-tellers (a most
painful description of mortals) who go on sounding your belief, and
only giving you as much as they see you can swallow at a time--the
nibbling pickpockets of your patience--but one who committed
downright, daylight depredations upon his neighbour's faith. He did
not stand shivering upon the brink, but was a hearty thoroughpaced
liar, and plunged at once into the depths of your credulity. I partly
believe, he made pretty sure of his company. Not many rich, not
many wise, or learned, composed at that time the common stowage
of a Margate packet. We were, I am afraid, a set of as unseasoned
Londoners (let our enemies give it a worse name) as Aldermanbury, or
Watling-street, at that time of day could have supplied. There might
be an exception or two among us, but I scorn to make any invidious
distinctions among such a jolly, companionable ship's company, as
those were whom I sailed with. Something too must be conceded to the
_Genius Loci_. Had the confident fellow told us half the legends on
land, which he favoured us with on the other element, I flatter myself
the good sense of most of us would have revolted. But we were in a new
world, with everything unfamiliar about us, and the time and place
disposed us to the reception of any prodigious marvel whatsoever. Time
has obliterated from my memory much of his wild fablings; and the
rest would appear but dull, as written, and to be read on shore. He
had been Aid-de-camp (among other rare accidents and fortunes) to
a Persian prince, and at one blow had stricken off the head of the
King of Carimania on horseback. He, of course, married the Prince's
daughter. I forget what unlucky turn in the politics of that court,
combining with the loss of his consort, was the reason of his quitting
Persia; but with the rapidity of a magician he transported himself,
along with his hearers, back to England, where we still found
him in the confidence of great ladies. There was some story of a
Princess--Elizabeth, if I remember--having intrusted to his care an
extraordinary casket of jewels, upon some extraordinary occasion--but
as I am not certain of the name or circumstance at this distance of
time, I must leave it to the Royal daughters of England to settle the
honour among themselves in private. I cannot call to mind half his
pleasant wonders; but I perfectly remember, that in the course of his
travels he had seen a phoenix; and he obligingly undeceived us of
the vulgar error, that there is but one of that species at a time,
assuring us that they were not uncommon in some parts of Upper Egypt.
Hitherto he had found the most implicit listeners. His dreaming
fancies had transported us beyond the "ignorant present." But when
(still hardying more and more in his triumphs over our simplicity) he
went on to affirm that he had actually sailed through the legs of the
Colossus at Rhodes, it really became necessary to make a stand. And
here I must do justice to the good sense and intrepidity of one of our
party, a youth, that had hitherto been one of his most deferential
auditors, who, from his recent reading, made bold to assure the
gentleman, that there must be some mistake, as "the Colossus in
question had been destroyed long since;" to whose opinion, delivered
with all modesty, our hero was obliging enough to concede thus much,
that "the figure was indeed a little damaged." This was the only
opposition he met with, and it did not at all seem to stagger him, for
he proceeded with his fables, which the same youth appeared to swallow
with still more complacency than ever,--confirmed, as it were, by the
extreme candour of that concession. With these prodigies he wheedled
us on till we came in sight of the Reculvers, which one of our own
company (having been the vogage before) immediately recognising, and
pointing out to us, was considered by us as no ordinary seaman.
All this time sat upon the edge of the deck quite a different
character. It was a lad, apparently very poor, very infirm, and very
patient. His eye was ever on the sea, with a smile: and, if he caught
now and then some snatches of these wild legends, it was by accident,
and they seemed not to concern him. The waves to him whispered more
pleasant stories. He was as one, being with us, but not of us. He
heard the bell of dinner ring without stirring; and when some of
us pulled out our private stores--our cold meat and our salads--he
produced none, and seemed to want none. Only a solitary biscuit he had
laid in; provision for the one or two days and nights, to which these
vessels then were oftentimes obliged to prolong their voyage Upon a
nearer acquaintance with him, which he seemed neither to court nor
decline, we learned that he was going to Margate, with the hope of
being admitted into the Infirmary there for sea-bathing. His disease
was a scrofula, which appeared to have eaten all over him. He
expressed great hopes of a cure; and when we asked him, whether he had
any friends where he was going, he replied, "he _had_ no friends."
These pleasant, and some mournful passages, with the first sight
of the sea, co-operating with youth, and a sense of holydays, and
out-of-door adventure, to me that had been pent up in populous cities
for many months before,--have left upon my mind the fragrance as of
summer days gone by, bequeathing nothing but their remembrance for
cold and wintry hours to chew upon.
Will it be thought a digression (it may spare some unwelcome
comparisons), if I endeavour to account for the _dissatisfaction_
which I have heard so many persons confess to have felt (as I did
myself feel in part on this occasion), _at the sight of the sea for
the first time?_ I think the reason usually given--referring to the
incapacity of actual objects for satisfying our preconceptions of
them--scarcely goes deep enough into the question. Let the same person
see a lion, an elephant, a mountain, for the first time in his life,
and he shall perhaps feel himself a little mortified. The things do
not fill up that space, which the idea of them seemed to take up in
his mind. But they have still a correspondency to his first notion,
and in time grow up to it, so as to produce a very similar impression:
enlarging themselves (if I may say so) upon familiarity. But the sea
remains a disappointment.--Is it not, that in _the latter_ we had
expected to behold (absurdly, I grant, but, I am afraid, by the law of
imagination unavoidably) not a definite object, as those wild beasts,
or that mountain compassable by the eye, but _all the sea at once_,
THE COMMENSURATE ANTAGONIST OF THE EARTH! I do not say we, tell
ourselves so much, but the craving of the mind is to be satisfied with
nothing less. I will suppose the case of a young person of fifteen
(as I then was) knowing nothing of the sea, but from description. He
comes to it for the first time--all that he has been reading of it all
his life, and _that_ the most enthusiastic part of life,--all he has
gathered from narratives of wandering seamen; what he has gained from
true voyages, and what he cherishes as credulously from romance and
poetry; crowding their images, and exacting strange tributes from
expectation.--He thinks of the great deep, and of those who go down
unto it; of its thousand isles, and of the vast continents it washes;
of its receiving the mighty Plata, or Orellana, into its bosom,
without disturbance, or sense of augmentation; of Biscay swells, and
the mariner
For many a day, and many a dreadful night,
Incessant labouring round the stormy Cape;
of fatal rocks, and the "still-vexed Bermoothes;" of great whirlpools,
and the water-spout; of sunken ships, and sumless treasures swallowed
up in the unrestoring depths: of fishes and quaint monsters, to which
all that is terrible on earth--
Be but as buggs to frighten babes withal,
Compared with the creatures in the sea's entral;
of naked savages, and Juan Fernandez; of pearls, and shells; of coral
beds, and of enchanted isles; of mermaids' grots--
I do not assert that in sober earnest he expects to be shown all these
wonders at once, but he is under the tyranny of a mighty faculty,
which haunts him with confused hints and shadows of all these; and
when the actual object opens first upon him, seen (in tame weather too
most likely) from our unromantic coasts--a speck, a slip of sea-water,
as it shows to him--what can it prove but a very unsatisfying and
even diminutive entertainment? Or if he has come to it from the mouth
of a river, was it much more than the river widening? and, even out
of sight of land, what had he but a flat watery horizon about him,
nothing comparable to the vast o'er-curtaining sky, his familiar
object, seen daily without dread or amazement?--Who, in similar
circumstances, has not been tempted to exclaim with Charoba, in the
poem of Gebir,--
Is this the mighty ocean?--is this _all_?
I love town, or country; but this detestable Cinque Port is neither. I
hate these scrubbed shoots, thrusting out their starved foliage from
between the horrid fissures of dusty innutritious rocks; which the
amateur calls "verdure to the edge of the sea." I require woods, and
they show me stunted coppices. I cry out for the water-brooks, and
pant for fresh streams, and inland murmurs. I cannot stand all day on
the naked beach, watching the capricious hues of the sea, shifting
like the colours of a dying mullet. I am tired of looking out at the
windows of this island-prison. I would fain retire into the interior
of my cage. While I gaze upon the sea, I want to be on it, over it,
across it. It binds me in with chains, as of iron. My thoughts are
abroad. I should not so feel in Staffordshire. There is no home for me
here. There is no sense of home at Hastings. It is a place of fugitive
resort, an heterogeneous assemblage of sea-mews and stock-brokers,
Amphitrites of the town, and misses that coquet with the Ocean. If
it were what it was in its primitive shape, and what it ought to
have remained, a fair honest fishing town, and no more, it were
something--with a few straggling fishermen's huts scattered about,
artless as its cliffs, and with their materials filched from them, it
were something. I could abide to dwell with Meschek; to assort with
fisher-swains, and smugglers. There are, or I dream there are, many
of this latter occupation here. Their faces become the place. I like
a smuggler. He is the only honest thief. He robs nothing but the
revenue,--an abstraction I never greatly cared about. I could go out
with them in their mackarel boats, or about their less ostensible
business, with some satisfaction. I can even tolerate those poor
victims to monotony, who from day to day pace along the beach,
in endless progress and recurrence, to watch their illicit
countrymen--townsfolk or brethren perchance--whistling to the
sheathing and unsheathing of their cutlasses (their only solace), who
under the mild name of preventive service, keep up a legitimated civil
warfare in the deplorable absence of a foreign one, to show their
detestation of run hollands, and zeal for old England. But it is the
visitants from town, that come here to _say_ that they have been here,
with no more relish of the sea than a pond perch, or a dace might be
supposed to have, that are my aversion. I feel like a foolish dace
in these regions, and have as little toleration for myself here, as
for them. What can they want here? if they had a true relish of the
ocean, why have they brought all this land luggage with them? or why
pitch their civilised tents in the desert? What mean these scanty
book-rooms--marine libraries as they entitle them--if the sea were, as
they would have us believe, a book "to read strange matter in?" what
are their foolish concert-rooms, if they come, as they would fain be
thought to do, to listen to the music of the waves? All is false and
hollow pretention. They come, because it is the fashion, and to
spoil the nature of the place. They are mostly, as I have said,
stockbrokers; but I have watched the better sort of them--now and
then, an honest citizen (of the old stamp), in the simplicity of his
heart, shall bring down his wife and daughters, to taste the sea
breezes. I always know the date of their arrival. It is easy to see it
in their countenance. A day or two they go wandering on the shingles,
picking up cockleshells, and thinking them great things; but, in a
poor week, imagination slackens: they begin to discover that cockles
produce no pearls, and then--O then!--if I could interpret for the
pretty creatures (I know they have not the courage to confess it
themselves) how gladly would they exchange their sea-side rambles
for a Sunday walk on the green-sward of their accustomed Twickenham
meadows!
I would ask of one of these sea-charmed emigrants, who think they
truly love the sea, with its wild usages, what would their feelings
be, if some of the unsophisticated aborigines of this place,
encouraged by their courteous questionings here, should venture, on
the faith of such assured sympathy between them, to return the visit,
and come up to see--London. I must imagine them with their fishing
tackle on their back, as we carry our town necessaries. What a
sensation would it cause in Lothbury? What vehement laughter would it
not excite among
The daughters of Cheapside, and wives of Lombard-street.
I am sure that no town-bred, or inland-born subjects, can feel their
true and natural nourishment at these sea-places. Nature, where she
does not mean us for mariners and vagabonds, bids us stay at home. The
salt foam seems to nourish a spleen. I am not half so good-natured
as by the milder waters of my natural river. I would exchange these
sea-gulls for swans, and scud a swallow for ever about the banks of
Thamesis.
THE CONVALESCENT
A pretty severe fit of indisposition which, under the name of a
nervous fever, has made a prisoner of me for some weeks past, and is
but slowly leaving me, has reduced me to an incapacity of reflecting
upon any topic foreign to itself. Expect no healthy conclusions from
me this month, reader; I can offer you only sick men's dreams.
And truly the whole state of sickness is such; for what else is it
but a magnificent dream for a man to lie a-bed, and draw day-light
curtains about him; and, shutting out the sun, to induce a total
oblivion of all the works which are going on under it? To become
insensible to all the operations of life, except the beatings of one
feeble pulse?
If there be a regal solitude, it is a sick bed. How the patient lords
it there! what caprices he acts without controul! how kinglike he
sways his pillow--tumbling, and tossing, and shifting, and lowering,
and thumping, and flatting, and moulding it, to the ever varying
requisitions of his throbbing temples.
He changes _sides_ oftener than a politician. Now he lies full length,
then half-length, obliquely, transversely, head and feet quite across
the bed; and none accuses him of tergiversation. Within the four
curtains he is absolute. They are his Mare Clausum.
How sickness enlarges the dimensions of a man's self to himself! he
is his own exclusive object. Supreme selfishness is inculcated upon
him as his only duty. 'Tis the Two Tables of the Law to him. He has
nothing to think of but how to get well. What passes out of doors, or
within them, so he hear not the jarring of them, affects him not.
A little while ago he was greatly concerned in the event of a
law-suit, which was to be the making or the marring of his dearest
friend. He was to be seen trudging about upon this man's errand to
fifty quarters of the town at once, jogging this witness, refreshing
that solicitor. The cause was to come on yesterday. He is absolutely
as indifferent to the decision, as if it were a question to be tried
at Pekin. Peradventure from some whispering, going on about the
house, not intended for his hearing, he picks up enough to make him
understand, that things went cross-grained in the Court yesterday,
and his friend is ruined. But the word "friend," and the word "ruin,"
disturb him no more than so much jargon. He is not to think of any
thing but how to get better.
What a world of foreign cares are merged in that absorbing
consideration!
He has put on the strong armour of sickness, he is wrapped in the
callous hide of suffering; he keeps his sympathy, like some curious
vintage, under trusty lock and key, for his own use only.
He lies pitying himself, honing and moaning to himself; he yearneth
over himself; his bowels are even melted within him, to think what he
suffers; he is not ashamed to weep over himself.
He is for ever plotting how to do some good to himself; studying
little stratagems and artificial alleviations.
He makes the most of himself; dividing himself, by an allowable
fiction, into as many distinct individuals, as he hath sore and
sorrowing members. Sometimes he meditates--as of a thing apart from
him--upon his poor aching head, and that dull pain which, dozing or
waking, lay in it all the past night like a log, or palpable substance
of pain, not to be removed without opening the very scull, as it
seemed, to take it thence. Or he pities his long, clammy, attenuated
fingers. He compassionates himself all over; and his bed is a very
discipline of humanity, and tender heart.
He is his own sympathiser; and instinctively feels that none can so
well perform that office for him. He cares for few spectators to his
tragedy. Only that punctual face of the old nurse pleases him, that
announces his broths, and his cordials. He likes it because it is
so unmoved, and because he can pour forth his feverish ejaculations
before it as unreservedly as to his bed-post.
To the world's business he is dead. He understands not what the
callings and occupations of mortals are; only he has a glimmering
conceit of some such thing, when the doctor makes his daily call:
and even in the lines of that busy face he reads no multiplicity of
patients, but solely conceives of himself as _the sick man_. To what
other uneasy couch the good man is hastening, when he slips out of
his chamber, folding up his thin douceur so carefully for fear of
rustling--is no speculation which he can at present entertain. He
thinks only of the regular return of the same phenomenon at the same
hour to-morrow.
Household rumours touch him not. Some faint murmur, indicative of life
going on within the house, soothes him, while he knows not distinctly
what it is. He is not to know any thing, not to think of any thing.
Servants gliding up or down the distant staircase, treading as
upon velvet, gently keep his ear awake, so long as he troubles not
himself further than with some feeble guess at their errands. Exacter
knowledge would be a burthen to him: he can just endure the pressure
of conjecture. He opens his eye faintly at the dull stroke of the
muffled knocker, and closes it again without asking "who was it?" He
is flattered by a general notion that inquiries are making after him,
but he cares not to know the name of the inquirer. In the general
stillness, and awful hush of the house, he lies in state, and feels
his sovereignty.
To be sick is to enjoy monarchal prerogatives. Compare the silent
tread, and quiet ministry, almost by the eye only, with which he is
served--with the careless demeanour, the unceremonious goings in
and out (slapping of doors, or leaving them open) of the very same
attendants, when he is getting a little better--and you will confess,
that from the bed of sickness (throne let me rather call it) to the
elbow chair of convalescence, is a fall from dignity, amounting to a
deposition.
How convalescence shrinks a man back to his pristine stature! where
is now the space, which he occupied so lately, in his own, in the
family's eye? The scene of his regalities, his sick room, which was
his presence chamber, where he lay and acted his despotic fancies--how
is it reduced to a common bedroom! The trimness of the very bed has
something petty and unmeaning about it. It is _made_ every day.
How unlike to that wavy, many-furrowed, oceanic surface, which it
presented so short a time since, when to _make_ it was a service not
to be thought of at oftener than three or four day revolutions, when
the patient was with pain and grief to be lifted for a little while
out of it, to submit to the encroachments of unwelcome neatness, and
decencies which his shaken frame deprecated; then to be lifted into it
again, for another three or four days' respite, to flounder it out of
shape again, while every fresh furrow was a historical record of some
shifting posture, some uneasy turning, some seeking for a little ease;
and the shrunken skin scarce told a truer story than the crumpled
coverlid.
Hushed are those mysterious sighs--those groans--so much more awful,
while we knew not from what caverns of vast hidden suffering they
proceeded. The Lernean pangs are quenched. The riddle of sickness is
solved; and Philoctetes is become an ordinary personage.
Perhaps some relic of the sick man's dream of greatness survives in
the still lingering visitations of the medical attendant. But how
is he too changed with everything else! Can this be he--this man of
news--of chat--of anecdote--of every thing but physic--can this be he,
who so lately came between the patient and his cruel enemy, as on some
solemn embassy from Nature, erecting herself into a high mediating
party? Pshaw!'tis some old woman.
Farewell with him all that made sickness pompous--the spell that
hushed the household--the desart-like stillness, felt throughout
its inmost chambers--the mute attendance--the inquiry by looks--the
still softer delicacies of self-attention--the sole and single eye of
distemper alonely fixed upon itself--world-thoughts excluded--the man
a world unto himself--his own theatre--
What a speck is he dwindled into!
In this flat swamp of convalescence, left by the ebb of sickness, yet
far enough from the terra firma of established health, your note,
dear Editor, reached me, requesting--an article. In Articulo Mortis,
thought I; but it is something hard--and the quibble, wretched as it
was, relieved me. The summons, unseasonable as it appeared, seemed to
link me on again to the petty businesses of life, which I had lost
sight of; a gentle call to activity, however trivial; a wholesome
weaning from that preposterous dream of self-absorption--the puffy
state of sickness--in which I confess to have lain so long, insensible
to the magazines and monarchies, of the world alike; to its laws, and
to its literature. The hypochondriac flatus is subsiding; the acres,
which in imagination I had spread over--for the sick man swells in
the sole contemplation of his single sufferings, till he becomes
a Tityus to himself--are wasting to a span; and for the giant of
self-importance, which I was so lately, you have me once again in my
natural pretensions--the lean and meagre figure of your insignificant
Essayist.
SANITY OF TRUE GENIUS
So far from the position holding true, that great wit (or genius, in
our modern way of speaking), has a necessary alliance with insanity,
the greatest wits, on the contrary, will ever be found to be the
sanest writers. It is impossible for the mind to conceive of a mad
Shakspeare. The greatness of wit, by which the poetic talent is here
chiefly to be understood, manifests itself in the admirable balance of
all the faculties. Madness is the disproportionate straining or excess
of any one of them. "So strong a wit," says Cowley, speaking of a
poetical friend,
"--did Nature to him frame,
As all things but his judgment overcame,
His judgment like the heavenly moon did show,
Tempering that mighty sea below."
The ground of the mistake is, that men, finding in the raptures of
the higher poetry a condition of exaltation, to which they have no
parallel in their own experience, besides the spurious resemblance of
it in dreams and fevers, impute a state of dreaminess and fever to the
poet. But the true poet dreams being awake. He is not possessed by
his subject, but has dominion over it. In the groves of Eden he walks
familiar as in his native paths. He ascends the empyrean heaven, and
is not intoxicated. He treads the burning marl without dismay; he wins
his flight without self-loss through realms of chaos "and old night."
Or if, abandoning himself to that severer chaos of a "human mind
untuned," he is content awhile to be mad with Lear, or to hate mankind
(a sort of madness) with Timon, neither is that madness, nor this
misanthropy, so unchecked, but that,--never letting the reins of
reason wholly go, while most he seems to do so,--he has his better
genius still whispering at his ear, with the good servant Kent
suggesting saner counsels, or with the honest steward Flavius
recommending kindlier resolutions. Where he seems most to recede from
humanity, he will be found the truest to it. From beyond the scope of
Nature if he summon possible existences, he subjugates them to the
law of her consistency. He is beautifully loyal to that sovereign
directress, even when he appears most to betray and desert her. His
ideal tribes submit to policy; his very monsters are tamed to his
hand, even as that wild sea-brood, shepherded by Proteus. He tames,
and he clothes them with attributes of flesh and blood, till they
wonder at themselves, like Indian Islanders forced to submit to
European vesture. Caliban, the Witches, are as true to the laws of
their own nature (ours with a difference), as Othello, Hamlet, and
Macbeth. Herein the great and the little wits are differenced; that if
the latter wander ever so little from nature or actual existence, they
lose themselves, and their readers. Their phantoms are lawless; their
visions nightmares. They do not create, which implies shaping and
consistency. Their imaginations are not active--for to be active is to
call something into act and form--but passive, as men in sick dreams.
For the super-natural, or something super-added to what we know of
nature, they give you the plainly non-natural. And if this were all,
and that these mental hallucinations were discoverable only in the
treatment of subjects out of nature, or transcending it, the judgment
might with some plea be pardoned if it ran riot, and a little
wantonized: but even in the describing of real and every day life,
that which is before their eyes, one of these lesser wits shall more
deviate from nature--show more of that inconsequence, which has a
natural alliance with frenzy,--than a great genius in his "maddest
fits," as Withers somewhere calls them. We appeal to any one that is
acquainted with the common run of Lane's novels,--as they existed some
twenty or thirty years back,--those scanty intellectual viands of the
whole female reading public, till a happier genius arose, and expelled
for ever the innutritious phantoms,--whether he has not found his
brain more "betossed," his memory more puzzled, his sense of when and
where more confounded, among the improbable events, the incoherent
incidents, the inconsistent characters, or no-characters, of some
third-rate love intrigue--where the persons shall be a Lord Glendamour
and a Miss Rivers, and the scene only alternate between Bath and
Bond-street--a more bewildering dreaminess induced upon him, than
he has felt wandering over all the fairy grounds of Spenser. In the
productions we refer to, nothing but names and places is familiar; the
persons are neither of this world nor of any other conceivable one; an
endless string of activities without purpose, of purposes destitute
of motive:--we meet phantoms in our known walks; _fantasques_ only
christened. In the poet we have names which announce fiction; and we
have absolutely no place at all, for the things and persons of the
Fairy Queen prate not of their "whereabout." But in their inner
nature, and the law of their speech and actions, we are at home and
upon acquainted ground. The one turns life into a dream; the other to
the wildest dreams gives the sobrieties of every day occurrences. By
what subtile art of tracing the mental processes it is effected, we
are not philosophers enough to explain, but in that wonderful episode
of the cave of Mammon, in which the Money God appears first in the
lowest form of a miser, is then a worker of metals, and becomes the
god of all the treasures of the world; and has a daughter, Ambition,
before whom all the world kneels for favours--with the Hesperian
fruit, the waters of Tantalus, with Pilate washing his hands vainly,
but not impertinently, in the same stream--that we should be at one
moment in the cave of an old hoarder of treasures, at the next at the
forge of the Cyclops, in a palace and yet in hell, all at once, with
the shifting mutations of the most rambling dream, and our judgment
yet all the time awake, and neither able nor willing to detect the
fallacy,--is a proof of that hidden sanity which still guides the poet
in his widest seeming-aberrations.
It is not enough to say that the whole episode is a copy of the mind's
conceptions in sleep; it is, in some sort--but what a copy! Let the
most romantic of us, that has been entertained all night with the
spectacle of some wild and magnificent vision, recombine it in the
morning, and try it by his waking judgment. That which appeared so
shifting, and yet so coherent, while that faculty was passive, when
it comes under cool examination, shall appear so reasonless and so
unlinked, that we are ashamed to have been so deluded; and to have
taken, though but in sleep, a monster for a god. But the transitions
in this episode are every whit as violent as in the most extravagant
dream, and yet the waking judgment ratifies them.
CAPTAIN JACKSON
Among the deaths in our obituary for this month, I observe with
concern "At his cottage on the Bath road, Captain Jackson." The
name and attribution are common enough; but a feeling like reproach
persuades me, that this could have been no other in fact than my dear
old friend, who some five-and-twenty years ago rented a tenement,
which he was pleased to dignify with the appellation here used, about
a mile from Westbourn Green. Alack, how good men, and the good turns
they do us, slide out of memory, and are recalled but by the surprise
of some such sad memento as that which now lies before us!
He whom I mean was a retired half-pay officer, with a wife and two
grown-up daughters, whom he maintained with the port and notions of
gentlewomen upon that slender professional allowance. Comely girls
they were too.
And was I in danger of forgetting this man?--his cheerful suppers--the
noble tone of hospitality, when first you set your foot in the
_cottage_--the anxious ministerings about you, where little or
nothing (God knows) was to be ministered.--Althea's horn in a poor
platter--the power of self-enchantment, by which, in his magnificent
wishes to entertain you, he multiplied his means to bounties.
You saw with your bodily eyes indeed what seemed a bare scrag--cold
savings from the foregone meal--remnant hardly sufficient to send
a mendicant from the door contented. But in the copious will--the
revelling imagination of your host--the "mind, the mind, Master
Shallow," whole beeves were spread before you--hecatombs--no end
appeared to the profusion.
It was the widow's cruse--the loaves and fishes; carving could not
lessen nor helping diminish it--the stamina were left--the elemental
bone still flourished, divested of its accidents.
"Let us live while we can," methinks I hear the open-handed creature
exclaim; "while we have, let us not want," "here is plenty left;"
"want for nothing"--with many more such hospitable sayings, the
spurs of appetite, and old concomitants of smoaking boards, and
feast-oppressed chargers. Then sliding a slender ratio of Single
Gloucester upon his wife's plate, or the daughter's, he would convey
the remanent rind into his own, with a merry quirk of "the nearer the
bone," &c., and declaring that he universally preferred the outside.
For we had our table distinctions, you are to know, and some of us in
a manner sate above the salt. None but his guest or guests dreamed of
tasting flesh luxuries at night, the fragments were _vere hospilibus
sacra_. But of one thing or another there was always enough, and
leavings: only he would sometimes finish the remainder crust, to show
that he wished no savings.
Wine he had none; nor, except on very rare occasions, spirits;
but the sensation of wine was there. Some thin kind of ale I
remember--"British beverage," he would say! "Push about, my boys;"
"Drink to your sweethearts, girls." At every meagre draught a toast
must ensue, or a song. All the forms of good liquor were there, with
none of the effects wanting. Shut your eyes, and you would swear
a capacious bowl of punch was foaming in the centre, with beams of
generous Port or Madeira radiating to it from each of the table
corners. You got flustered, without knowing whence; tipsy upon
words; and reeled under the potency of his unperforming Bacchanalian
encouragements.
We had our songs--"Why, Soldiers, Why"--and the "British
Grenadiers"--in which last we were all obliged to bear chorus. Both
the daughters sang. Their proficiency was a nightly theme--the masters
he had given them--the "no-expence" which he spared to accomplish them
in a science "so necessary to young women." But then--they could not
sing "without the instrument."
Sacred, and by me, never-to-be violated, Secrets of Poverty! Should
I disclose your honest aims at grandeur, your make-shift efforts
of magnificence? Sleep, sleep, with all thy broken keys, if one of
the bunch be extant; thrummed by a thousand ancestral thumbs; dear,
cracked spinnet of dearer Louisa! Without mention of mine, be dumb,
thou thin accompanier of her thinner warble! A veil be spread over
the dear delighted face of the well-deluded father, who now haply
listening to cherubic notes, scarce feels sincerer pleasure than when
she awakened thy time-shaken chords responsive to the twitterings of
that slender image of a voice.
We were not without our literary talk either. It did not extend far,
but as far as it went, it was good. It was bottomed well; had good
grounds to go upon. In _the cottage_ was a room, which tradition
authenticated to have been the same in which Glover, in his occasional
retirements, had penned the greater part of his Leonidas. This
circumstance was nightly quoted, though none of the present inmates,
that I could discover, appeared ever to have met with the poem in
question. But that was no matter. Glover had written there, and the
anecdote was pressed into the account of the family importance. It
diffused a learned air through the apartment, the little side casement
of which (the poet's study window), opening upon a superb view as far
as to the pretty spire of Harrow, over domains and patrimonial acres,
not a rood nor square yard whereof our host could call his own, yet
gave occasion to an immoderate expansion of--vanity shall I call
it?--in his bosom, as he showed them in a glowing summer evening. It
was all his, he took it all in, and communicated rich portions of it
to his guests. It was a part of his largess, his hospitality; it was
going over his grounds; he was lord for the time of showing them, and
you the implicit lookers-up to his magnificence.
He was a juggler, who threw mists before your eyes--you had no time
to detect his fallacies. He would say "hand me the _silver_ sugar
tongs;" and, before you could discover it was a single spoon, and
that _plated_, he would disturb and captivate your imagination by a
misnomer of "the urn" for a tea kettle; or by calling a homely bench
a sofa. Rich men direct you to their furniture, poor ones divert you
from it; he neither did one nor the other, but by simply assuming that
everything was handsome about him, you were positively at a demur what
you did, or did not see, at _the cottage_. With nothing to live on, he
seemed to live on everything. He had a stock of wealth in his mind;
not that which is properly termed _Content_, for in truth he was not
to be _contained_ at all, but overflowed all bounds by the force of a
magnificent self-delusion.
Enthusiasm is catching; and even his wife, a sober native of North
Britain, who generally saw things more as they were, was not proof
against the continual collision of his credulity. Her daughters
were rational and discreet young women; in the main, perhaps, not
insensible to their true circumstances. I have seen them assume a
thoughtful air at times. But such was the preponderating opulence of
his fancy, that I am persuaded, not for any half hour together, did
they ever look their own prospects fairly in the face. There was no
resisting the vortex of his temperament. His riotous imagination
conjured up handsome settlements before their eyes, which kept them
up in the eye of the world too, and seem at last to have realised
themselves; for they both have married since, I am told, more than
respectably.
It is long since, and my memory waxes dim on some subjects, or I
should wish to convey some notion of the manner in which the pleasant
creature described the circumstances of his own wedding-day. I faintly
remember something of a chaise and four, in which he made his entry
into Glasgow on that morning to fetch the bride home, or carry her
thither, I forget which. It so completely made out the stanza of the
old ballad--
When we came down through Glasgow town,
We were a comely sight to see;
My love was clad in black velve,
And I myself in cramasie.
I suppose it was the only occasion, upon which his own actual
splendour at all corresponded with the world's notions on that
subject. In homely cart, or travelling caravan, by whatever humble
vehicle they chanced to be transported in less prosperous days, the
ride through Glasgow came back upon his fancy, not as a humiliating
contrast, but as a fair occasion for reverting to that one day's
state. It seemed an "equipage etern" from which no power of fate or
fortune, once mounted, had power thereafter to dislodge him.
There is some merit in putting a handsome face upon indigent
circumstances. To bully and swagger away the sense of them, before
strangers, may be not always discommendable. Tibbs, and Bobadil, even
when detected, have more of our admiration than contempt. But for a
man to put the cheat upon himself; to play the Bobadil at home; and,
steeped in poverty up to the lips, to fancy himself all the while
chin-deep in riches, is a strain of constitutional philosophy, and a
mastery over fortune, which was reserved for my old friend Captain
Jackson.
THE SUPERANNUATED MAN
Sera tamen respexit
Libertas.
VIRGIL.
A Clerk I was in London gay.
O'KEEFE.
If peradventure, Reader, it has been thy lot to waste the golden years
of thy life--thy shining youth--in the irksome confinement of an
office; to have thy prison days prolonged through middle age down to
decrepitude and silver hairs, without hope of release or respite; to
have lived to forget that there are such things as holidays, or to
remember them but as the prerogatives of childhood; then, and then
only, will you be able to appreciate my deliverance.
It is now six and thirty years since I took my seat at the desk in
Mincing-lane. Melancholy was the transition at fourteen from the
abundant play-time, and the frequently-intervening vacations of school
days, to the eight, nine, and sometimes ten hours' a-day attendance
at a counting-house. But time partially reconciles us to anything.
I gradually became content--doggedly contented, as wild animals in
cages.
It is true I had my Sundays to myself; but Sundays, admirable as the
institution of them is for purposes of worship, are for that very
reason the very worst adapted for days of unbending and recreation. In
particular, there is a gloom for me attendant upon a city Sunday, a
weight in the air. I miss the cheerful cries of London, the music, and
the ballad-singers--the buzz and stirring murmur of the streets. Those
eternal bells depress me. The closed shops repel me. Prints, pictures,
all the glittering and endless succession of knacks and gewgaws,
and ostentatiously displayed wares of tradesmen, which make a
week-day saunter through the less busy parts of the metropolis so
delightful--are shut out. No book-stalls deliciously to idle over--No
busy faces to recreate the idle man who contemplates them ever passing
by--the very face of business a charm by contrast to his temporary
relaxation from it. Nothing to be seen but unhappy countenances--or
half-happy at best--of emancipated 'prentices and little trades-folks,
with here and there a servant maid that has got leave to go out, who,
slaving all the week, with the habit has lost almost the capacity of
enjoying a free hour; and livelily expressing the hollowness of a
day's pleasuring. The very strollers in the fields on that day look
anything but comfortable.
But besides Sundays I had a day at Easter, and a day at Christmas,
with a full week in the summer to go and air myself in my native
fields of Hertfordshire. This last was a great indulgence; and the
prospect of its recurrence, I believe, alone kept me up through the
year, and made my durance tolerable. But when the week came round, did
the glittering phantom of the distance keep touch with me? or rather
was it not a series of seven uneasy days, spent in restless pursuit
of pleasure, and a wearisome anxiety to find out how to make the most
of them? Where was the quiet, where the promised rest? Before I had a
taste of it, it was vanished. I was at the desk again, counting upon
the fifty-one tedious weeks that must intervene before such another
snatch would come. Still the prospect of its coming threw something of
an illumination upon the darker side of my captivity. Without it, as I
have said, I could scarcely have sustained my thraldom.
Independently of the rigours of attendance, I have ever been haunted
with a sense (perhaps a mere caprice) of incapacity for business.
This, during my latter years, had increased to such a degree, that it
was visible in all the lines of my countenance. My health and my good
spirits flagged. I had perpetually a dread of some crisis, to which I
should be found unequal. Besides my daylight servitude, I served over
again all night in my sleep, and would awake with terrors of imaginary
false entries, errors in my accounts, and the like. I was fifty years
of age, and no prospect of emancipation presented itself. I had grown
to my desk, as it were; and the wood had entered into my soul.
My fellows in the office would sometimes rally me upon the trouble
legible in my countenance; but I did not know that it had raised the
suspicions of any of my employers, when, on the 5th of last month,
a day ever to be remembered by me, L----, the junior partner in the
firm, calling me on one side, directly taxed me with my bad looks,
and frankly inquired the cause of them. So taxed, I honestly made
confession of my infirmity, and added that I was afraid I should
eventually be obliged to resign his service. He spoke some words of
course to hearten me, and there the matter rested. A whole week I
remained labouring under the impression that I had acted imprudently
in my disclosure; that I had foolishly given a handle against myself,
and had been anticipating my own dismissal. A week passed in this
manner, the most anxious one, I verily believe, in my whole life, when
on the evening of the 12th of April, just as I was about quitting my
desk to go home (it might be about eight o'clock) I received an awful
summons to attend the presence of the whole assembled firm in the
formidable back parlour. I thought, now my time is surely come, I
have done for myself, I am going to be told that they have no longer
occasion for me. L----, I could see, smiled at the terror I was in,
which was a little relief to me,--when to my utter astonishment B----,
the eldest partner, began a formal harangue to me on the length of
my services, my very meritorious conduct during the whole of the time
(the deuce, thought I, how did he find out that? I protest I never
had the confidence to think as much). He went on to descant on the
expediency of retiring at a certain time of life (how my heart
panted!) and asking me a few questions as to the amount of my own
property, of which I have a little, ended with a proposal, to which
his three partners nodded a grave assent, that I should accept from
the house, which I had served so well, a pension for life to the
amount of two-thirds of my accustomed salary--a magnificent offer! I
do not know what I answered between surprise and gratitude, but it was
understood that I accepted their proposal, and I was told that I was
free from that hour to leave their service. I stammered out a bow,
and at just ten minutes after eight I went home--for ever. This noble
benefit--gratitude forbids me to conceal their names--I owe to the
kindness of the most munificent firm in the world--the house of
Boldero, Merryweather, Bosanquet, and Lacy.
_Esto perpetua!_
For the first day or two I felt stunned, overwhelmed. I could only
apprehend my felicity; I was too confused to taste it sincerely. I
wandered about, thinking I was happy, and knowing that I was not. I
was in the condition of a prisoner in the old Bastile, suddenly let
loose after a forty years' confinement. I could scarce trust myself
with myself. It was like passing out of Time into Eternity--for it
is a sort of Eternity for a man to have his Time all to himself.
It seemed to me that I had more time on my hands than I could ever
manage. From a poor man, poor in Time, I was suddenly lifted up into
a vast revenue; I could see no end of my possessions; I wanted some
steward, or judicious bailiff, to manage my estates in Time for me.
And here let me caution persons grown old in active business, not
lightly, nor without weighing their own resources, to forego their
customary employment all at once, for there may be danger in it. I
feel it by myself, but I know that my resources are sufficient; and
now that those first giddy raptures have subsided, I have a quiet
home-feeling of the blessedness of my condition. I am in no hurry.
Having all holidays, I am as though I had none. If Time hung heavy
upon me, I could walk it away; but I do _not_ walk all day long, as
I used to do in those old transient holidays, thirty miles a day, to
make the most of them. If Time were troublesome, I could read it away,
but I do _not_ read in that violent measure, with which, having no
Time my own but candlelight Time, I used to weary out my head and
eyesight in by-gone winters. I walk, read or scribble (as now) just
when the fit seizes me. I no longer hunt after pleasure; I let it come
to me. I am like the man
--That's born, and has his years come to him,
In some green desart.
"Years," you will say! "what is this superannuated simpleton
calculating upon? He has already told us, he is past fifty."
I have indeed lived nominally fifty years, but deduct out of them the
hours which I have lived to other people, and not to myself, and you
will find me still a young fellow. For _that_ is the only true Time,
which a man can properly call his own, that which he has all to
himself; the rest, though in some sense he may be said to live it, is
other people's time, not his. The remnant of my poor days, long or
short, is at least multiplied for me three-fold. My ten next years, if
I stretch so far, will be as long as any preceding thirty. 'Tis a fair
rule-of-three sum.
Among the strange fantasies which beset me at the commencement of my
freedom, and of which all traces are not yet gone, one was, that a
vast tract of time had intervened since I quitted the Counting House.
I could not conceive of it as an affair of yesterday. The partners,
and the clerks, with whom I had for so many years, and for so many
hours in each day of the year, been closely associated--being suddenly
removed from them--they seemed as dead to me. There is a fine passage,
which may serve to illustrate this fancy, in a Tragedy by Sir Robert
Howard, speaking of a friend's death:
--'Twas but just now he went away;
I have not since had time to shed a tear;
And yet the distance does the same appear
As if he had been a thousand years from me.
Time takes no measure in Eternity.
To dissipate this awkward feeling, I have been fain to go among them
once or twice since; to visit my old desk-fellows--my co-brethren of
the quill--that I had left below in the state militant. Not all the
kindness with which they received me could quite restore to me that
pleasant familiarity, which I had heretofore enjoyed among them.
We cracked some of our old jokes, but methought they went off but
faintly. My old desk; the peg where I hung my hat, were appropriated
to another. I knew it must be, but I could not take it kindly. D----l
take me, if I did not feel some remorse--beast, if I had not,--at
quitting my old compeers, the faithful partners of my toils for six
and thirty years, that smoothed for me with their jokes and conundrums
the ruggedness of my professional road. Had it been so rugged then
after all? or was I a coward simply? Well, it is too late to repent;
and I also know, that these suggestions are a common fallacy of the
mind on such occasions. But my heart smote me. I had violently broken
the bands betwixt us. It was at least not courteous. I shall be some
time before I get quite reconciled to the separation. Farewell, old
cronies, yet not for long, for again and again I will come among
ye, if I shall have your leave. Farewell Ch----, dry, sarcastic,
and friendly! Do----, mild, slow to move, and gentlemanly! Pl----,
officious to do, and to volunteer, good services!--and thou, thou
dreary pile, fit mansion for a Gresham or a Whittington of old,
stately House of Merchants; with thy labyrinthine passages, and
light-excluding, pent-up offices, where candles for one half the year
supplied the place of the sun's light; unhealthy contributor to my
weal, stern fosterer of my living, farewell! In thee remain, and not
in the obscure collection of some wandering bookseller, my "works!"
There let them rest, as I do from my labours, piled on thy massy
shelves, more MSS. in folio than ever Aquinas left, and full as
useful! My mantle I bequeath among ye.
A fortnight has passed since the date of my first communication. At
that period I was approaching to tranquillity, but had not reached it.
I boasted of a calm indeed, but it was comparative only. Something of
the first flutter was left; an unsettling sense of novelty; the dazzle
to weak eyes of unaccustomed light. I missed my old chains, forsooth,
as if they had been some necessary part of my apparel. I was a
poor Carthusian, from strict cellular discipline suddenly by some
revolution returned upon the world. I am now as if I had never been
other than my own master. It is natural to me to go where I please,
to do what I please. I find myself at eleven o'clock in the day in
Bond-street, and it seems to me that I have been sauntering there
at that very hour for years past. I digress into Soho, to explore a
book-stall. Methinks I have been thirty years a collector. There is
nothing strange nor new in it. I find myself before a fine picture
in a morning. Was it ever otherwise? What is become of Fish-street
Hill? Where is Fenchurch-street? Stones of old Mincing-lane, which I
have worn with my daily pilgrimage for six and thirty years, to the
footsteps of what toil-worn clerk are your everlasting flints now
vocal? I indent the gayer flags of Pall Mall. It is Change time, and
I am strangely among the Elgin marbles. It was no hyperbole when I
ventured to compare the change in my condition to a passing into
another world. Time stands still in a manner to me. I have lost all
distinction of season. I do not know the day of the week, or of the
month. Each day used to be individually felt by me in its reference
to the foreign post days; in its distance from, or propinquity to,
the next Sunday. I had my Wednesday feelings, my Saturday nights'
sensations. The genius of each day was upon me distinctly during the
whole of it, affecting my appetite, spirits, &c. The phantom of the
next day, with the dreary five to follow, sate as a load upon my poor
Sabbath recreations. What charm has washed that Ethiop white? What
is gone of Black Monday? All days are the same. Sunday itself--that
unfortunate failure of a holyday as it too often proved, what with my
sense of its fugitiveness, and over-care to get the greatest quantity
of pleasure out of it--is melted down into a week day. I can spare
to go to church now, without grudging the huge cantle which it used
to seem to cut out of the holyday. I have Time for everything. I
can visit a sick friend. I can interrupt the man of much occupation
when he is busiest. I can insult over him with an invitation to take
a day's pleasure with me to Windsor this fine May-morning. It is
Lucretian pleasure to behold the poor drudges, whom I have left behind
in the world, carking and caring; like horses in a mill, drudging on
in the same eternal round--and what is it all for? A man can never
have too much Time to himself, nor too little to do. Had I a little
son, I would christen him NOTHING-TO-DO; he should do nothing. Man, I
verily believe, is out of his element as long as he is operative. I am
altogether for the life contemplative. Will no kindly earthquake come
and swallow up those accursed cotton mills? Take me that lumber of a
desk there, and bowl it down
As low as to the fiends.
I am no longer ******, clerk to the Firm of &c. I am Retired Leisure.
I am to be met with in trim gardens. I am already come to be known by
my vacant face and careless gesture, perambulating at no fixed pace,
nor with any settled purpose. I walk about; not to and from. They tell
me, a certain _cum dignitate_ air, that has been buried so long with
my other good parts, has begun to shoot forth in my person. I grow
into gentility perceptibly. When I take up a newspaper, it is to read
the state of the opera. _Opus operatum est_. I have done all that I
came into this world to do. I have worked task work, and have the rest
of the day to myself.
THE GENTEEL STYLE IN WRITING
It is an ordinary criticism, that my Lord Shaftesbury, and Sir William
Temple, are models of the genteel style in writing. We should prefer
saying--of the lordly, and the gentlemanly. Nothing can be more unlike
than the inflated finical rhapsodies of Shaftesbury, and the plain
natural chit-chat of Temple. The man of rank is discernible in both
writers; but in the one it is only insinuated gracefully, in the other
it stands out offensively. The peer seems to have written with his
coronet on, and his Earl's mantle before him; the commoner in his
elbow chair and undress.--What can be more pleasant than the way in
which the retired statesman peeps out in the essays, penned by the
latter in his delightful retreat at Shene? They scent of Nimeguen,
and the Hague. Scarce an authority is quoted under an ambassador.
Don Francisco de Melo, a "Portugal Envoy in England," tells him it
was frequent in his country for men, spent with age or other decays,
so as they could not hope for above a year or two of life, to ship
themselves away in a Brazil fleet, and after their arrival there to
go on a great length, sometimes of twenty or thirty years, or more,
by the force of that vigour they recovered with that remove. "Whether
such an effect (Temple beautifully adds) might grow from the air, or
the fruits of that climate, or by approaching nearer the sun, which
is the fountain of light and heat, when their natural heat was so
far decayed: or whether the piecing out of an old man's life were
worth the pains; I cannot tell: perhaps the play is not worth the
candle."--Monsieur Pompone, "French Ambassador in his (Sir William's)
time at the Hague," certifies him, that in his life he had never
heard of any man in France that arrived at a hundred years of age; a
limitation of life which the old gentleman imputes to the excellence
of their climate, giving them such a liveliness of temper and humour,
as disposes them to more pleasures of all kinds than in other
countries; and moralises upon the matter very sensibly. The "late
Robert Earl of Leicester" furnishes him with a story of a Countess of
Desmond, married out of England in Edward the Fourth's time, and who
lived far in King James's reign. The "same noble person" gives him
an account, how such a year, in the same reign, there went about the
country a set of morrice-dancers, composed of ten men who danced, a
Maid Marian, and a tabor and pipe; and how these twelve, one with
another, made up twelve hundred years. "It was not so much (says
Temple) that so many in one small county (Herefordshire) should live
to that age, as that they should be in vigour and in humour to travel
and to dance." Monsieur Zulichem, one of his "colleagues at the
Hague," informs him of a cure for the gout; which is confirmed by
another "Envoy," Monsieur Serinchamps, in that town, who had tried
it.--Old Prince Maurice of Nassau recommends to him the use of
hammocks in that complaint; having been allured to sleep, while
suffering under it himself, by the "constant motion or swinging of
those airy beds." Count Egmont, and the Rhinegrave who "was killed
last summer before Maestricht," impart to him their experiences.
But the rank of the writer is never more innocently disclosed, than
where he takes for granted the compliments paid by foreigners to his
fruit-trees. For the taste and perfection of what we esteem the best,
he can truly say, that the French, who have eaten his peaches and
grapes at Shene in no very ill year, have generally concluded that
the last are as good as any they have eaten in France on this side
Fontainebleau; and the first as good as any they have eat in Gascony.
Italians have agreed his white figs to be as good as any of that sort
in Italy, which is the earlier kind of white fig there; for in the
later kind and the blue, we cannot come near the warm climates, no
more than in the Frontignac or Muscat grape. His orange-trees too, are
as large as any he saw when he was young in France, except those of
Fontainebleau, or what he has seen since in the Low Countries; except
some very old ones of the Prince of Orange's. Of grapes he had the
honour of bringing over four sorts into England, which he enumerates,
and supposes that they are all by this time pretty common among some
gardeners in his neighbourhood, as well as several persons of quality;
for he ever thought all things of this kind "the commoner they are
made the better." The garden pedantry with which he asserts that 'tis
to little purpose to plant any of the best fruits, as peaches or
grapes, hardly, he doubts, beyond Northamptonshire at the furthest
northwards; and praises the "Bishop of Munster at Cosevelt," for
attempting nothing beyond cherries in that cold climate; is equally
pleasant and in character. "I may perhaps" (he thus ends his sweet
Garden Essay with a passage worthy of Cowley) "be allowed to know
something of this trade, since I have so long allowed myself to be
good for nothing else, which few men will do, or enjoy their gardens,
without often looking abroad to see how other matters play, what
motions in the state, and what invitations they may hope for into
other scenes. For my own part, as the country life, and this part of
it more particularly, were the inclination of my youth itself, so they
are the pleasure of my age; and I can truly say that, among many great
employments that have fallen to my share, I have never asked or sought
for any of them, but have often endeavoured to escape from them, into
the ease and freedom of a private scene, where a man may go his own
way and his own pace, in the common paths and circles of life. The
measure of choosing well is whether a man likes what he has chosen,
which I thank God has befallen me; and though among the follies of my
life, building and planting have not been the least, and have cost
me more than I have the confidence to own; yet they have been fully
recompensed by the sweetness and satisfaction of this retreat, where,
since my resolution taken of never entering again into any public
employments, I have passed five years without ever once going to town,
though I am almost in sight of it, and have a house there always ready
to receive me. Nor has this been any sort of affectation, as some have
thought it, but a mere want of desire or humour to make so small a
remove; for when I am in this corner, I can truly say with Horace, _Me
quoties reficit, &c._
"Me, when the cold Digentian stream revives,
What does my friend believe I think or ask?
Let me yet less possess, so I may live,
Whate'er of life remains, unto myself.
May I have books enough; and one year's store,
Not to depend upon each doubtful hour:
This is enough of mighty Jove to pray,
Who, as he pleases, gives and takes away."
The writings of Temple are, in general, after this easy copy. On one
occasion, indeed, his wit, which was mostly subordinate to nature and
tenderness, has seduced him into a string of felicitous antitheses;
which, it is obvious to remark, have been a model to Addison and
succeeding essayists. "Who would not be covetous, and with reason,"
he says, "if health could be purchased with gold? who not ambitious,
if it were at the command of power, or restored by honour? but, alas!
a white staff will not help gouty feet to walk better than a common
cane; nor a blue riband bind up a wound so well as a fillet. The
glitter of gold, or of diamonds, will but hurt sore eyes instead of
curing them; and an aching head will be no more eased by wearing a
crown, than a common night-cap." In a far better style, and more
accordant with his own humour of plainness, are the concluding
sentences of his "Discourse upon Poetry." Temple took a part in the
controversy about the ancient and the modern learning; and, with
that partiality so natural and so graceful in an old man, whose
state engagements had left him little leisure to look into modern
productions, while his retirement gave him occasion to look back upon
the classic studies of his youth--decided in favour of the latter.
"Certain it is," he says, "that, whether the fierceness of the Gothic
humours, or noise of their perpetual wars, frighted it away, or that
the unequal mixture of the modern languages would not bear it--the
great heights and excellency both of poetry and music fell with
the Roman learning and empire, and have never since recovered the
admiration and applauses that before attended them. Yet, such as they
are amongst us, they must be confessed to be the softest and sweetest,
the most general and most innocent amusements of common time and life.
They still find room in the courts of princes, and the cottages of
shepherds. They serve to revive and animate the dead calm of poor
and idle lives, and to allay or divert the violent passions and
perturbations of the greatest and the busiest men. And both these
effects are of equal use to human life; for the mind of man is like
the sea, which is neither agreeable to the beholder nor the voyager,
in a calm or in a storm, but is so to both when a little agitated by
gentle gales; and so the mind, when moved by soft and easy passions or
affections. I know very well that many who pretend to be wise by the
forms of being grave, are apt to despise both poetry and music, as
toys and trifles too light for the use or entertainment of serious
men. But whoever find themselves wholly insensible to their charms,
would, I think, do well to keep their own counsel, for fear of
reproaching their own temper, and bringing the goodness of their
natures, if not of their understandings, into question. While this
world lasts, I doubt not but the pleasure and request of these two
entertainments will do so too; and happy those that content themselves
with these, or any other so easy and so innocent, and do no trouble
the world or other men, because they cannot be quiet themselves,
though nobody hurts them." "When all is done (he concludes), human
life is at the greatest and the best but like a froward child, that
must be played with, and humoured a little, to keep it quiet, till it
falls asleep, and then the care is over."
BARBARA S----
On the noon of the 14th of November, 1743 or 4, I forget which it was,
just as the clock had struck one, Barbara S----, with her accustomed
punctuality ascended the long rambling staircase, with awkward
interposed landing-places, which led to the office, or rather a sort
of box with a desk in it, whereat sat the then Treasurer of (what few
of our readers may remember) the Old Bath Theatre. All over the island
it was the custom, and remains so I believe to this day, for the
players to receive their weekly stipend on the Saturday. It was not
much that Barbara had to claim.
This little maid had just entered her eleventh year; but her important
station at the theatre, as it seemed to her, with the benefits which
she felt to accrue from her pious application of her small earnings,
had given an air of womanhood to her steps and to her behaviour. You
would have taken her to have been at least five years older.
Till latterly she had merely been employed in choruses, or where
children were wanted to fill up the scene. But the manager, observing
a diligence and adroitness in her above her age, had for some few
months past intrusted to her the performance of whole parts. You may
guess the self-consequence of the promoted Barbara. She had already
drawn tears in young Arthur; had rallied Richard with infantine
petulance in the Duke of York; and in her turn had rebuked that
petulance when she was Prince of Wales. She would have done the elder
child in Morton's pathetic after-piece to the life; but as yet the
"Children in the Wood" was not.
Long after this little girl was grown an aged woman, I have seen some
of these small parts, each making two or three pages at most, copied
out in the rudest hand of the then prompter, who doubtless transcribed
a little more carefully and fairly for the grown-up tragedy ladies
of the establishment. But such as they were, blotted and scrawled,
as for a child's use, she kept them all; and in the zenith of her
after reputation it was a delightful sight to behold them bound up in
costliest Morocco, each single--each small part making a _book_--with
fine clasps, gilt-splashed, &c. She had conscientiously kept them
as they had been delivered to her; not a blot had been effaced
or tampered with. They were precious to her for their affecting
remembrancings. They were her principia, her rudiments; the elementary
atoms; the little steps by which she pressed forward to perfection.
"What," she would say, "could Indian rubber, or a pumice stone, have
done for these darlings?"
I am in no hurry to begin my story--indeed I have little or none to
tell--so I will just mention an observation of hers connected with
that interesting time.
Not long before she died I had been discoursing with her on the
quantity of real present emotion which a great tragic performer
experiences during acting. I ventured to think, that though in the
first instance such players must have possessed the feelings which
they so powerfully called up in others, yet by frequent repetition
those feelings must become deadened in great measure, and the
performer trust to the memory of past emotion, rather than express a
present one. She indignantly repelled the notion, that with a truly
great tragedian the operation, by which such effects were produced
upon an audience, could ever degrade itself into what was purely
mechanical. With much delicacy, avoiding to instance in her
_self_-experience, she told me, that so long ago as when she used to
play the part of the Little Son to Mrs. Porter's Isabella, (I think it
was) when that impressive actress has been bending over her in some
heart-rending colloquy, she has felt real hot tears come trickling
from her, which (to use her powerful expression) have perfectly
scalded her back.
I am not quite so sure that it was Mrs. Porter; but it was some great
actress of that day. The name is indifferent; but the fact of the
scalding tears I most distinctly remember.
I was always fond of the society of players, and am not sure that an
impediment in my speech (which certainly kept me out of the pulpit)
even more than certain personal disqualifications, which are often got
over in that profession, did not prevent me at one time of life from
adopting it. I have had the honour (I must ever call it) once to
have been admitted to the tea-table of Miss Kelly. I have played at
serious whist with Mr. Listen. I have chatted with ever good-humoured
Mrs. Charles Kemble. I have conversed as friend to friend with her
accomplished husband. I have been indulged with a classical conference
with Macready; and with a sight of the Player-picture gallery, at Mr.
Matthews's, when the kind owner, to remunerate me for my love of the
old actors (whom he loves so much) went over it with me, supplying
to his capital collection, what alone the artist could not give
them--voice; and their living motion. Old tones, half-faded, of Dodd
and Parsons, and Baddeley, have lived again for me at his bidding.
Only Edwin he could not restore to me. I have supped with ----; but I
am growing a coxcomb.
As I was about to say--at the desk of the then treasurer of the old
Bath theatre--not Diamond's--presented herself the little Barbara
S----.
The parents of Barbara had been in reputable circumstances. The father
had practised, I believe, as an apothecary in the town. But his
practice from causes which I feel my own infirmity too sensibly that
way to arraign--or perhaps from that pure infelicity which accompanies
some people in their walk through life, and which it is impossible to
lay at the door of imprudence--was now reduced to nothing. They were
in fact in the very teeth of starvation, when the manager, who knew
and respected them in better days, took the little Barbara into his
company.
At the period I commenced with, her slender earnings were the sole
support of the family, including two younger sisters. I must throw
a veil over some mortifying circumstances. Enough to say, that her
Saturday's pittance was the only chance of a Sunday's (generally their
only) meal of meat.
One thing I will only mention, that in some child's part, where in
her theatrical character she was to sup off a roast fowl (O joy to
Barbara!) some comic actor, who was for the night caterer for this
dainty--in the misguided humour of his part, threw over the dish
such a quantity of salt (O grief and pain of heart to Barbara!) that
when he crammed a portion of it into her mouth, she was obliged
sputteringly to reject it; and what with shame of her ill-acted part,
and pain of real appetite at missing such a dainty, her little heart
sobbed almost to breaking, till a flood of tears, which the well-fed
spectators were totally unable to comprehend, mercifully relieved her.
This was the little starved, meritorious maid, who stood before old
Ravenscroft, the treasurer, for her Saturday's payment.
Ravenscroft was a man, I have heard many old theatrical people besides
herself say, of all men least calculated for a treasurer. He had no
head for accounts, paid away at random, kept scarce any books, and
summing up at the week's end, if he found himself a pound or so
deficient, blest himself that it was no worse.
Now Barbara's weekly stipend was a bare half guinea.--By mistake he
popped into her hand a--whole one.
Barbara tripped away.
She was entirely unconscious at first of the mistake: God knows,
Ravenscroft would never have discovered it.
But when she had got down to the first of those uncouth
landing-places, she became sensible of an unusual weight of metal
pressing her little hand.
Now mark the dilemma.
She was by nature a good child. From her parents and those about her
she had imbibed no contrary influence. But then they had taught her
nothing. Poor men's smoky cabins are not always porticoes of moral
philosophy. This little maid had no instinct to evil, but then she
might be said to have no fixed principle. She had heard honesty
commended, but never dreamed of its application to herself. She
thought of it as something which concerned grown-up people--men
and women. She had never known temptation, or thought of preparing
resistance against it.
Her first impulse was to go back to the old treasurer, and explain
to him his blunder. He was already so confused with age, besides a
natural want of punctuality, that she would have had some difficulty
in making him understand it. She saw _that_ in an instant. And then
it was such a bit of money! and then the image of a larger allowance
of butcher's meat on their table next day came across her, till
her little eyes glistened, and her mouth moistened. But then Mr.
Ravenscroft had always been so good-natured, had stood her friend
behind the scenes, and even recommended her promotion to some of her
little parts. But again the old man was reputed to be worth a world
of money. He was supposed to have fifty pounds a year clear of the
theatre. And then came staring upon her the figures of her little
stockingless and shoeless sisters. And when she looked at her own neat
white cotton stockings, which her situation at the theatre had made it
indispensable for her mother to provide for her, with hard straining
and pinching from the family stock, and thought how glad she should
be to cover their poor feet with the same--and how then they could
accompany her to rehearsals, which they had hitherto been precluded
from doing, by reason of their unfashionable attire--in these thoughts
she reached the second landing-place--the second, I mean from the
top--for there was still another left to traverse.
Now virtue support Barbara!
And that never-failing friend did step in--for at that moment a
strength not her own, I have heard her say, was revealed to her--a
reason above reasoning--and without her own agency, as it seemed (for
she never felt her feet to move) she found herself transported back to
the individual desk she had just quitted, and her hand in the old hand
of Ravenscroft, who in silence took back the refunded treasure, and
who had been sitting (good man) insensible to the lapse of minutes,
which to her were anxious ages; and from that moment a deep peace fell
upon her heart, and she knew the quality of honesty.
A year or two's unrepining application to her profession brightened
up the feet, and the prospects, of her little sisters, set the whole
family upon their legs again, and released her from the difficulty of
discussing moral dogmas upon a landing-place.
I have heard her say, that it was a surprise, not much short of
mortification to her, to see the coolness with which the old man
pocketed the difference, which had caused her such mortal throes.
This anecdote of herself I had in the year 1800, from the mouth of
the late Mrs. Crawford,[1] then sixty-seven years of age (she died
soon after); and to her struggles upon this childish occasion I have
sometimes ventured to think her indebted for that power of rending
the heart in the representation of conflicting emotions, for which in
after years she was considered as little inferior (if at all so in the
part of Lady Randolph) even to Mrs. Siddons.
[Footnote 1: The maiden name of this lady was Street, which she
changed, by successive marriages, for those of Dancer, Barry, and
Crawford. She was Mrs. Crawford, and a third time a widow, when I
knew her.]
THE TOMBS IN THE ABBEY
IN A LETTER TO R---- S----, ESQ.
Though in some points of doctrine, and perhaps of discipline I am
diffident of lending a perfect assent to that church which you have
so worthily _historified_, yet may the ill time never come to me,
when with a chilled heart, or a portion of irreverent sentiment, I
shall enter her beautiful and time-hallowed Edifices. Judge then
of my mortification when, after attending the choral anthems of
last Wednesday at Westminster, and being desirous of renewing my
acquaintance, after lapsed years, with the tombs and antiquities
there, I found myself excluded; turned out like a dog, or some profane
person, into the common street, with feelings not very congenial to
the place, or to the solemn service which I had been listening to. It
was a jar after that music.
You had your education at Westminster; and doubtless among those dim
aisles and cloisters, you must have gathered much of that devotional
feeling in those young years, on which your purest mind feeds
still--and may it feed! The antiquarian spirit, strong in you, and
gracefully blending ever with the religious, may have been sown in
you among those wrecks of splendid mortality. You owe it to the
place of your education; you owe it to your learned fondness for the
architecture of your ancestors; you owe it to the venerableness of
your ecclesiastical establishment, which is daily lessened and called
in question through these practices--to speak aloud your sense of
them; never to desist raising your voice against them, till they be
totally done away with and abolished; till the doors of Westminster
Abbey be no longer closed against the decent, though low-in-purse,
enthusiast, or blameless devotee, who must commit an injury against
his family economy, if he would be indulged with a bare admission
within its walls. You owe it to the decencies, which you wish to see
maintained in its impressive services, that our Cathedral be no longer
an object of inspection to the poor at those times only, in which they
must rob from their Attendance on the worship every minute which they
can bestow upon the fabric. In vain the public prints have taken up
this subject, in vain such poor nameless writers as myself express
their indignation. A word from you, Sir--a hint in your Journal--would
be sufficient to fling open the doors of the Beautiful Temple again,
as we can remember them when we were boys. At that time of life, what
would the imaginative faculty (such as it is) in both of us, have
suffered, if the entrance to so much reflection had been obstructed
by the demand of so much silver!--If we had scraped it up to gain an
occasional admission (as we certainly should have done) would the
sight of those old tombs have been as impressive to us (while we had
been weighing anxiously prudence against sentiment) as when the gates
stood open, as those of the adjacent Park; when we could walk in at
any time, as the mood brought us, for a shorter or longer time, as
that lasted? Is the being shown over a place the same as silently for
ourselves detecting the genius of it? In no part of our beloved Abbey
now can a person find entrance (out of service time) under the sum of
_two shillings_. The rich and the great will smile at the anticlimax,
presumed to lie in these two short words. But you can tell them, Sir,
how much quiet worth, how much capacity for enlarged feeling, how
much taste and genius, may coexist, especially in youth, with a purse
incompetent to this demand.--A respected friend of ours, during his
late visit to the metropolis, presented himself for admission to Saint
Paul's. At the same time a decently clothed man, with as decent a
wife, and child, were bargaining for the same indulgence. The price
was only two-pence each person. The poor but decent man hesitated,
desirous to go in; but there were three of them, and he turned away
reluctantly. Perhaps he wished to have seen the tomb of Nelson.
Perhaps the Interior of the Cathedral was his object. But in the state
of his finances, even sixpence might reasonably seem too much. Tell
the Aristocracy of the country (no man can do it more impressively);
instruct them of what value these insignificant pieces of money, these
minims to their sight, may be to their humbler brethren. Shame these
Sellers out of the Temple. Stifle not the suggestions of your better
nature with the pretext, that an indiscriminate admission would expose
the Tombs to violation. Remember your boy-days. Did you ever see,
or hear, of a mob in the Abbey, while it was free to all? Do the
rabble come there, or trouble their heads about such speculations?
It is all that you can do to drive them into your churches; they do
not voluntarily offer themselves. They have, alas! no passion for
antiquities; for tomb of king or prelate, sage or poet. If they had,
they would be no longer the rabble.
For forty years that I have known the Fabric, the only well-attested
charge of violation adduced, has been--a ridiculous dismemberment
committed upon the effigy of that amiable spy, Major Andre. And is it
for this--the wanton mischief of some schoolboy, fired perhaps with
raw notions of Transatlantic Freedom--or the remote possibility
of such a mischief occurring again, so easily to be prevented
by stationing a constable within the walls, if the vergers are
incompetent to the duty--is it upon such wretched pretences, that
the people of England are made to pay a new Peter's Pence, so long
abrogated; or must content themselves with contemplating the ragged
Exterior of their Cathedral? The mischief was done about the time that
you were a scholar there. Do you know any thing about the unfortunate
relic?--
AMICUS REDIVIVUS
Where were ye, Nymphs, when the remorseless deep
Clos'd o'er the head of your loved Lycidas?
I do not know when I have experienced a stranger sensation, than
on seeing my old friend G.D., who had been paying me a morning
visit a few Sundays back, at my cottage at Islington, upon taking
leave, instead of turning down the right hand path by which he had
entered--with staff in hand, and at noon day, deliberately march right
forwards into the midst of the stream that runs by us, and totally
disappear. A spectacle like this at dusk would have been appalling
enough; but, in the broad open daylight, to witness such an unreserved
motion towards self-destruction in a valued friend, took from me all
power of speculation.
How I found my feet, I know not. Consciousness was quite gone. Some
spirit, not my own, whirled me to the spot. I remember nothing but the
silvery apparition of a good white head emerging; nigh which a staff
(the hand unseen that wielded it) pointed upwards, as feeling for the
skies. In a moment (if time was in that time) he was on my shoulders,
and I--freighted with a load more precious than his who bore Anchises.
And here I cannot but do justice to the officious zeal of sundry
passers by, who, albeit arriving a little too late to participate in
the honours of the rescue, in philanthropic shoals came thronging to
communicate their advice as to the recovery; prescribing variously
the application, or non-application, of salt, &c., to the person of
the patient. Life meantime was ebbing fast away, amidst the stifle of
conflicting judgments, when one, more sagacious than the rest, by a
bright thought, proposed sending for the Doctor. Trite as the counsel
was, and impossible, as one should think, to be missed on,--shall I
confess?--in this emergency, it was to me as if an Angel had spoken.
Great previous exertions--and mine had not been inconsiderable--are
commonly followed by a debility of purpose. This was a moment of
irresolution.
MONOCULUS--for so, in default of catching his true name, I choose
to designate the medical gentleman who now appeared--is a grave,
middle-aged person, who, without having studied at the college, or
truckled to the pedantry of a diploma, hath employed a great portion
of his valuable time in experimental processes upon the bodies of
unfortunate fellow-creatures, in whom the vital spark, to mere
vulgar thinking, would seem extinct, and lost for ever. He omitteth
no occasion of obtruding his services, from a case of common
surfeit-suffocation to the ignobler obstructions, sometimes induced by
a too wilful application of the plant _Cannabis_ outwardly. But though
he declineth not altogether these drier extinctions, his occupation
tendeth for the most part to water-practice; for the convenience
of which, he hath judiciously fixed his quarters near the grand
repository of the stream mentioned, where, day and night, from his
little watch-tower, at the Middleton's-Head, he listeneth to detect
the wrecks of drowned mortality--partly, as he saith, to be upon the
spot--and partly, because the liquids which he useth to prescribe
to himself and his patients, on these distressing occasions, are
ordinarily more conveniently to be found at these common hostelries,
than in the shops and phials of the apothecaries. His ear hath arrived
to such finesse by practice, that it is reported, he can distinguish
a plunge at a half furlong distance; and can tell, if it be casual or
deliberate. He weareth a medal, suspended over a suit, originally of a
sad brown, but which, by time, and frequency of nightly divings, has
been dinged into a true professional sable. He passeth by the name of
Doctor, and is remarkable for wanting his left eye. His remedy--after
a sufficient application of warm blankets, friction, &c., is a simple
tumbler, or more, of the purest Cognac, with water, made as hot as
the convalescent can bear it. Where he findeth, as in the case of my
friend, a squeamish subject, he condescendeth to be the taster; and
showeth, by his own example, the innocuous nature of the prescription.
Nothing can be more kind or encouraging than this procedure. It addeth
confidence to the patient, to see his medical adviser go hand in
hand with himself in the remedy. When the doctor swalloweth his own
draught, what peevish invalid can refuse to pledge him in the potion?
In fine, MONOCULUS is a humane, sensible man, who, for a slender
pittance, scarce enough to sustain life, is content to wear it out
in the endeavour to save the lives of others--his pretensions so
moderate, that with difficulty I could press a crown upon him, for the
price of restoring the existence of such an invaluable creature to
society as G.D.
It was pleasant to observe the effect of the subsiding alarm upon
the nerves of the dear absentee. It seemed to have given a shake
to memory, calling up notice after notice, of all the providential
deliverances he had experienced in the course of his long and innocent
life. Sitting up in my couch--my couch which, naked and void of
furniture hitherto, for the salutary repose which it administered,
shall be honoured with costly valance, at some price, and henceforth
be a state-bed at Colebrooke,--he discoursed of marvellous escapes--by
carelessness of nurses--by pails of gelid, and kettles of the
boiling element, in infancy--by orchard pranks, and snapping twigs,
in schoolboy frolics--by descent of tiles at Trumpington, and of
heavier tomes at Pembroke--by studious watchings, inducing frightful
vigilance--by want, and the fear of want, and all the sore throbbings
of the learned head.--Anon, he would burst out into little fragments
of chaunting--of songs long ago--ends of deliverance-hymns, not
remembered before since childhood, but coming up now, when his
heart was made tender as a child's--for the _tremor cordis_, in the
retrospect of a recent deliverance, as in a case of impending danger,
acting upon an innocent heart, will produce a self-tenderness, which
we should do ill to christen cowardice; and Shakspeare, in the latter
crisis, has made his good Sir Hugh to remember the sitting by Babylon,
and to mutter of shallow rivers.
Waters of Sir Hugh Middleton--what a spark you were like to have
extinguished for ever! Your salubrious streams to this City, for now
near two centuries, would hardly have atoned for what you were in a
moment washing away. Mockery of a river--liquid artifice--wretched
conduit! henceforth rank with canals, and sluggish aqueducts. Was
it for this, that, smit in boyhood with the explorations of that
Abyssinian traveller, I paced the vales of Amwell to explore your
tributary springs, to trace your salutary waters sparkling through
green Hertfordshire, and cultured Enfield parks?--Ye have no swans--no
Naiads--no river God--or did the benevolent hoary aspect of my friend
tempt ye to suck him in, that ye also might have the tutelary genius
of your waters?
Had he been drowned in Cam there would have been some consonancy
in it; but what willows had ye to wave and rustle over his moist
sepulture?--or, having no _name_, besides that unmeaning assumption
of _eternal novity_, did ye think to get one by the noble prize, and
henceforth to be termed the STREAM DYERIAN?
And could such spacious virtue find a grave
Beneath the imposthumed bubble of a wave?
I protest, George, you shall not venture out again--no, not by
daylight--without a sufficient pair of spectacles--in your musing
moods especially. Your absence of mind we have borne, till your
presence of body came to be called in question by it. You shall not go
wandering into Euripus with Aristotle, if we can help it. Fie, man,
to turn dipper at your years' after your many tracts in favour of
sprinkling only!
I have nothing but water in my head o' nights since this frightful
accident. Sometimes I am with Clarence in his dream. At others, I
behold Christian beginning to sink, and crying out to his good brother
Hopeful (that is to me), "I sink in deep waters; the billows go over
my head, all the waves go over me. Selah." Then I have before me
Palinurus, just letting go the steerage. I cry out too late to save.
Next follow--a mournful procession--_suicidal faces_, saved against
their wills from drowning; dolefully trailing a length of reluctant
gratefulness, with ropy weeds pendant from locks of watchet
hue-constrained Lazari--Pluto's half-subjects--stolen fees from the
grave-bilking Charon of his fare. At their head Arion--or is it
G.D.?--in his singing garments marcheth singly, with harp in hand,
and votive garland, which Machaon (or Dr. Hawes) snatcheth straight,
intending to suspend it to the stern God of Sea. Then follow dismal
streams of Lethe, in which the half-drenched on earth are constrained
to drown downright, by wharfs where Ophelia twice acts her muddy
death.
And, doubtless, there is some notice in that invisible world, when one
of us approacheth (as my friend did so lately) to their inexorable
precincts. When a soul knocks once, twice, at death's door, the
sensation aroused within the palace must be considerable; and the grim
Feature, by modern science so often dispossessed of his prey, must
have learned by this time to pity Tantalus.
A pulse assuredly was felt along the line of the Elysian shades, when
the near arrival of G.D. was announced by no equivocal indications.
From their seats of Asphodel arose the gentler and the graver
ghosts-poet, or historian--of Grecian or of Roman lore--to crown with
unfading chaplets the half-finished love-labours of their unwearied
scholiast. Him Markland expected--him Tyrwhitt hoped to encounter--him
the sweet lyrist of Peter House, whom he had barely seen upon
earth[1], with newest airs prepared to greet ----; and, patron of
the gentle Christ's boy,--who should have been his patron through
life--the mild Askew, with longing aspirations, leaned foremost from
his venerable AEsculapian chair, to welcome into that happy company the
matured virtues of the man, whose tender scions in the boy he himself
upon earth had so prophetically fed and watered.
[Footnote 1: Graium _tantum vidit_.]
SOME SONNETS OF SIR PHILIP SYDNEY
Sydney's Sonnets--I speak of the best of them--are among the very best
of their sort. They fall below the plain moral dignity, the sanctity,
and high yet modest spirit of self-approval, of Milton, in his
compositions of a similar structure. They are in truth what Milton,
censuring the Arcadia, says of that work (to which they are a sort
of after-tune or application), "vain and amatorious" enough, yet the
things in their kind (as he confesses to be true of the romance) may
be "full of worth and wit." They savour of the Courtier, it must be
allowed, and not of the Commonwealthsman. But Milton was a Courtier
when he wrote the Masque at Ludlow Castle, and still more a Courtier
when he composed the Arcades. When the national struggle was to begin,
he becomingly cast these vanities behind him; and if the order of time
had thrown Sir Philip upon the crisis which preceded the Revolution,
there is no reason why he should not have acted the same part in that
emergency, which has glorified the name of a later Sydney. He did not
want for plainness or boldness of spirit. His letter on the French
match may testify, he could speak his mind freely to Princes. The
times did not call him to the scaffold.
The Sonnets which we oftenest call to mind of Milton were the
compositions of his maturest years. Those of Sydney, which I am about
to produce, were written in the very hey-day of his blood. They are
stuck full of amorous fancies--far-fetched conceits, befitting his
occupation; for True Love thinks no labour to send out Thoughts
upon the vast, and more than Indian voyages, to bring home rich
pearls, outlandish wealth, gums, jewels, spicery, to sacrifice in
self-depreciating similitudes, as shadows of true amiabilities in the
Beloved. We must be Lovers--or at least the cooling touch of time,
the _circum praecordia frigus_, must not have so damped our faculties,
as to take away our recollection that we were once so--before we can
duly appreciate the glorious vanities, and graceful hyperboles, of
the passion. The images which lie before our feet (though by some
accounted the only natural) are least natural for the high Sydnean
love to express its fancies by. They may serve for the loves of
Tibullus, or the dear Author of the Schoolmistress; for passions that
creep and whine in Elegies and Pastoral Ballads. I am sure Milton
never loved at this rate. I am afraid some of his addresses (_ad
Leonoram_ I mean) have rather erred on the farther side; and that the
poet came not much short of a religious indecorum, when he could thus
apostrophise a singing-girl:--
Angelus unicuique suus (sic credite gentes)
Obtigit aetheriis ales ab ordinibus.
Quid mirum, Leonora, tibi si gloria major,
Nam tua praesentem vox sonat ipsa Deum?
Aut Deus, aut vacui certe mens tertia coeli,
Per tua secreto guttura serpit agens;
Serpit agens, facilisque docet mortalia corda
Sensim immortali assuescere posse sono.
QUOD SI CUNCTA QUIDEM DEUS EST, PER CUNCTAQUE FUSUS,
IN TE UNA LOQUITUR, CAETERA MUTUS HABET.
This is loving in a strange fashion; and it requires some candour of
construction (besides the slight darkening of a dead language) to cast
a veil over the ugly appearance of something very like blasphemy in
the last two verses. I think the Lover would have been staggered, if
he had gone about to express the same thought in English. I am sure,
Sydney has no nights like this. His extravaganzas do not strike at the
sky, though he takes leave to adopt the pale Dian into a fellowship
with his mortal passions.
I
With how sad steps, O Moon, thou climb'st the skies;
How silently; and with how wan a face!
What! may it be, that even in heavenly place
That busy Archer his sharp arrows tries?
Sure, if that long-with-love-acquainted eyes
Can judge of love, thou feel'st a lover's case;
I read it in thy looks; thy languish! grace
To me, that feel the like, thy state descries.
Then, even of fellowship, O Moon, tell me,
Is constant love deem'd there but want of wit?
Are beauties there as proud as here they be?
Do they above love to be loved, and yet
Those lovers scorn, whom that love doth possess?
Do they call _virtue_ there--_ungratefulness_!
The last line of this poem is a little obscured by transposition. He
means, Do they call ungratefulness there a virtue?
II
Come, Sleep, O Sleep, the certain knot of peace,
The baiting place of wit, the balm of woe,
The poor man's wealth, the prisoner's release,
The indifferent judge between the high and low;
With shield of proof shield me from out the prease[1]
Of those fierce darts despair at me doth throw;
O make in me those civil wars to cease:
I will good tribute pay, if thou do so.
Take thou of me sweet pillows, sweetest bed;
A chamber deaf to noise, and blind to light;
A rosy garland, and a weary head.
And if these things, as being thine by right,
Move not thy heavy grace, thou shalt in me,
Livelier than elsewhere, STELLA'S image see.
III
The curious wits, seeing dull pensiveness
Bewray itself in my long-settled eyes,
Whence those same fumes of melancholy rise,
With idle pains, and missing aim, do guess.
Some, that know how my spring I did address,
Deem that my Muse some fruit of knowledge plies;
Others, because the Prince my service tries,
Think, that I think state errors to redress;
But harder judges judge, ambition's rage,
Scourge of itself, still climbing slippery place,
Holds my young brain captiv'd in golden cage.
O fools, or over-wise! alas, the race
Of all my thoughts hath neither stop nor start,
But only STELLA'S eyes, and STELLA'S heart.
IV
Because I oft in dark abstracted guise
Seem most alone in greatest company,
With dearth of words, or answers quite awry,
To them that would make speech of speech arise;
They deem, and of their doom the rumour flies,
That poison foul of bubbling _Pride_ doth lie
So in my swelling breast, that only I
Fawn on myself, and others do despise;
Yet _Pride_, I think, doth not my Soul possess,
Which looks too oft in his unflattering glass:
But one worse fault--_Ambition_--I confess,
That makes me oft my best friends overpass,
Unseen, unheard--while Thought to highest place
Bends all his powers, even unto STELLA'S grace.
V
Having this day, my horse, my hand, my lance,
Guided so well that I obtained the prize,
Both by the judgment of the English eyes,
And of some sent from that _sweet enemy_,--France;
Horsemen my skill in horsemanship advance;
Townsfolk my strength; a daintier judge applies
His praise to sleight, which from good use doth rise;
Some lucky wits impute it but to chance;
Others, because of both sides I do take
My blood from them, who did excel in this,
Think Nature me a man of arms did make.
How far they shot awry! the true cause is,
STELLA look'd on, and from her heavenly face
Sent forth the beams which made so fair my race.
VI
In martial sports I had my cunning tried,
And yet to break more staves did me address,
While with the people's shouts (I must confess)
Youth, luck, and praise, even fill'd my veins with pride--
When Cupid, having me (his slave) descried
In Mars's livery, prancing in the press,
"What now, Sir Fool!" said he; "I would no less:
Look here, I say." I look'd, and STELLA spied,
Who hard by made a window send forth light.
My heart then quak'd, then dazzled were mine eyes;
One hand forgot to rule, th'other to fight;
Nor trumpet's sound I heard, nor friendly cries.
My foe came on, and beat the air for me--
Till that her blush made me my shame to see.
VII
No more, my dear, no more these counsels try;
O give my passions leave to run their race;
Let Fortune lay on me her worst disgrace;
Let folk o'er-charged with brain against me cry;
Let clouds bedim my face, break in mine eye;
Let me no steps, but of lost labour, trace;
Let all the earth with scorn recount my case--
But do not will me from my love to fly.
I do not envy Aristotle's wit,
Nor do aspire to Caesar's bleeding fame;
Nor aught do care, though some above me sit;
Nor hope, nor wish, another course to frame.
But that which once may win thy cruel heart:
Thou art my wit, and thou my virtue art.
VIII
Love still a boy, and oft a wanton, is,
School'd only by his mother's tender eye;
What wonder then, if he his lesson miss,
When for so soft a rod dear play he try?
And yet my STAR, because a sugar'd kiss
In sport I suck'd, while she asleep did lie,
Doth lour, nay chide, nay threat, for only this.
Sweet, it was saucy LOVE, not humble I.
But no 'scuse serves; she makes her wrath appear
In beauty's throne--see now, who dares come near
Those scarlet judges, threat'ning bloody pain?
O heav'nly Fool, thy most kiss-worthy face
Anger invests with such a lovely grace,
That anger's self I needs must kiss again.
IX
I never drank of Aganippe well,
Nor ever did in shade of Tempe sit,
And Muses scorn with vulgar brains to dwell;
Poor lay-man I, for sacred rites unfit.
Some do I bear of Poets' fury tell,
But (God wot) wot not what they mean by it;
And this I swear by blackest brook of hell,
I am no pick-purse of another's wit.
How falls it then, that with so smooth an ease
My thoughts I speak, and what I speak doth flow
In verse, and that my verse best wits doth please?
Guess me the cause--what is it thus?--fye, no.
Or so?--much less. How then? sure thus it is,
My lips are sweet, inspired with STELLA'S kiss.
X
Of all the kings that ever here did reign,
Edward, named Fourth, as first in praise I name,
Not for his fair outside, nor well-lined brain--
Although less gifts imp feathers oft on Fame.
Nor that he could, young-wise, wise-valiant, frame
His sire's revenge, join'd with a kingdom's gain;
And, gain'd by Mars could yet mad Mars so tame,
That Balance weigh'd what Sword did late obtain.
Nor that he made the Floure-de-luce so 'fraid,
Though strongly hedged of bloody Lions' paws
That witty Lewis to him a tribute paid.
Nor this, nor that, nor any such small cause--
But only, for this worthy knight durst prove
To lose his crown rather than fail his love.
XI
O happy Thames, that didst my STELLA bear,
I saw thyself, with many a smiling line
Upon thy cheerful face, Joy's livery wear,
While those fair planets on thy streams did shine;
The boat for joy could not to dance forbear,
While wanton winds, with beauty so divine
Ravish'd, stay'd not, till in her golden hair
They did themselves (O sweetest prison) twine.
And fain those AEol's youth there would their stay
Have made; but, forced by nature still to fly,
First did with puffing kiss those locks display.
She, so dishevell'd, blush'd; from window I
With sight thereof cried out, O fair disgrace,
Let honour's self to thee grant highest place!
XII
Highway, since you my chief Parnassus be;
And that my Muse, to some ears not unsweet,
Tempers her words to trampling horses' feet,
More soft than to a chamber melody,--
Now blessed You bear onward blessed Me
To Her, where I my heart safe left shall meet,
My Muse and I must you of duty greet
With thanks and wishes, wishing thankfully.
Be you still fair, honour'd by public heed,
By no encroachment wrong'd, nor time forgot;
Nor blam'd for blood, nor shamed for sinful deed.
And that you know, I envy you no lot
Of highest wish, I wish you so much bliss,
Hundreds of years you STELLA'S feet may kiss.
[Footnote 1: Press.]
Of the foregoing, the first, the second, and the last sonnet, are
my favourites. But the general beauty of them all is, that they
are so perfectly characteristical. The spirit of "learning and of
chivalry,"--of which union, Spenser has entitled Sydney to have been
the "president,"--shines through them. I confess I can see nothing
of the "jejune" or "frigid" in them; much less of the "stiff" and
"cumbrous"--which I have sometimes heard objected to the Arcadia. The
verse runs off swiftly and gallantly. It might have been tuned to the
trumpet; or tempered (as himself expresses it) to "trampling horses'
feet." They abound in felicitous phrases--
O heav'nly Fool, thy most kiss-worthy face--
_8th Sonnet._
--Sweet pillows, sweetest bed;
A chamber deaf to noise, and blind to light;
A rosy garland, and a weary head.
_2nd Sonnet._
--That sweet enemy,--France--
_5th Sonnet._
But they are not rich in words only, in vague and unlocalised
feelings--the failing too much of some poetry of the present day--they
are full, material, and circumstantiated. Time and place appropriates
every one of them. It is not a fever of passion wasting itself upon a
thin diet of dainty words, but a transcendent passion pervading and
illuminating action, pursuits, studies, feats of arms, the opinions
of contemporaries and his judgment of them. An historical thread runs
through them, which almost affixes a date to them; marks the _when_
and _where_ they were written.
I have dwelt the longer upon what I conceive the merit of these poems,
because I have been hurt by the wantonness (I wish I could treat it
by a gentler name) with which W.H. takes every occasion of insulting
the memory of Sir Philip Sydney. But the decisions of the Author of
Table Talk, &c., (most profound and subtle where they are, as for the
most part, just) are more safely to be relied upon, on subjects and
authors he has a partiality for, than on such as he has conceived
an accidental prejudice against. Milton wrote Sonnets, and was a
king-hater; and it was congenial perhaps to sacrifice a courtier to
a patriot. But I was unwilling to lose a _fine idea_ from my mind.
The noble images, passions, sentiments, and poetical delicacies of
character, scattered all over the Arcadia (spite of some stiffness and
encumberment), justify to me the character which his contemporaries
have left us of the writer. I cannot think with the Critic, that Sir
Philip Sydney was that _opprobrious thing_ which a foolish nobleman in
his insolent hostility chose to term him. I call to mind the epitaph
made on him, to guide me to juster thoughts of him; and I repose upon
the beautiful lines in the "Friend's Passion for his Astrophel,"
printed with the Elegies of Spenser and others.
You knew--who knew not Astrophel?
(That I should live to say I knew,
And have not in possession still!)--
Things known permit me to renew--
Of him you know his merit such,
I cannot say--you hear--too much.
Within these woods of Arcady
He chief delight and pleasure took;
And on the mountain Partheny.
Upon the crystal liquid brook,
The Muses met him every day,
That taught him sing, to write, and say.
When he descended down the mount,
His personage seemed most divine:
A thousand graces one might count
Upon his lovely chearful eyne.
To hear him speak, and sweetly smile,
You were in Paradise the while,
_A sweet attractive kind of grace;
A full assurance given by looks;
Continual comfort in a face,
The lineaments of Gospel books--_
I trow that count'nance cannot lye,
Whose thoughts are legible in the eye.
* * * * *
Above all others this is he,
Which erst approved in his song,
That love and honour might agree,
And that pure love will do no wrong.
Sweet saints, it is no sin or blame
To love a man of virtuous name.
Did never Love so sweetly breathe
In any mortal breast before:
Did never Muse inspire beneath
A Poet's brain with finer store.
He wrote of Love with high conceit,
And beauty rear'd above her height.
Or let any one read the deeper sorrows (grief running into rage) in
the Poem,--the last in the collection accompanying the above,--which
from internal testimony I believe to be Lord Brooke's,--beginning with
"Silence augmenteth grief,"--and then seriously ask himself, whether
the subject of such absorbing and confounding regrets could have been
_that thing_ which Lord Oxford termed him.
NEWSPAPERS THIRTY-FIVE YEARS AGO
Dan Stuart once told us, that he did not remember that he ever
deliberately walked into the Exhibition at Somerset House in his life.
He might occasionally have escorted a party of ladies across the way
that were going in; but he never went in of his own head. Yet the
office of the Morning Post newspaper stood then just where it does
now--we are carrying you back, Reader, some thirty years or more--with
its gilt-globe-topt front facing that emporium of our artists' grand
Annual Exposure. We sometimes wish, that we had observed the same
abstinence with Daniel.
A word or two of D.S. He ever appeared to us one of the finest
tempered of Editors. Perry, of the Morning Chronicle, was equally
pleasant, with a dash, no slight one either, of the courtier. S. was
frank, plain, and English all over. We have worked for both these
gentlemen.
It is soothing to contemplate the head of the Ganges; to trace the
first little bubblings of a mighty river;
With holy reverence to approach the rocks,
Whence glide the streams renowned in ancient song.
Fired with a perusal of the Abyssinian Pilgrim's exploratory ramblings
after the cradle of the infant Nilus, we well remember on one fine
summer holyday (a "whole day's leave" we called it at Christ's
Hospital) sallying forth at rise of sun, not very well provisioned
either for such an undertaking, to trace the current of the New
River--Middletonian stream!--to its scaturient source, as we had read,
in meadows by fair Amwell. Gallantly did we commence our solitary
quest--for it was essential to the dignity of a DISCOVERY, that no eye
of schoolboy, save our own, should beam on the detection. By flowery
spots, and verdant lanes, skirting Hornsey, Hope trained us on in many
a baffling turn; endless, hopeless meanders, as it seemed; or as if
the jealous waters had _dodged_ us, reluctant to have the humble spot
of their nativity revealed; till spent, and nigh famished, before set
of the same sun, we sate down somewhere by Bowes Farm, near Tottenham,
with a tithe of our proposed labours only yet accomplished; sorely
convinced in spirit, that that Brucian enterprise was as yet too
arduous for our young shoulders.
Not more refreshing to the thirsty curiosity of the traveller is the
tracing of some mighty waters up to their shallow fontlet, than it is
to a pleased and candid reader to go back to the inexperienced essays,
the first callow flights in authorship, of some established name in
literature; from the Gnat which preluded to the AEneid, to the Duck
which Samuel Johnson trod on.
In those days every Morning Paper, as an essential retainer to its
establishment, kept an author, who was bound to furnish daily a
quantum of witty paragraphs. Sixpence a joke--and it was thought
pretty high too--was Dan Stuart's settled remuneration in these cases.
The chat of the day, scandle, but, above all, _dress_, furnished
the material. The length of no paragraph was to exceed seven lines.
Shorter they might be, but they must be poignant.
A fashion of _flesh_, or rather _pink_- hose for the ladies,
luckily coming up at the juncture, when we were on our probation for
the place of Chief Jester to S.'s Paper, established our reputation in
that line. We were pronounced a "capital hand." O the conceits which
we varied upon _red_ in all its prismatic differences! from the trite
and obvious flower of Cytherea, to the flaming costume of the lady
that has her sitting upon "many waters." Then there was the collateral
topic of ancles. What an occasion to a truly chaste writer, like
ourself, of touching that nice brink, and yet never tumbling over it,
of a seemingly ever approximating something "not quite proper;" while,
like a skilful posture-master, balancing betwixt decorums and their
opposites, he keeps the line, from which a hair's-breadth deviation is
destruction; hovering in the confines of light and darkness, or where
"both seem either;" a hazy uncertain delicacy; Autolycus-like in the
Play, still putting off his expectant auditory with "Whoop, do me no
harm, good man!" But, above all, that conceit arrided us most at that
time, and still tickles our midriff to remember, where, allusively
to the flight of Astraea--_ultima Calestum terras reliquit_--we
pronounced--in reference to the stockings still--that MODESTY TAKING
HER FINAL LEAVE OF MORTALS, HER LAST BLUSH WAS VISIBLE IN HER ASCENT
TO THE HEAVENS BY THE TRACT OF THE GLOWING INSTEP. This might be
called the crowning conceit; and was esteemed tolerable writing in
those days.
But the fashion of jokes, with all other things, passes away; as did
the transient mode which had so favoured us. The ancles of our fair
friends in a few weeks began to reassume their whiteness, and left us
scarce a leg to stand upon. Other female whims followed, but none,
methought, so pregnant, so invitatory of shrewd conceits, and more
than single meanings.
Somebody has said, that to swallow six cross-buns daily consecutively
for a fortnight would surfeit the stoutest digestion. But to have to
furnish as many jokes daily, and that not for a fortnight, but for a
long twelvemonth, as we were constrained to do, was a little harder
execution. "Man goeth forth to his work until the evening"--from a
reasonable hour in the morning, we presume it was meant. Now as our
main occupation took us up from eight till five every day in the City;
and as our evening hours, at that time of life, had generally to do
with any thing rather than business, it follows, that the only time
we could spare for this manufactory of jokes--our supplementary
livelihood, that supplied us in every want beyond mere bread and
cheese--was exactly that part of the day which (as we have heard of No
Man's Land) may be fitly denominated No Man's Time; that is, no time
in which a man ought to be up, and awake, in. To speak more plainly,
it is that time, of an hour, or an hour and a half's duration, in
which a man, whose occasions call him up so preposterously, has to
wait for his breakfast.
O those headaches at dawn of day, when at five, or half-past-five in
summer, and not much later in the dark seasons, we were compelled to
rise, having been perhaps not above four hours in bed--(for we were no
go-to-beds with the lamb, though we anticipated the lark ofttimes in
her rising--we liked a parting cup at midnight, as all young men did
before these effeminate times, and to have our friends about us--we
were not constellated under Aquarius, that watery sign, and therefore
incapable of Bacchus, cold, washy, bloodless--we were none of your
Basilian water-sponges, nor had taken our degrees at Mount Ague--we
were right toping Capulets, jolly companions, we and they)--but to
have to get up, as we said before, curtailed of half our fair sleep,
fasting, with only a dim vista of refreshing Bohea in the distance--to
be necessitated to rouse ourselves at the detestable rap of an old
hag of a domestic, who seemed to take a diabolical pleasure in her
announcement that it was "time to rise;" and whose chappy knuckles
we have often yearned to amputate, and string them up at our chamber
door, to be a terror to all such unseasonable rest-breakers in
future--
"Facil" and sweet, as Virgil sings, had been the "descending" of the
over-night, balmy the first sinking of the heavy head upon the pillow;
but to get up, as he goes on to say,
--revocare gradus, superasque evadere ad auras--
and to get up moreover to make jokes with malice prepended--there was
the "labour," there the "work."
No Egyptian taskmaster ever devised a slavery like to that, our
slavery. No fractious operants ever turned out for half the tyranny,
which this necessity exercised upon us. Half a dozen jests in a day
(bating Sundays too), why, it seems nothing! We make twice the number
every day in our lives as a matter of course, and claim no Sabbatical
exemptions. But then they come into our head. But when the head has to
go out to them--when the mountain must go to Mahomet--
Reader, try it for once, only for one short twelvemonth.
It was not every week that a fashion of pink stockings came up; but
mostly, instead of it, some rugged, untractable subject; some topic
impossible to be contorted into the risible; some feature, upon which
no smile could play; some flint, from which no process of ingenuity
could procure a distillation. There they lay; there your appointed
tale of brick-making was set before you, which you must finish,
with or without straw, as it happened. The craving Dragon--_the
Public_--like him in Bel's temple--must be fed; it expected its daily
rations; and Daniel, and ourselves, to do us justice, did the best we
could on this side bursting him.
While we were wringing our coy sprightlinesses for the Post, and
writhing under the toil of what is called "easy writing," Bob Allen,
our quondam schoolfellow, was tapping his impracticable brains in a
like service for the "Oracle." Not that Robert troubled himself much
about wit. If his paragraphs had a sprightly air about them, it was
sufficient. He carried this nonchalance so far at last, that a matter
of intelligence, and that no very important one, was not seldom palmed
upon his employers for a good jest; for example sake--"_Walking
yesterday morning casually down Snow Hill, who should we meet but Mr.
Deputy Humphreys! we rejoice to add, that the worthy Deputy appeared
to enjoy a good state of health. We do not remember ever to have seen
him look better._" This gentleman, so surprisingly met upon Snow Hill,
from some peculiarities in gait or gesture, was a constant butt for
mirth to the small paragraph-mongers of the day; and our friend
thought that he might have his fling at him with the rest. We met
A. in Holborn shortly after this extraordinary rencounter, which he
told with tears of satisfaction in his eyes, and chuckling at the
anticipated effects of its announcement next day in the paper. We did
not quite comprehend where the wit of it lay at the time; nor was it
easy to be detected, when the thing came out, advantaged by type and
letter-press. He had better have met any thing that morning than a
Common Council Man. His services were shortly after dispensed with,
on the plea that his paragraphs of late had been deficient in point.
The one in question, it must be owned, had an air, in the opening
especially, proper to awaken curiosity; and the sentiment, or moral,
wears the aspect of humanity, and good neighbourly feeling. But
somehow the conclusion was not judged altogether to answer to the
magnificent promise of the premises. We traced our friend's pen
afterwards in the "True Briton," the "Star," the "Traveller,"--from
all which he was successively dismissed, the Proprietors having "no
further occasion for his services." Nothing was easier than to detect
him. When wit failed, or topics ran low, there constantly appeared the
following--"_It is not generally known that the three Blue Balls at
the Pawnbrokers' shops are the ancient arms of Lombardy. The Lombards
were the first money-brokers in Europe._" Bob has done more to set
the public right on this important point of blazonry, than the whole
College of Heralds.
The appointment of a regular wit has long ceased to be a part of the
economy of a Morning Paper. Editors find their own jokes, or do as
well without them. Parson Este, and Topham, brought up the set custom
of "witty paragraphs," first in the "World." Boaden was a reigning
paragraphist in his day, and succeeded poor Allen in the Oracle.
But, as we said, the fashion of jokes passes away; and it would be
difficult to discover in the Biographer of Mrs. Siddons, any traces
of that vivacity and fancy which charmed the whole town at the
commencement of the present century. Even the prelusive delicacies
of the present writer--the curt "Astraean allusion"--would be thought
pedantic, and out of date, in these days.
From the office of the Morning Post (for we may as well exhaust our
Newspaper Reminiscences at once) by change of property in the paper,
we were transferred, mortifying exchange! to the office of the
Albion Newspaper, late Rackstrow's Museum, in Fleet-street. What a
transition--from a handsome apartment, from rose-wood desks, and
silver-inkstands, to an office--no office, but a _den_ rather, but
just redeemed from the occupation of dead monsters, of which it
seemed redolent--from the centre of loyalty and fashion, to a focus
of vulgarity and sedition! Here in murky closet, inadequate from its
square contents to the receipt of the two bodies of Editor, and humble
paragraph-maker, together at one time, sat in the discharge of his new
Editorial functions (the "Bigod" of Elia) the redoubted John Fenwick.
F., without a guinea in his pocket, and having left not many in the
pockets of his friends whom he might command, had purchased (on tick
doubtless) the whole and sole Editorship, Proprietorship, with all the
rights and titles (such as they were worth) of the Albion, from one
Lovell; of whom we know nothing, save that he had stood in the pillory
for a libel on the Prince of Wales. With this hopeless concern--for
it had been sinking ever since its commencement, and could now reckon
upon not more than a hundred subscribers--F. resolutely determined
upon pulling down the Government in the first instance, and making
both our fortunes by way of corollary. For seven weeks and mote did
this infatuated Democrat go about borrowing seven shilling pieces,
and lesser coin, to meet the daily demands of the Stamp Office, which
allowed no credit to publications of that side in politics. An outcast
from politer bread, we attached our small talents to the forlorn
fortunes of our friend. Our occupation now was to write treason.
Recollections of feelings--which were all that now remained from our
first boyish heats kindled by the French Revolution, when if we were
misled, we erred in the company of some, who are accounted very
good men now--rather than any tendency at this time to Republican
doctrines--assisted us in assuming a style of writing, while the
paper lasted, consonant in no very under-tone to the right earnest
fanaticism of F. Our cue was now to insinuate, rather than recommend,
possible abdications. Blocks, axes, Whitehall tribunals, were covered
with flowers of so cunning a periphrasis--as Mr. Bayes says, never
naming the _thing_ directly--that the keen eye of an Attorney General
was insufficient to detect the lurking snake among them. There were
times, indeed, when we sighed for our more gentleman-like occupation
under Stuart. But with change of masters it is ever change of service.
Already one paragraph, and another, as we learned afterwards from a
gentleman at the Treasury, had begun to be marked at that office, with
a view of its being submitted at least to the attention of the proper
Law Officers--when an unlucky, or rather lucky epigram from our pen,
aimed at Sir J----s M----h, who was on the eve of departing for India
to reap the fruits of his apostacy, as F. pronounced it, (it is hardly
worth particularising), happening to offend the nice sense of Lord,
or, as he then delighted to be called, Citizen Stanhope, deprived F.
at once of the last hopes of a guinea from the last patron that had
stuck by us; and breaking up our establishment, left us to the safe,
but somewhat mortifying, neglect of the Crown Lawyers.--It was about
this time, or a little earlier, that Dan. Stuart made that curious
confession to us, that he had "never deliberately walked into an
Exhibition at Somerset House in his life."
BARRENNESS OF THE IMAGINATIVE FACULTY IN THE PRODUCTIONS OF MODERN ART
Hogarth excepted, can we produce any one painter within the last fifty
years, or since the humour of exhibiting began, that has treated a
story _imaginatively_? By this we mean, upon whom his subject has
so acted, that it has seemed to direct _him_--not to be arranged by
him? Any upon whom its leading or collateral points have impressed
themselves so tyrannically, that he dared not treat it otherwise,
lest he should falsify a revelation? Any that has imparted to his
compositions, not merely so much truth as is enough to convey a story
with clearness, but that individualising property, which should keep
the subject so treated distinct in feature from every other subject,
however similar, and to common apprehensions almost identical; so as
that we might say, this and this part could have found an appropriate
place in no other picture in the world but this? Is there anything in
modern art--we will not demand that it should be equal--but in any
way analogous to what Titian has effected, in that wonderful bringing
together of two times in the "Ariadne," in the National Gallery?
Precipitous, with his reeling Satyr rout about him, re-peopling and
re-illuming suddenly the waste places, drunk with a new fury beyond
the grape, Bacchus, born in fire, fire-like flings himself at the
Cretan. This is the time present. With this telling of the story an
artist, and no ordinary one, might remain richly proud. Guido, in
his harmonious version of it, saw no further. But from the depths of
the imaginative spirit Titian has recalled past time, and laid it
contributory with the present to one simultaneous effect. With the
desert all ringing with the mad cymbals of his followers, made lucid
with the presence and new offers of a god,--as if unconscious of
Bacchus, or but idly casting her eyes as upon some unconcerning
pageant--her soul undistracted from Theseus--Ariadne is still pacing
the solitary shore, in as much heart-silence, and in almost the same
local solitude, with which she awoke at day-break to catch the forlorn
last glances of the sail that bore away the Athenian.
Here are two points miraculously co-uniting; fierce society, with
the feeling of solitude still absolute; noon-day revelations, with
the accidents of the dull grey dawn unquenched and lingering; the
_present_ Bacchus, with the _past_ Ariadne; two stories, with double
Time; separate, and harmonising. Had the artist made the woman one
shade less indifferent to the God; still more, had she expressed a
rapture at his advent, where would have been the story of the mighty
desolation of the heart previous? merged in the insipid accident of a
flattering offer met with a welcome acceptance. The broken heart for
Theseus was not lightly to be pieced up by a God.
We have before us a fine rough print, from a picture by Raphael in
the Vatican. It is the Presentation of the newborn Eve to Adam by the
Almighty. A fairer mother of mankind we might imagine, and a goodlier
sire perhaps of men since born. But these are matters subordinate to
the conception of the _situation_, displayed in this extraordinary
production. A tolerably modern artist would have been satisfied with
tempering certain raptures of connubial anticipation, with a suitable
acknowledgment to the Giver of the blessing, in the countenance of the
first bridegroom; something like the divided attention of the child
(Adam was here a child man) between the given toy, and the mother
who had just blest it with the bauble. This is the obvious, the
first-sight view, the superficial. An artist of a higher grade,
considering the awful presence they were in, would have taken care
to subtract something from the expression of the more human passion,
and to heighten the more spiritual one. This would be as much as an
exhibition-goer, from the opening of Somerset House to last year's
show, has been encouraged to look for. It is obvious to hint at a
lower expression, yet in a picture, that for respects of drawing
and colouring, might be deemed not wholly inadmissible within these
art-fostering walls, in which the raptures should be as ninety-nine,
the gratitude as one, or perhaps Zero! By neither the one passion nor
the other has Raphael expounded the situation of Adam. Singly upon his
brow sits the absorbing sense of wonder at the created miracle. The
_moment_ is seized by the intuitive artist, perhaps not self-conscious
of his art, in which neither of the conflicting emotions--a moment how
abstracted--have had time to spring up, or to battle for indecorous
mastery.--We have seen a landscape of a justly admired neoteric, in
which he aimed at delineating a fiction, one of the most severely
beautiful in antiquity--the gardens of the Hesperides. To do Mr. ----
justice, he had painted a laudable orchard, with fitting seclusion,
and a veritable dragon (of which a Polypheme by Poussin is somehow a
fac-simile for the situation), looking over into the world shut out
backwards, so that none but a "still-climbing Hercules" could hope to
catch a peep at the admired Ternary of Recluses. No conventual porter
could keep his keys better than this custos with the "lidless eyes."
He not only sees that none _do_ intrude into that privacy, but, as
clear as daylight, that none but _Hercules aut Diabolus_ by any manner
of means _can_. So far all is well. We have absolute solitude here
or nowhere. _Ab extra_ the damsels are snug enough. But here the
artist's courage seems to have failed him. He began to pity his pretty
charge, and, to comfort the irksomeness, has peopled their solitude
with a bevy of fair attendants, maids of honour, or ladies of the
bed-chamber, according to the approved etiquette at a court of the
nineteenth century; giving to the whole scene the air of a _fete
champetre_, if we will but excuse the absence of the gentlemen.
This is well, and Watteauish. But what is become of the solitary
mystery--the
Daughters three,
That sing around the golden tree?
This is not the way in which Poussin would have treated this subject.
The paintings, or rather the stupendous architectural designs, of a
modern artist, have been urged as objections to the theory of our
motto. They are of a character, we confess, to stagger it. His towered
structures are of the highest order of the material sublime. Whether
they were dreams, or transcripts of some elder workmanship--Assyrian
ruins old--restored by this mighty artist, they satisfy our most
stretched and craving conceptions of the glories of the antique
world. It is a pity that they were ever peopled. On that side, the
imagination of the artist halts, and appears defective. Let us examine
the point of the story in the "Belshazzar's Feast." We will introduce
it by an apposite anecdote.
The court historians of the day record, that at the first dinner given
by the late King (then Prince Regent) at the Pavilion, the following
characteristic frolic was played off. The guests were select and
admiring; the banquet profuse and admirable; the lights lustrous and
oriental; the eye was perfectly dazzled with the display of plate,
among which the great gold salt-cellar, brought from the regalia in
the Tower for this especial purpose, itself a tower! stood conspicuous
for its magnitude. And now the Rev. **** the then admired court
Chaplain, was proceeding with the grace, when, at a signal given, the
lights were suddenly overcast, and a huge transparency was discovered,
in which glittered in golden letters--
"BRIGHTON-EARTHQUAKE-SWALLOW-UP-ALIVE!"
Imagine the confusion of the guests; the Georges and garters, jewels,
bracelets, moulted upon the occasion! The fans dropt, and picked up
the next morning by the sly court pages! Mrs. Fitz-what's-her-name
fainting, and the Countess of **** holding the smelling bottle,
till the good-humoured Prince caused harmony to be restored by calling
in fresh candles, and declaring that the whole was nothing but a
pantomime _hoax_, got up by the ingenious Mr. Farley, of Covent
Garden, from hints which his Royal Highness himself had furnished!
Then imagine the infinite applause that followed, the mutual
rallyings, the declarations that "they were not much frightened," of
the assembled galaxy.
The point of time in the picture exactly answers to the appearance of
the transparency in the anecdote. The huddle, the flutter, the bustle,
the escape, the alarm, and the mock alarm; the prettinesses heightened
by consternation; the courtier's fear which was flattery, and the
lady's which was affectation; all that we may conceive to have taken
place in a mob of Brighton courtiers, sympathising with the well-acted
surprise of their sovereign; all this, and no more, is exhibited by
the well-dressed lords and ladies in the Hall of Belus. Just this sort
of consternation we have seen among a flock of disquieted wild geese
at the report only of a gun having gone off!
But is this vulgar fright, this mere animal anxiety for the
preservation of their persons,--such as we have witnessed at a
theatre, when a slight alarm of fire has been given--an adequate
exponent of a supernatural terror? the way in which the finger of God,
writing judgments, would have been met by the withered conscience?
There is a human fear, and a divine fear. The one is disturbed,
restless, and bent upon escape. The other is bowed down, effortless,
passive. When the spirit appeared before Eliphaz in the visions of the
night, and the hair of his flesh stood up, was it in the thoughts
of the Temanite to ring the bell of his chamber, or to call up the
servants? But let us see in the text what there is to justify all this
huddle of vulgar consternation.
From the words of Daniel it appears that Belshazzar had made a great
feast to a thousand of his lords, and drank wine before the thousand.
The golden and silver vessels are gorgeously enumerated, with the
princes, the king's concubines, and his wives. Then follows--
"In the same hour came forth fingers of a man's hand, and wrote over
against the candlestick upon the plaster of the wall of the king's
palace; and the _king_ saw the part of the hand that wrote. Then the
_king's_ countenance was changed, and his thoughts troubled him, so
that the joints of his loins were loosened, and his knees smote one
against another."
This is the plain text. By no hint can it be otherwise inferred, but
that the appearance was solely confined to the fancy of Belshazzar,
that his single brain was troubled. Not a word is spoken of its being
seen by any else there present, not even by the queen herself, who
merely undertakes for the interpretation of the phenomenon, as related
to her, doubtless, by her husband. The lords are simply said to be
astonished; _i.e._ at the trouble and the change of countenance in
their sovereign. Even the prophet does not appear to have seen the
scroll, which the king saw. He recals it only, as Joseph did the Dream
to the King of Egypt. "Then was the part of the hand sent from him
[the Lord], and this writing was written." He speaks of the phantasm
as past.
Then what becomes of this needless multiplication of the miracle? this
message to a royal conscience, singly expressed--for it was said,
"thy kingdom is divided,"--simultaneously impressed upon the fancies
of a thousand courtiers, who were implied in it neither directly nor
grammatically? But admitting the artist's own version of the story,
and that the sight was seen also by the thousand courtiers--let it
have been visible to all Babylon--as the knees of Belshazzar were
shaken, and his countenance troubled, even so would the knees of every
man in Babylon, and their countenances, as of an individual man, been
troubled; bowed, bent down, so would they have remained, stupor-fixed,
with no thought of struggling with that inevitable judgment.
Not all that is optically possible to be seen, is to be shown in every
picture. The eye delightedly dwells upon the brilliant individualities
in a "Marriage at Cana," by Veronese, or Titian, to the very texture
and colour of the wedding garments, the ring glittering upon the
bride's fingers, the metal and fashion of the wine pots; for at such
seasons there is leisure and luxury to be curious. But in a "day of
judgment," or in a "day of lesser horrors, yet divine," as at the
impious feast of Belshazzar, the eye should see, as the actual eye of
an agent or patient in the immediate scene would see, only in masses
and indistinction. Not only the female attire and jewelry exposed
to the critical eye of the fashion, as minutely as the dresses in
a lady's magazine, in the criticised picture,--but perhaps the
curiosities of anatomical science, and studied diversities of posture
in the falling angels and sinners of Michael Angelo,--have no business
in their great subjects. There was no leisure of them.
By a wise falsification, the great masters of painting got at their
true conclusions; by not showing the actual appearances, that is, all
that was to be seen at any given moment by an indifferent eye, but
only what the eye might be supposed to see in the doing or suffering
of some portentous action. Suppose the moment of the swallowing up of
Pompeii. There they were to be seen--houses, columns, architectural
proportions, differences of public and private buildings, men and
women at their standing occupations, the diversified thousand
postures, attitudes, dresses, in some confusion truly, but physically
they were visible. But what eye saw them at that eclipsing moment,
which reduces confusion to a kind of unity, and when the senses
are upturned from their proprieties, when sight and hearing are a
feeling only? A thousand years have passed, and we are at leisure to
contemplate the weaver fixed standing at his shuttle, the baker at his
oven, and to turn over with antiquarian coolness the pots and pans of
Pompeii.
"Sun, stand thou still upon Gibeah, and thou, Moon, in the valley of
Ajalon." Who, in reading this magnificent Hebraism, in his conception,
sees aught but the heroic son of Nun, with the out-stretched arm,
and the greater and lesser light obsequious? Doubtless there were to
be seen hill and dale, and chariots and horsemen, on open plain, or
winding by secret defiles, and all the circumstances and stratagems
of war. But whose eyes would have been conscious of this array at the
interposition of the synchronic miracle? Yet in the picture of this
subject by the artist of the "Belshazzar's Feast"--no ignoble work
either--the marshalling and landscape of the war is everything, the
miracle sinks into an anecdote of the day; and the eye may "dart
through rank and file traverse" for some minutes, before it shall
discover, among his armed followers, _which is Joshua_! Not modern art
alone, but ancient, where only it is to be found if anywhere, can be
detected erring, from defect of this imaginative faculty. The world
has nothing to show of the preternatural in painting, transcending the
figure of Lazarus bursting his grave-clothes, in the great picture at
Angerstein's. It seems a thing between two beings. A ghastly horror
at itself struggles with newly-apprehending gratitude at second life
bestowed. It cannot forget that it was a ghost. It has hardly felt
that it is a body. It has to tell of the world of spirits.--Was it
from a feeling, that the crowd of half-impassioned by-standers, and
the still more irrelevant herd of passers-by at a distance, who have
not heard or but faintly have been told of the passing miracle,
admirable as they are in design and hue--for it is a glorified
work--do not respond adequately to the action--that the single figure
of the Lazarus has been attributed to Michael Angelo, and the mighty
Sebastian unfairly robbed of the fame of the greater half of the
interest? Now that there were not indifferent passers-by within actual
scope of the eyes of those present at the miracle, to whom the sound
of it had but faintly, or not at all, reached, it would be hardihood
to deny; but would they see them? or can the mind in the conception of
it admit of such unconcerning objects? can it think of them at all? or
what associating league to the imagination can there be between the
seers, and the seers not, of a presential miracle?
Were an artist to paint upon demand a picture of a Dryad, we will ask
whether, in the present low state of expectation, the patron would
not, or ought not to be fully satisfied with a beautiful naked figure
recumbent under wide-stretched oaks? Disseat those woods, and place
the same figure among fountains, and falls of pellucid water, and
you have a--Naiad! Not so in a rough print we have seen after Julio
Romano, we think--for it is long since--_there_, by no process, with
mere change of scene, could the figure have reciprocated characters.
Long, grotesque, fantastic, yet with a grace of her own, beautiful in
convolution and distortion, linked to her connatural tree, co-twisting
with its limbs her own, till both seemed either--these, animated
branches; those, disanimated members--yet the animal and vegetable
lives sufficiently kept distinct--_his_ Dryad lay--an approximation of
two natures, which to conceive, it must be seen; analogous to, not the
same with, the delicacies of Ovidian transformations.
To the lowest subjects, and, to a superficial comprehension, the
most barren, the Great Masters gave loftiness and fruitfulness. The
large eye of genius saw in the meanness of present objects their
capabilities of treatment from their relations to some grand
Past or Future. How has Raphael--we must still linger about the
Vatican--treated the humble craft of the ship-builder, in _his_
"Building of the Ark?" It is in that scriptural series, to which we
have referred, and which, judging from some fine rough old graphic
sketches of them which we possess, seem to be of a higher and more
poetic grade than even the Cartoons. The dim of sight are the
timid and the shrinking. There is a cowardice in modern art. As
the Frenchmen, of whom Coleridge's friend made the prophetic guess
at Rome, from the beard and horns of the Moses of Michael Angelo
collected no inferences beyond that of a He Goat and a Cornuto; so
from this subject, of mere mechanic promise, it would instinctively
turn away, as from one incapable of investiture with any grandeur. The
dock-yards at Woolwich would object derogatory associations. The depot
at Chatham would be the mote and the beam in its intellectual eye. But
not to the nautical preparations in the ship-yards of Civita Vecchia
did Raphael look for instructions, when he imagined the Building of
the Vessel that was to be conservatory of the wrecks of the species of
drowned mankind. In the intensity of the action, he keeps ever out of
sight the meanness of the operation. There is the Patriarch, in calm
forethought, and with holy prescience, giving directions. And there
are his agents--the solitary but sufficient Three--hewing, sawing,
every one with the might and earnestness of a Demiurgus; under some
instinctive rather than technical guidance; giant-muscled; every one a
Hercules, or liker to those Vulcanian Three, that in sounding caverns
under Mongibello wrought in fire--Brontes, and black Steropes, and
Pyracmon. So work the workmen that should repair a world!
Artists again err in the confounding of _poetic_ with _pictorial
subjects_. In the latter, the exterior accidents are nearly
everything, the unseen qualities as nothing. Othello's colour--the
infirmities and corpulence of a Sir John Falstaff--do they haunt us
perpetually in the reading? or are they obtruded upon our conceptions
one time for ninety-nine that we are lost in admiration at the
respective moral or intellectual attributes of the character? But in
a picture Othello is _always_ a Blackamoor; and the other only Plump
Jack. Deeply corporealised, and enchained hopelessly in the grovelling
fetters of externality, must be the mind, to which, in its better
moments, the image of the high-souled, high-intelligenced Quixote--the
errant Star of Knighthood, made more tender by eclipse--has never
presented itself, divested from the unhallowed accompaniment of a
Sancho, or a rabblement at the heels of Rosinante. That man has read
his book by halves; he has laughed, mistaking his author's purport,
which was--tears. The artist that pictures Quixote (and it is in this
degrading point that he is every season held up at our Exhibitions)
in the shallow hope of exciting mirth, would have joined the rabble
at the heels of his starved steed. We wish not to see _that_
counterfeited, which we would not have wished to see in the reality.
Conscious of the heroic inside of the noble Quixote, who, on hearing
that his withered person was passing, would have stepped over his
threshold to gaze upon his forlorn habiliments, and the "strange
bed-fellows which misery brings a man acquainted with?" Shade of
Cervantes! who in thy Second Part could put into the mouth of thy
Quixote those high aspirations of a super-chivalrous gallantry, where
he replies to one of the shepherdesses, apprehensive that he would
spoil their pretty networks, and inviting him to be a guest with them,
in accents like these: "Truly, fairest Lady, Actaeon was not more
astonished when he saw Diana bathing herself at the fountain, than
I have been in beholding your beauty: I commend the manner of your
pastime, and thank you for your kind offers; and, if I may serve
you, so I may be sure you will be obeyed, you may command me: for my
profession is this, To shew myself thankful, and a doer of good to all
sorts of people, especially of the rank that your person shows you to
be; and if those nets, as they take up but a little piece of ground,
should take up the whole world, I would seek out new worlds to pass
through, rather than break them: and (he adds,) that you may give
credit to this my exaggeration, behold at least he that promiseth you
this, is Don Quixote de la Mancha, if haply this name hath come to
your hearing." Illustrious Romancer! were the "fine frenzies," which
possessed the brain of thy own Quixote, a fit subject, as in this
Second Part, to be exposed to the jeers of Duennas and Serving Men? to
be monstered, and shown up at the heartless banquets of great men? Was
that pitiable infirmity, which in thy First Part misleads him, _always
from within_, into half-ludicrous, but more than half-compassionable
and admirable errors, not infliction enough from heaven, that men by
studied artifices must devise and practise upon the humour, to inflame
where they should soothe it? Why, Goneril would have blushed to
practise upon the abdicated king at this rate, and the she-wolf Regan
not have endured to play the pranks upon his fled wits, which thou
hast made thy Quixote suffer in Duchesses' halls, and at the hands of
that unworthy nobleman.[1]
In the First Adventures, even, it needed all the art of the most
consummate artist in the Book way that the world hath yet seen,
to keep up in the mind of the reader the heroic attributes of the
character without relaxing; so as absolutely that they shall suffer no
alloy from the debasing fellowship of the clown. If it ever obtrudes
itself as a disharmony, are we inclined to laugh; or not, rather,
to indulge a contrary emotion?--Cervantes, stung, perchance, by the
relish with which _his_ Reading Public had received the fooleries of
the man, more to their palates than the generosities of the master, in
the sequel let his pen run riot, lost the harmony and the balance, and
sacrificed a great idea to the taste of his contemporaries. We know
that in the present day the Knight has fewer admirers than the Squire.
Anticipating, what did actually happen to him--as afterwards it did
to his scarce inferior follower, the Author of "Guzman de
Alfarache"--that some less knowing hand would prevent him by a
spurious Second Part: and judging, that it would be easier for his
competitor to out-bid him in the comicalities, than in the _romance_,
of his work, he abandoned his Knight, and has fairly set up the Squire
for his Hero. For what else has he unsealed the eyes of Sancho; and
instead of that twilight state of semi-insanity--the madness at
second-hand--the contagion, caught from a stronger mind infected--that
war between native cunning, and hereditary deference, with which he
has hitherto accompanied his master--two for a pair almost--does he
substitute a downright Knave, with open eyes, for his own ends only
following a confessed Madman; and offering at one time to lay, if not
actually laying, hands upon him! From the moment that Sancho loses his
reverence, Don Quixote is become a--treatable lunatic. Our artists
handle him accordingly.
[Footnote 1: Yet from this Second Part, our cried-up pictures are
mostly selected; the waiting-women with beards, &c.]
REJOICINGS UPON THE NEW YEAR'S COMING OF AGE
The _Old Year_ being dead, and the _New Year_ coming of age, which
he does, by Calendar Law, as soon as the breath is out of the old
gentleman's body, nothing would serve the young spark but he must
give a dinner upon the occasion, to which all the _Days_ in the year
were invited. The _Festivals_, whom he deputed as his stewards, were
mightily taken with the notion. They had been engaged time out of
mind, they said, in providing mirth and good cheer for mortals below;
and it was time they should have a taste of their own bounty. It was
stiffly debated among them, whether the _Fasts_ should be admitted.
Some said, the appearance of such lean, starved guests, with their
mortified faces, would pervert the ends of the meeting. But the
objection was over-ruled by _Christmas Day_, who had a design upon
_Ash Wednesday_ (as you shall hear), and a mighty desire to see how
the old Domine would behave himself in his cups. Only the _Vigils_
were requested to come with their lanterns, to light the gentlefolks
home at night.
All the _Days_ came to their day. Covers were provided for three
hundred and sixty-five guests at the principal table: with an
occasional knife and fork at the side-board for the _Twenty-Ninth of
February_.
I should have told you, that cards of invitation had been issued. The
carriers were the _Hours_; twelve little, merry, whirligig foot-pages,
as you should desire to see, that went all round, and found out the
persons invited well enough, with the exception of _Easter Day_,
_Shrove Tuesday_, and a few such _Moveables_, who had lately shifted
their quarters.
Well, they all met at last, foul _Days_, fine _Days_, all sorts of
_Days_, and a rare din they made of it. There was nothing but, Hail!
fellow _Day_,--well met--brother _Day_--sister _Day_,--only _Lady Day_
kept a little on the aloof, and seemed somewhat scornful. Yet some
said, _Twelfth Day_ cut her out and out, for she came in a tiffany
suit, white and gold, like a queen on a frost-cake, all royal,
glittering, and _Epiphanous_. The rest came, some in green, some in
white--but old _Lent and his family_ were not yet out of mourning.
Rainy _Days_ came in, dripping; and sun-shiny _Days_ helped them
to change their stockings. _Wedding Day_ was there in his marriage
finery, a little the worse for wear. _Pay Day_ came late, as he always
does; and _Doomsday_ sent word--he might be expected.
_April Fool_ (as my young lord's jester) took upon himself to marshal
the guests, and wild work he made with it. It would have posed old
Erra Pater to have found out any given _Day_ in the year, to erect a
scheme upon--good _Days_, bad _Days_, were so shuffled together, to
the confounding of all sober horoscopy.
He had stuck the _Twenty First of June_ next to the _Twenty Second of
December_, and the former looked like a Maypole siding a marrow-bone.
_Ash Wednesday_ got wedged in (as was concerted) betwixt _Christmas_
and _Lord Mayor's Days_. Lord! how he laid about him! Nothing but
barons of beef and turkeys would go down with him--to the great
greasing and detriment of his new sackcloth bib and tucker. And still
_Christmas Day_ was at his elbow, plying him the wassail-bowl, till
he roared, and hiccup'd, and protested there was no faith in dried
ling, but commended it to the devil for a sour, windy, acrimonious,
censorious, hy-po-crit-crit-cri-tical mess, and no dish for a
gentleman. Then he dipt his fist into the middle of the great custard
that stood before his _left-hand neighbour_, and daubed his hungry
beard all over with it, till you would have taken him for the _Last
Day in December_, it so hung in icicles.
At another part of the table, _Shrove Tuesday_ was helping the _Second
of September_ to some cock broth,--which courtesy the latter returned
with the delicate thigh of a hen pheasant--so there was no love lost
for that matter. The _Last of Lent_ was spunging upon _Shrovetide's_
pancakes; which _April Fool_ perceiving, told him he did well, for
pancakes were proper to a _good fry-day_.
In another part, a hubbub arose about the _Thirtieth of January_, who,
it seems, being a sour puritanic character, that thought nobody's meat
good or sanctified enough for him, had smuggled into the room a calf's
head, which he had had cooked at home for that purpose, thinking
to feast thereon incontinently; but as it lay in the dish, _March
manyweathers_, who is a very fine lady, and subject to the megrims,
screamed out there was a "human head in the platter," and raved about
Herodias' daughter to that degree, that the obnoxious viand was
obliged to be removed; nor did she recover her stomach till she had
gulped down a _Restorative_, confected of _Oak Apple_, which the merry
_Twenty Ninth of May_ always carries about with him for that purpose.
The King's health[1] being called for after this, a notable
dispute arose between the _Twelfth of August_ (a zealous old Whig
gentlewoman,) and the _Twenty Third of April_ (a new-fangled lady of
the Tory stamp,) as to which of them should have the honour to propose
it. _August_ grew hot upon the matter, affirming time out of mind the
prescriptive right to have lain with her, till her rival had basely
supplanted her; whom she represented as little better than a _kept_
mistress, who went about in _fine clothes_, while she (the legitimate
BIRTHDAY) had scarcely a rag, &c.
_April fool_, being made mediator, confirmed the right in the
strongest form of words to the appellant, but decided for peace' sake
that the exercise of it should remain with the present possessor. At
the same time, he slily rounded the first lady in the ear, that an
action might lie against the Crown for _bi-geny_.
It beginning to grow a little duskish, _Candlemas_ lustily bawled out
for lights, which was opposed by all the _Days_, who protested against
burning daylight. Then fair water was handed round in silver ewers,
and the _same lady_ was observed to take an unusual time in _Washing_
herself.
_May Day_, with that sweetness which is peculiar to her, in a neat
speech proposing the health of the founder, crowned her goblet (and by
her example the rest of the company) with garlands. This being done,
the lordly _New Year_ from the upper end of the table, in a cordial
but somewhat lofty tone, returned thanks. He felt proud on an occasion
of meeting so many of his worthy father's late tenants, promised to
improve their farms, and at the same time to abate (if any thing was
found unreasonable) in their rents.
At the mention of this, the four _Quarter Days_ involuntarily looked
at each other, and smiled; _April Fool_ whistled to an old tune of
"New Brooms;" and a surly old rebel at the farther end of the table
(who was discovered to be no other than the _Fifth of November_,)
muttered out, distinctly enough to be heard by the whole company,
words to this effect, that, "when the old one is gone, he is a fool
that looks for a better." Which rudeness of his, the guests resenting,
unanimously voted his expulsion; and the male-content was thrust out
neck and heels into the cellar, as the properest place for such a
_boutefeu_ and firebrand as he had shown himself to be.
Order being restored--the young lord (who to say truth, had been a
little ruffled, and put beside his oratory) in as few, and yet as
obliging words as possible, assured them of entire welcome; and, with
a graceful turn, singling out poor _Twenty Ninth of February_, that
had sate all this while mumchance at the side-board, begged to couple
his health with that of the good company before him--which he drank
accordingly; observing, that he had not seen his honest face any time
these four years, with a number of endearing expressions besides. At
the same time, removing the solitary _Day_ from the forlorn seat which
had been assigned him, he stationed him at his own board, somewhere
between the _Greek Calends_ and _Latter Lammas_.
_Ash Wednesday_, being now called upon for a song, with his eyes fast
stuck in his head, and as well as the Canary he had swallowed would
give him leave, struck up a Carol, which _Christmas Day_ had taught
him for the nonce; and was followed by the latter, who gave "Miserere"
in fine style, hitting off the mumping notes and lengthened drawl of
_Old Mortification_ with infinite humour. _April Fool_ swore they had
exchanged conditions: but _Good Friday_ was observed to look extremely
grave; and _Sunday_ held her fan before her face, that she might not
be seen to smile.
_Shrove-tide_, _Lord Mayor's Day_, and _April Fool_, next joined in a
glee--
Which is the properest day to drink?
in which all the _Days_ chiming in, made a merry burden.
They next fell to quibbles and conundrums. The question being
proposed, who had the greatest number of followers--the _Quarter Days_
said, there could be no question as to that; for they had all the
creditors in the world dogging their heels. But _April Fool_ gave it
in favour of the _Forty Days before Easter_; because the debtors in
all cases outnumbered the creditors, and they kept _lent_ all the
year.
All this while, _Valentine's Day_ kept courting pretty _May_, who sate
next him, slipping amorous _billets-doux_ under the table, till the
_Dog Days_ (who are naturally of a warm constitution) began to be
jealous, and to bark and rage exceedingly. _April Fool_, who likes
a bit of sport above measure, and had some pretensions to the lady
besides, as being but a cousin once removed,--clapped and halloo'd
them on; and as fast as their indignation cooled, those mad wags, the
_Ember Days_, were at it with their bellows, to blow it into a flame;
and all was in a ferment: till old Madam _Septuagesima_ (who boasts
herself the _Mother of the Days_) wisely diverted the conversation
with a tedious tale of the lovers which she could reckon when she was
young; and of one Master _Rogation Day_ in particular, who was for
ever putting the _question_ to her; but she kept him at a distance, as
the chronicle would tell--by which I apprehend she meant the Almanack.
Then she rambled on to the _Days that were gone_, the _good old Days_,
and so to the _Days before the Flood_--which plainly showed her old
head to be little better than crazed and doited.
Day being ended, the _Days_ called for their cloaks and great coats,
and took their leaves. _Lord Mayor's Day_ went off in a Mist, as
usual; _Shortest Day_ in a deep black Fog, that wrapt the little
gentleman all round like a hedge-hog. Two _Vigils_--so watchmen are
called in heaven--saw _Christmas Day_ safe home--they had been used to
the business before. Another _Vigil_--a stout, sturdy patrole, called
the _Eve of St. Christopher_--seeing _Ash Wednesday_ in a condition
little better than he should be--e'en whipt him over his shoulders,
pick-a-back fashion, and _Old Mortification_ went floating home,
singing--
On the bat's back do I fly,
and a number of old snatches besides, between drunk and sober, but
very few Aves or Penitentiaries (you may believe me) were among them.
_Longest Day_ set off westward in beautiful crimson and gold--the
rest, some in one fashion, some in another; but _Valentine_ and pretty
_May_ took their departure together in one of the prettiest silvery
twilights a Lover's Day could wish to set in.
[Footnote 1: The late King.]
THE WEDDING
I do not know when I have been better pleased than at being invited
last week to be present at the wedding of a friend's daughter. I like
to make one at these ceremonies, which to us old people give back our
youth in a manner, and restore our gayest season, in the remembrance
of our own success, or the regrets, scarcely less tender, of our own
youthful disappointments, in this point of a settlement. On these
occasions I am sure to be in good-humour for a week or two after, and
enjoy a reflected honey-moon. Being without a family, I am flattered
with these temporary adoptions into a friend's family; I feel a
sort of cousinhood, or uncleship, for the season; I am inducted
into degrees of affinity; and, in the participated socialities of
the little community, I lay down for a brief while my solitary
bachelorship. I carry this humour so far, that I take it unkindly to
be left out, even when a funeral is going on in the house of a dear
friend. But to my subject.--
The union itself had been long settled, but its celebration had been
hitherto deferred, to an almost unreasonable state of suspense in the
lovers, by some invincible prejudices which the bride's father had
unhappily contracted upon the subject of the too early marriages of
females. He has been lecturing any time these five years--for to
that length the courtship has been protracted--upon the propriety of
putting off the solemnity, till the lady should have completed her
five and twentieth year. We all began to be afraid that a suit, which
as yet had abated of none of its ardours, might at last be lingered
on, till passion had time to cool, and love go out in the experiment.
But a little wheedling on the part of his wife, who was by no means
a party to these overstrained notions, joined to some serious
expostulations on that of his friends, who, from the growing
infirmities of the old gentleman, could not promise ourselves many
years' enjoyment of his company, and were anxious to bring matters to
a conclusion during his life-time, at length prevailed; and on Monday
last the daughter of my old friend, Admiral ---- having attained the
_womanly_ age of nineteen, was conducted to the church by her pleasant
cousin J----, who told some few years older.
Before the youthful part of my female readers express their
indignation at the abominable loss of time occasioned to the lovers
by the preposterous notions of my old friend, they will do well to
consider the reluctance which a fond parent naturally feels at parting
with his child. To this unwillingness, I believe, in most cases may
be traced the difference of opinion on this point between child and
parent, whatever pretences of interest or prudence may be held out to
cover it. The hard-heartedness of fathers is a fine theme for romance
writers, a sure and moving topic; but is there not something untender,
to say no more of it, in the hurry which a beloved child is sometimes
in to tear herself from the parental stock, and commit herself to
strange graftings? The case is heightened where the lady, as in the
present instance, happens to be an only child. I do not understand
these matters experimentally, but I can make a shrewd guess at
the wounded pride of a parent upon these occasions. It is no new
observation, I believe, that a lover in most cases has no rival so
much to be feared as the father. Certainly there is a jealousy in
_unparallel subjects_, which is little less heart-rending than the
passion which we more strictly christen by that name. Mothers'
scruples are more easily got over; for this reason, I suppose, that
the protection transferred to a husband is less a derogation and a
loss to their authority than to the paternal. Mothers, besides, have a
trembling foresight, which paints the inconveniences (impossible to be
conceived in the same degree by the other parent) of a life of forlorn
celibacy, which the refusal of a tolerable match may entail upon
their child. Mothers' instinct is a surer guide here, than the cold
reasonings of a father on such a topic. To this instinct may be
imputed, and by it alone may be excused, the unbeseeming artifices, by
which some wives push on the matrimonial projects of their daughters,
which the husband, however approving, shall entertain with comparative
indifference. A little shamelessness on this head is pardonable.
With this explanation, forwardness becomes a grace, and maternal
importunity receives the name of a virtue.--But the parson stays,
while I preposterously assume his office; I am preaching, while the
bride is on the threshold.
Nor let any of my female readers suppose that the sage reflections
which have just escaped me have the obliquest tendency of application
to the young lady, who, it will be seen, is about to venture upon a
change in her condition, at a _mature and competent age_, and not
without the fullest approbation of all parties. I only deprecate _very
hasty marriages_.
It had been fixed that the ceremony should be gone through at an early
hour, to give time for a little _dejeune_ afterwards, to which a
select party of friends had been invited. We were in church a little
before the clock struck eight.
Nothing could be more judicious or graceful than the dress of the
bride-maids--the three charming Miss Foresters--on this morning. To
give the bride an opportunity of shining singly, they had come habited
all in green. I am ill at describing female apparel; but, while _she_
stood at the altar in vestments white and candid as her thoughts, a
sacrificial whiteness, _they_ assisted in robes, such as might become
Diana's nymphs--Foresters indeed--as such who had not yet come to the
resolution of putting off cold virginity. These young maids, not being
so blest as to have a mother living, I am told, keep single for their
father's sake, and live altogether so happy with their remaining
parent, that the hearts of their lovers are ever broken with the
prospect (so inauspicious to their hopes) of such uninterrupted
and provoking home-comfort. Gallant girls! each a victim worthy of
Iphigenia!
I do not know what business I have to be present in solemn places. I
cannot divest me of an unseasonable disposition to levity upon the
most awful occasions. I was never cut out for a public functionary.
Ceremony and I have long shaken hands; but I could not resist the
importunities of the young lady's father, whose gout unhappily
confined him at home, to act as parent on this occasion, and _give
away the bride._ Something ludicrous occurred to me at this most
serious of all moments--a sense of my unfitness to have the disposal,
even in imagination, of the sweet young creature beside me. I fear I
was betrayed to some lightness, for the awful eye of the parson--and
the rector's eye of Saint Mildred's in the Poultry is no trifle of a
rebuke--was upon me in an instant, souring my incipient jest to the
tristful severities of a funeral.
This was the only misbehaviour which I can plead to upon this solemn
occasion, unless what was objected to me after the ceremony by one of
the handsome Miss T----s, be accounted a solecism. She was pleased to
say that she had never seen a gentleman before me give away a bride in
black. Now black has been my ordinary apparel so long--indeed I take
it to be the proper costume of an author--the stage sanctions it--that
to have appeared in some lighter colour would have raised more mirth
at my expense, than the anomaly had created censure. But I could
perceive that the bride's mother, and some elderly ladies present (God
bless them!) would have been well content, if I had come in any other
colour than that. But I got over the omen by a lucky apologue, which
I remembered out of Pilpay, or some Indian author, of all the birds
being invited to the linnets' wedding, at which, when all the rest
came in their gayest feathers, the raven alone apologised for his
cloak because "he had no other." This tolerably reconciled the elders.
But with the young people all was merriment, and shakings of hands,
and congratulations, and kissing away the bride's tears, and kissings
from her in return, till a young lady, who assumed some experience in
these matters, having worn the nuptial bands some four or five weeks
longer than her friend, rescued her, archly observing, with half an
eye upon the bridegroom, that at this rate she would have "none left."
My friend the admiral was in fine wig and buckle on this occasion--a
striking contrast to his usual neglect of personal appearance. He did
not once shove up his borrowed locks (his custom ever at his morning
studies) to betray the few grey stragglers of his own beneath them.
He wore an aspect of thoughtful satisfaction. I trembled for the
hour, which at length approached, when after a protracted _breakfast_
of three hours--if stores of cold fowls, tongues, hams, botargoes,
dried fruits, wines, cordials, &c., can deserve so meagre an
appellation--the coach was announced, which was come to carry off the
bride and bridegroom for a season, as custom has sensibly ordained,
into the country; upon which design, wishing them a felicitous
journey, let us return to the assembled guests.
As when a well-graced actor leaves the stage,
The eyes of men
Are idly bent on him that enters next,
so idly did we bend our eyes upon one another, when the chief
performers in the morning's pageant had vanished. None told his tale.
None sipt her glass. The poor Admiral made an effort--it was not much.
I had anticipated so far. Even the infinity of full satisfaction, that
had betrayed itself through the prim looks and quiet deportment of his
lady, began to wane into something of misgiving. No one knew whether
to take their leaves or stay. We seemed assembled upon a silly
occasion. In this crisis, betwixt tarrying and departure, I must do
justice to a foolish talent of mine, which had otherwise like to
have brought me into disgrace in the fore-part of the day; I mean a
power, in any emergency, of thinking and giving vent to all manner
of strange nonsense. In this awkward dilemma I found it sovereign. I
rattled off some of my most excellent absurdities. All were willing
to be relieved, at any expense of reason, from the pressure of the
intolerable vacuum which had succeeded to the morning bustle. By this
means I was fortunate in keeping together the better part of the
company to a late hour: and a rubber of whist (the Admiral's favourite
game) with some rare strokes of chance as well as skill, which came
opportunely on his side--lengthened out till midnight--dismissed the
old gentleman at last to his bed with comparatively easy spirits.
I have been at my old friend's various times since. I do not know a
visiting place where every guest is so perfectly at his ease; nowhere,
where harmony is so strangely the result of confusion. Every body is
at cross purposes, yet the effect is so much better than uniformity.
Contradictory orders; servants pulling one way; master and mistress
driving some other, yet both diverse; visitors huddled up in corners;
chairs unsymmetrised; candles disposed by chance; meals at odd hours,
tea and supper at once, or the latter preceding the former; the host
and the guest conferring, yet each upon a different topic, each
understanding himself, neither trying to understand or hear the
other; draughts and politics, chess and political economy, cards and
conversation on nautical matters, going on at once, without the hope,
or indeed the wish, of distinguishing them, make it altogether the
most perfect _concordia discors_ you shall meet with. Yet somehow the
old house is not quite what it should be. The Admiral still enjoys
his pipe, but he has no Miss Emily to fill it for him. The instrument
stands where it stood, but she is gone, whose delicate touch could
sometimes for a short minute appease the warring elements. He has
learnt, as Marvel expresses it, to "make his destiny his choice." He
bears bravely up, but he does not come out with his flashes of wild
wit so thick as formerly. His sea songs seldomer escape him. His wife,
too, looks as if she wanted some younger body to scold and set to
rights. We all miss a junior presence. It is wonderful how one young
maiden freshens up, and keeps green, the paternal roof. Old and young
seem to have an interest in her, so long as she is not absolutely
disposed of. The youthfulness of the house is flown. Emily is married.
THE CHILD ANGEL
A DREAM
I chanced upon the prettiest, oddest, fantastical thing of a dream the
other night, that you shall hear of. I had been reading the "Loves
of the Angels," and went to bed with my head full of speculations,
suggested by that extraordinary legend. It had given birth to
innumerable conjectures; and, I remember, the last waking thought,
which I gave expression to on my pillow, was a sort of wonder, "what
could come of it."
I was suddenly transported, how or whither I could scarcely make
out--but to some celestial region. It was not the real heavens
neither--not the downright Bible heaven--but a kind of fairyland
heaven, about which a poor human fancy may have leave to sport and air
itself, I will hope, without presumption.
Methought--what wild things dreams are!--I was present--at what would
you imagine?--at an angel's gossiping.
Whence it came, or how it came, or who bid it come, or whether it came
purely of its own head, neither you nor I know--but there lay, sure
enough, wrapped in its little cloudy swaddling bands--a Child Angel.
Sun-threads--filmy beams--ran through the celestial napery of what
seemed its princely cradle. All the winged orders hovered round,
watching when the new-born should open its yet closed eyes; which,
when it did, first one, and then the other--with a solicitude and
apprehension, yet not such as, stained with fear, dims the expanding
eye-lids of mortal infants, but as if to explore its path in those
its unhereditary palaces--what an inextinguishable titter that time
spared not celestial visages! Nor wanted there to my seeming--O the
inexplicable simpleness of dreams!--bowls of that cheering nectar,
--which mortals _caudle_ call below--
Nor were wanting faces of female ministrants,--stricken in years,
as it might seem,--so dexterous were those heavenly attendants to
counterfeit kindly similitudes of earth, to greet, with terrestrial
child-rites the young _present_, which earth had made to heaven.
Then were celestial harpings heard, not in full symphony as those by
which the spheres are tutored; but, as loudest instruments on earth
speak oftentimes, muffled; so to accommodate their sound the better
to the weak ears of the imperfect-born. And, with the noise of those
subdued soundings, the Angelet sprang forth, fluttering its rudiments
of pinions--but forthwith flagged and was recovered into the arms of
those full-winged angels. And a wonder it was to see how, as years
went round in heaven--a year in dreams is as a day--continually its
white shoulders put forth buds of wings, but, wanting the perfect
angelic nutriment, anon was shorn of its aspiring, and fell
fluttering--still caught by angel hands--for ever to put forth shoots,
and to fall fluttering, because its birth was not of the unmixed
vigour of heaven.
And a name was given to the Babe Angel, and it was to be called
_Ge-Urania_, because its production was of earth and heaven.
And it could not taste of death, by reason of its adoption into
immortal palaces: but it was to know weakness, and reliance, and the
shadow of human imbecility; and it went with a lame gait; but in its
goings it exceeded all mortal children in grace and swiftness. Then
pity first sprang up in angelic bosoms; and yearnings (like the human)
touched them at the sight of the immortal lame one.
And with pain did then first those Intuitive Essences, with pain
and strife to their natures (not grief), put back their bright
intelligences, and reduce their ethereal minds, schooling them to
degrees and slower processes, so to adapt their lessons to the gradual
illumination (as must needs be) of the half-earth-born; and what
intuitive notices they could not repel (by reason that their nature
is, to know all things at once), the half-heavenly novice, by the
better part of its nature, aspired to receive into its understanding;
so that Humility and Aspiration went on even-paced in the instruction
of the glorious Amphibium.
But, by reason that Mature Humanity is too gross to breathe the air of
that super-subtile region, its portion was, and is, to be a child for
ever.
And because the human part of it might not press into the heart and
inwards of the palace of its adoption, those full-natured angels
tended it by turns in the purlieus of the palace, where were shady
groves and rivulets, like this green earth from which it came: so
Love, with Voluntary Humility, waited upon the entertainment of the
new-adopted.
And myriads of years rolled round (in dreams Time is nothing), and
still it kept, and is to keep, perpetual childhood, and is the Tutelar
Genius of Childhood upon earth, and still goes lame and lovely.
By the banks of the river Pison is seen, lone-sitting by the grave of
the terrestrial Adah, whom the angel Nadir loved, a Child; but not the
same which I saw in heaven. A mournful hue overcasts its lineaments;
nevertheless, a correspondency is between the child by the grave, and
that celestial orphan, whom I saw above; and the dimness of the grief
upon the heavenly, is as a shadow or emblem of that which stains
the beauty of the terrestrial. And this correspondency is not to be
understood but by dreams.
And in the archives of heaven I had grace to read, how that once
the angel Nadir, being exiled from his place for mortal passion,
upspringing on the wings of parental love (such power had parental
love for a moment to suspend the else-irrevocable law) appeared for
a brief instant in his station; and, depositing a wondrous Birth,
straightway disappeared, and the palaces knew him no more. And this
charge was the self-same Babe, who goeth lame and lovely--but Adah
sleepeth by the river Pison.
A DEATH-BED
IN A LETTER TO R.H. ESQ. OF B----
I called upon you this morning, and found that you were gone to visit
a dying friend. I had been upon a like errand. Poor N.R. has lain
dying now for almost a week; such is the penalty we pay for having
enjoyed through life a strong constitution. Whether he knew me or not,
I know not, or whether he saw me through his poor glazed eyes; but the
group I saw about him I shall not forget. Upon the bed, or about it,
were assembled his Wife, their two Daughters, and poor deaf Robert,
looking doubly stupified. There they were, and seemed to have been
sitting all the week. I could only reach out a hand to Mrs. R.
Speaking was impossible in that mute chamber. By this time it must be
all over with him. In him I have a loss the world cannot make up. He
was my friend, and my father's friend, for all the life that I can
remember. I seem to have made foolish friendships since. Those are the
friendships, which outlast a second generation. Old as I am getting,
in his eyes I was still the child he knew me. To the last he called
me Jemmy. I have none to call me Jemmy now. He was the last link that
bound me to B----. You are but of yesterday. In him I seem to have
lost the old plainness of manners and singleness of heart. Lettered
he was not; his reading scarcely exceeded the Obituary of the old
Gentleman's Magazine, to which he has never failed of having recourse
for these last fifty years. Yet there was the pride of literature
about him from that slender perusal; and moreover from his office of
archive-keeper to your ancient city, in which he must needs pick up
some equivocal Latin; which, among his less literary friends, assumed
the air of a very pleasant pedantry. Can I forget the erudite look
with which, having tried to puzzle out the text of a Black lettered
Chaucer in your Corporation Library, to which he was a sort of
Librarian, he gave it up with this consolatory reflection--"Jemmy,"
said he, "I do not know what you find in these very old books, but I
observe, there is a deal of very indifferent spelling in them." His
jokes (for he had some) are ended; but they were old Perennials,
staple, and always as good as new. He had one Song, that spake of the
"flat bottoms of our foes coming over in darkness," and alluded to a
threatened Invasion, many years since blown over; this he reserved to
be sung on Christmas Night, which we always passed with him, and he
sung it with the freshness of an impending event. How his eyes would
sparkle when he came to the passage:
We'll still make 'em run, and we'll still make 'em sweat,
In spite of the devil and Brussels' Gazette!
What is the Brussels' Gazette now? I cry, while I endite these
trifles. His poor girls who are, I believe, compact of solid goodness,
will have to receive their afflicted mother at an unsuccessful home
in a petty village in ----shire, where for years they have been
struggling to raise a Girls' School with no effect. Poor deaf Robert
(and the less hopeful for being so) is thrown upon a deaf world,
without the comfort to his father on his death-bed of knowing him
provided for. They are left almost provisionless. Some life assurance
there is; but, I fear, not exceeding ----. Their hopes must be from
your Corporation, which their father has served for fifty years. Who
or what are your Leading Members now, I know not. Is there any, to
whom without impertinence, you can represent the true circumstances of
the family? You cannot say good enough of poor R., and his poor wife.
Oblige me and the dead, if you can.
OLD CHINA
I have an almost feminine partiality for old china. When I go to see
any great house, I inquire for the china-closet, and next for the
picture gallery. I cannot defend the order of preference, but by
saying, that we have all some taste or other, of too ancient a date
to admit of our remembering distinctly that it was an acquired one. I
can call to mind the first play, and the first exhibition, that I was
taken to; but I am not conscious of a time when china jars and saucers
were introduced into my imagination.
I had no repugnance then--why should I now have?--to those little,
lawless, azure-tinctured grotesques, that under the notion of men and
women, float about, uncircumscribed by any element, in that world
before perspective--a china tea-cup.
I like to see my old friends--whom distance cannot diminish--figuring
up in the air (so they appear to our optics), yet on _terra firma_
still--for so we must in courtesy interpret that speck of deeper blue,
which the decorous artist, to prevent absurdity, has made to spring up
beneath their sandals.
I love the men with women's faces, and the women, if possible, with
still more womanish expressions.
Here is a young and courtly Mandarin, handing tea to a lady from a
salver--two miles off. See how distance seems to set off respect!
And here the same lady, or another--for likeness is identity on
tea-cups--is stepping into a little fairy boat, moored on the hither
side of this calm garden river, with a dainty mincing foot, which in a
right angle of incidence (as angles go in our world) must infallibly
land her in the midst of a flowery mead--a furlong off on the other
side of the same strange stream!
Farther on--if far or near can be predicated of their world--see
horses, trees, pagodas, dancing the hays.
Here--a cow and rabbit couchant, and co-extensive--so objects show,
seen through the lucid atmosphere of fine Cathay.
I was pointing out to my cousin last evening, over our Hyson (which we
are old fashioned enough to drink unmixed still of an afternoon) some
of these _speciosa miracula_ upon a set of extraordinary old blue
china (a recent purchase) which we were now for the first time using;
and could not help remarking, how favourable circumstances had been
to us of late years, that we could afford to please the eye sometimes
with trifles of this sort--when a passing sentiment seemed to
over-shade the brows of my companion. I am quick at detecting these
summer clouds in Bridget.
"I wish the good old times would come again," she said, "when we were
not quite so rich. I do not mean, that I want to be poor; but there
was a middle state;"--so she was pleased to ramble on,--"in which I am
sure we were a great deal happier. A purchase is but a purchase, now
that you have money enough and to spare. Formerly it used to be a
triumph. When we coveted a cheap luxury (and, O! how much ado I had to
get you to consent in those times!) we were used to have a debate two
or three days before, and to weigh the _for_ and _against_, and think
what we might spare it out of, and what saving we could hit upon, that
should be an equivalent. A thing was worth buying then, when we felt
the money that we paid for it.
"Do you remember the brown suit, which you made to hang upon you, till
all your friends cried shame upon you, it grew so thread-bare--and all
because of that folio Beaumont and Fletcher, which you dragged home
late at night from Barker's in Covent-garden? Do you remember how we
eyed it for weeks before we could make up our minds to the purchase,
and had not come to a determination till it was near ten o'clock of
the Saturday night, when you set off from Islington, fearing you
should be too late--and when the old bookseller with some grumbling
opened his shop, and by the twinkling taper (for he was setting
bedwards) lighted out the relic from his dusty treasures--and when
you lugged it home, wishing it were twice as cumbersome--and when you
presented it to me--and when we were exploring the perfectness of it
(_collating_ you called it)--and while I was repairing some of the
loose leaves with paste, which your impatience would not suffer to be
left till day-break--was there no pleasure in being a poor man? or can
those neat black clothes which you wear now, and are so careful to
keep brushed, since we have become rich and finical, give you half
the honest vanity, with which you flaunted it about in that over-worn
suit--your old corbeau--for four or five weeks longer than you should
have done, to pacify your conscience for the mighty sum of fifteen--or
sixteen shillings was it?--a great affair we thought it then--which
you had lavished on the old folio. Now you can afford to buy any book
that pleases you, but I do not see that you ever bring me home any
nice old purchases now.
"When you come home with twenty apologies for laying out a less number
of shillings upon that print after Lionardo, which we christened the
'Lady Blanch;' when you looked at the purchase, and thought of the
money--and thought of the money, and looked again at the picture--was
there no pleasure in being a poor man? Now, you have nothing to do but
to walk into Colnaghi's, and buy a wilderness of Lionardos. Yet do
you?
"Then, do you remember our pleasant walks to Enfield, and Potter's
Bar, and Waltham, when we had a holyday--holydays, and all other fun,
are gone, now we are rich--and the little hand-basket, in which I used
to deposit our day's fare of savory cold lamb and salad--and how you
would pry about at noon-tide for some decent house, where we might go
in, and produce our store--only paying for the ale that you must call
for--and speculate upon the looks of the landlady, and whether she was
likely to allow us a table-cloth--and wish for such another honest
hostess, as Izaak Walton has described many a one on the pleasant
banks of the Lea, when he went a fishing--and sometimes they would
prove obliging enough, and sometimes they would look grudgingly upon
us--but we had cheerful looks still for one another, and would eat
our plain food savorily, scarcely grudging Piscator his Trout Hall?
Now, when we go out a day's pleasuring, which is seldom moreover, we
_ride_ part of the way--and go into a fine inn, and order the best of
dinners, never debating the expense--which, after all, never has half
the relish of those chance country snaps, when we were at the mercy of
uncertain usage, and a precarious welcome.
"You are too proud to see a play anywhere now but in the pit. Do
you remember where it was we used to sit, when we saw the battle of
Hexham, and the surrender of Calais, and Bannister and Mrs. Bland
in the Children in the Wood--when we squeezed out our shillings
a-piece to sit three or four times in a season in the one-shilling
gallery--where you felt all the time that you ought not to have
brought me--and more strongly I felt obligation to you for having
brought me--and the pleasure was the better for a little shame--and
when the curtain drew up, what cared we for our place in the house, or
what mattered it where we were sitting, when our thoughts were with
Rosalind in Arden, or with Viola at the Court of Illyria? You used to
say, that the gallery was the best place of all for enjoying a play
socially--that the relish of such exhibitions must be in proportion
to the infrequency of going--that the company we met there, not being
in general readers of plays, were obliged to attend the more, and
did attend, to what was going on, on the stage--because a word lost
would have been a chasm, which it was impossible for them to fill
up. With such reflections we consoled our pride then--and I appeal
to you, whether, as a woman, I met generally with less attention and
accommodation, than I have done since in more expensive situations
in the house? The getting in indeed, and the crowding up those
inconvenient staircases, was bad enough,--but there was still a law of
civility to women recognised to quite as great an extent as we ever
found in the other passages--and how a little difficulty overcome
heightened the snug seat, and the play, afterwards! Now we can only
pay our money, and walk in. You cannot see, you say, in the galleries
now. I am sure we saw, and heard too, well enough then--but sight, and
all, I think, is gone with our poverty.
"There was pleasure in eating strawberries, before they became quite
common--in the first dish of peas, while they were yet dear--to have
them for a nice supper, a treat. What treat can we have now? If we
were to treat ourselves now--that is, to have dainties a little above
our means, it would be selfish and wicked. It is the very little more
that we allow ourselves beyond what the actual poor can get at, that
makes what I call a treat--when two people living together, as we have
done, now and then indulge themselves in a cheap luxury, which both
like; while each apologises, and is willing to take both halves of
the blame to his single share. I see no harm in people making much of
themselves in that sense of the word. It may give them a hint how to
make much of others. But now--what I mean by the word--we never do
make much of ourselves. None but the poor can do it. I do not mean the
veriest poor of all, but persons as we were, just above poverty.
"I know what you were going to say, that it is mighty pleasant at the
end of the year to make all meet--and much ado we used to have every
Thirty-first Night of December to account for our exceedings--many a
long face did you make over your puzzled accounts, and in contriving
to make it out how we had spent so much--or that we had not spent so
much--or that it was impossible we should spend so much next year--and
still we found our slender capital decreasing--but then, betwixt ways,
and projects, and compromises of one sort or another, and talk of
curtailing this charge, and doing without that for the future--and the
hope that youth brings, and laughing spirits (in which you were never
poor till now,) we pocketed up our loss, and in conclusion, with
'lusty brimmers' (as you used to quote it out of _hearty cheerful Mr.
Cotton_, as you called him), we used to welcome in the 'coming guest.'
Now we have no reckoning at all at the end of the old year--no
flattering promises about the new year doing better for us."
Bridget is so sparing of her speech on most occasions, that when she
gets into a rhetorical vein, I am careful how I interrupt it. I could
not help, however, smiling at the phantom of wealth which her dear
imagination had conjured up out of a clear income of poor--hundred
pounds a year. "It is true we were happier when we were poorer, but
we were also younger, my cousin. I am afraid we must put up with the
excess, for if we were to shake the superflux into the sea, we should
not much mend ourselves. That we had much to struggle with, as we grew
up together, we have reason to be most thankful. It strengthened, and
knit our compact closer. We could never have been what we have been
to each other, if we had always had the sufficiency which you now
complain of. The resisting power--those natural dilations of the
youthful spirit, which circumstances cannot straiten--with us are long
since passed away. Competence to age is supplementary youth; a sorry
supplement indeed, but I fear the best that is to be had. We must
ride, where we formerly walked: live better, and lie softer--and shall
be wise to do so--than we had means to do in those good old days you
speak of. Yet could those days return--could you and I once more walk
our thirty miles a-day--could Bannister and Mrs. Bland again be young,
and you and I be young to see them--could the good old one shilling
gallery days return--they are dreams, my cousin, now--but could
you and I at this moment, instead of this quiet argument, by our
well-carpeted fireside, sitting on this luxurious sofa--be once
more struggling up those inconvenient stair-cases, pushed about,
and squeezed, and elbowed by the poorest rabble of poor gallery
scramblers--could I once more hear those anxious shrieks of yours--and
the delicious _Thank God, we are safe_, which always followed when the
topmost stair, conquered, let in the first light of the whole cheerful
theatre down beneath us--I know not the fathom line that ever touched
a descent so deep as I would be willing to bury more wealth in than
Croesus had, or the great Jew R---- is supposed to have, to purchase
it. And now do just look at that merry little Chinese waiter holding
an umbrella, big enough for a bed-tester, over the head of that
pretty insipid half-Madona-ish chit of a lady in that very blue
summer-house."
POPULAR FALLACIES
I.--THAT A BULLY IS ALWAYS A COWARD
This axiom contains a principle of compensation, which disposes us to
admit the truth of it. But there is no safe trusting to dictionaries
and definitions. We should more willingly fall in with this popular
language, if we did not find _brutality_ sometimes awkwardly coupled
with _valour_ in the same vocabulary. The comic writers, with their
poetical justice, have contributed not a little to mislead us upon
this point. To see a hectoring fellow exposed and beaten upon the
stage, has something in it wonderfully diverting. Some people's
share of animal spirits is notoriously low and defective. It has not
strength to raise a vapour, or furnish out the wind of a tolerable
bluster. These love to be told that huffing is no part of valour.
The truest courage with them is that which is the least noisy and
obtrusive. But confront one of these silent heroes with the swaggerer
of real life, and his confidence in the theory quickly vanishes.
Pretensions do not uniformly bespeak non-performance. A modest
inoffensive deportment does not necessarily imply valour; neither does
the absence of it justify us in denying that quality. Hickman wanted
modesty--we do not mean _him_ of Clarissa--but who ever doubted his
courage? Even the poets--upon whom this equitable distribution of
qualities should be most binding--have thought it agreeable to nature
to depart from the rule upon occasion. Harapha, in the "Agonistes," is
indeed a bully upon the received notions. Milton has made him at once
a blusterer, a giant, and a dastard. But Almanzor, in Dryden, talks
of driving armies singly before him--and does it. Tom Brown had a
shrewder insight into this kind of character than either of his
predecessors. He divides the palm more equably, and allows his hero
a sort of dimidiate pre-eminence:--"Bully Dawson kicked by half
the town, and half the town kicked by Bully Dawson." This was true
distributive justice.
II.--THAT ILL-GOTTEN GAIN NEVER PROSPERS
The weakest part of mankind have this saying commonest in their mouth.
It is the trite consolation administered to the easy dupe, when he has
been tricked out of his money or estate, that the acquisition of
it will do the owner _no good_. But the rogues of this world--the
prudenter part of them, at least--know better; and, if the observation
had been as true as it is old, would not have failed by this time
to have discovered it. They have pretty sharp distinctions of the
fluctuating and the permanent. "Lightly come, lightly go," is a
proverb, which they can very well afford to leave, when they leave
little else, to the losers. They do not always find manors, got by
rapine or chicanery, insensibly to melt away, as the poets will have
it; or that all gold glides, like thawing snow, from the thief's hand
that grasps it. Church land, alienated to lay uses, was formerly
denounced to have this slippery quality. But some portions of it
somehow always stuck so fast, that the denunciators have been vain to
postpone the prophecy of refundment to a late posterity.
III.--THAT A MAN MUST NOT LAUGH AT HIS OWN JEST
The severest exaction surely ever invented upon the self-denial of
poor human nature! This is to expect a gentleman to give a treat
without partaking of it; to sit esurient at his own table, and commend
the flavour of his venison upon the absurd strength of his never
touching it himself. On the contrary, we love to see a wag _taste_
his own joke to his party; to watch a quirk, or a merry conceit,
flickering upon the lips some seconds before the tongue is delivered
of it. If it be good, fresh, and racy--begotten of the occasion; if he
that utters it never thought it before, he is naturally the first to
be tickled with it; and any suppression of such complacence we hold to
be churlish and insulting. What does it seem to imply, but that your
company is weak or foolish enough to be moved by an image or a fancy,
that shall stir you not at all, or but faintly? This is exactly the
humour of the fine gentleman in Mandeville, who, while he dazzles his
guests with the display of some costly toy, affects himself to "see
nothing considerable in it."
IV.--THAT SUCH A ONE SHOWS HIS BREEDING.--THAT IT IS EASY TO PERCEIVE
HE IS NO GENTLEMAN
A speech from the poorer sort of people, which always indicates that
the party vituperated is a gentleman. The very fact which they deny,
is that which galls and exasperates them to use this language. The
forbearance with which it is usually received, is a proof what
interpretation the bystander sets upon it. Of a kin to this, and still
less politic, are the phrases with which, in their street rhetoric,
they ply one another more grossly:--_He is a poor creature._--_He has
not a rag to cover_--_&c._; though this last, we confess, is more
frequently applied by females to females. They do not perceive that
the satire glances upon themselves. A poor man, of all things in
the world, should not upbraid an antagonist with poverty. Are there
no other topics--as, to tell him his father was hanged--his sister,
&c.--, without exposing a secret, which should be kept snug between
them; and doing an affront to the order to which they have the honour
equally to belong? All this while they do not see how the wealthier
man stands by and laughs in his sleeve at both.
V.--THAT THE POOR COPY THE VICES OF THE RICH
A smooth text to the latter; and, preached from the pulpit, is sure of
a docile audience from the pews lined with satin. It is twice sitting
upon velvet to a foolish squire to be told, that _he_--and not
_perverse nature_, as the homilies would make us imagine, is the true
cause of all the irregularities in his parish. This is striking at the
root of free-will indeed, and denying the originality of sin in any
sense. But men are not such implicit sheep as this comes to. If the
abstinence from evil on the part of the upper classes is to derive
itself from no higher principle, than the apprehension of setting
ill patterns to the lower, we beg leave to discharge them from
all squeamishness on that score: they may even take their fill of
pleasures, where they can find them. The Genius of Poverty, hampered
and straitened as it is, is not so barren of invention but it can
trade upon the staple of its own vice, without drawing upon their
capital. The poor are not quite such servile imitators as they take
them for. Some of them are very clever artists in their way. Here and
there we find an original. Who taught the poor to steal, to pilfer?
They did not go to the great for schoolmasters in these faculties
surely. It is well if in some vices they allow us to be--no copyists.
In no other sense is it true that the poor copy them, than as servants
may be said to _take after_ their masters and mistresses, when
they succeed to their reversionary cold meats. If the master, from
indisposition or some other cause, neglect his food, the servant dines
notwithstanding.
"O, but (some will say) the force of example is great." We knew a lady
who was so scrupulous on this head, that she would put up with the
calls of the most impertinent visitor, rather than let her servant say
she was not at home, for fear of teaching her maid to tell an untruth;
and this in the very face of the fact, which she knew well enough,
that the wench was one of the greatest liars upon the earth without
teaching; so much so, that her mistress possibly never heard two words
of consecutive truth from her in her life. But nature must go for
nothing: example must be every thing. This liar in grain, who never
opened her mouth without a lie, must be guarded against a remote
inference, which she (pretty casuist!) might possibly draw from a form
of words--literally false, but essentially deceiving no one--that
under some circumstances a fib might not be so exceedingly sinful--a
fiction, too, not at all in her own way, or one that she could be
suspected of adopting, for few servant-wenches care to be denied to
visitors.
This word _example_ reminds us of another fine word which is in use
upon these occasions--_encouragement_. "People in our sphere must
not be thought to give encouragement to such proceedings." To such
a frantic height is this principle capable of being carried, that
we have known individuals who have thought it within the scope of
their influence to sanction despair, and give _eclat_ to--suicide. A
domestic in the family of a county member lately deceased, for love,
or some unknown cause, cut his throat, but not successfully. The poor
fellow was otherwise much loved and respected; and great interest was
used in his behalf, upon his recovery, that he might be permitted
to retain his place; his word being first pledged, not without some
substantial sponsors to promise for him, than the like should never
happen again. His master was inclinable to keep him, but his mistress
thought otherwise; and John in the end was dismissed, her ladyship
declaring that she "could not think of encouraging any such doings in
the county."
VI.--THAT ENOUGH IS AS GOOD AS A FEAST
Not a man, woman, or child in ten miles round Guildhall, who really
believes this saying. The inventor of it did not believe it himself.
It was made in revenge by somebody, who was disappointed of a regale.
It is a vile cold-scrag-of-mutton sophism; a lie palmed upon the
palate, which knows better things. If nothing else could be said for
a feast, this is sufficient, that from the superflux there is usually
something left for the next day. Morally interpreted, it belongs to
a class of proverbs, which have a tendency to make us undervalue
_money_. Of this cast are those notable observations, that money is
not health; riches cannot purchase every thing: the metaphor which
makes gold to be mere muck, with the morality which traces fine
clothing to the sheep's back, and denounces pearl as the unhandsome
excretion of an oyster. Hence, too, the phrase which imputes dirt to
acres--a sophistry so barefaced, that even the literal sense of it is
true only in a wet season. This, and abundance of similar sage saws
assuming to inculcate _content_, we verily believe to have been the
invention of some cunning borrower, who had designs upon the purse of
his wealthier neighbour, which he could only hope to carry by force of
these verbal jugglings. Translate any one of these sayings out of the
artful metonyme which envelops it, and the trick is apparent. Goodly
legs and shoulders of mutton, exhilarating cordials, books, pictures,
the opportunities of seeing foreign countries, independence, heart's
ease, a man's own time to himself, are not _muck_--however we may be
pleased to scandalise with that appellation the faithful metal that
provides them for us.
VII.--OF TWO DISPUTANTS, THE WARMEST IS GENERALLY IN THE WRONG
Our experience would lead us to quite an opposite conclusion. Temper,
indeed, is no test of truth; but warmth and earnestness are a proof
at least of a man's own conviction of the rectitude of that which
he maintains. Coolness is as often the result of an unprincipled
indifference to truth or falsehood, as of a sober confidence in a
man's own side in a dispute. Nothing is more insulting sometimes than
the appearance of this philosophic temper. There is little Titubus,
the stammering law-stationer in Lincoln's Inn--we have seldom known
this shrewd little fellow engaged in an argument where we were not
convinced he had the best of it, if his tongue would but fairly have
seconded him. When he has been spluttering excellent broken sense
for an hour together, writhing and labouring to be delivered of the
point of dispute--the very gist of the controversy knocking at his
teeth, which like some obstinate iron-grating still obstructed its
deliverance--his puny frame convulsed, and face reddening all over at
an unfairness in the logic which he wanted articulation to expose, it
has moved our gall to see a smooth portly fellow of an adversary, that
cared not a button for the merits of the question, by merely laying
his hand upon the head of the stationer, and desiring him to be _calm_
(your tall disputants have always the advantage), with a provoking
sneer carry the argument clean from him in the opinion of all the
bystanders, who have gone away clearly convinced that Titubus must
have been in the wrong, because he was in a passion; and that Mr.----,
meaning his opponent, is one of the fairest, and at the same time one
of the most dispassionate arguers breathing.
VIII.--THAT VERBAL ALLUSIONS ARE NOT WIT, BECAUSE THEY WILL NOT BEAR A
TRANSLATION
The same might be said of the wittiest local allusions. A custom is
sometimes as difficult to explain to a foreigner as a pun. What would
become of a great part of the wit of the last age, if it were tried by
this test? How would certain topics, as aldermanity, cuckoldry, have
sounded to a Terentian auditory, though Terence himself had been alive
to translate them? _Senator urbanus_, with _Curruca_ to boot for a
synonime, would but faintly have done the business. Words, involving
notions, are hard enough to render; it is too much to expect us to
translate a sound, and give an elegant version to a jingle. The
Virgilian harmony is not translatable, but by substituting harmonious
sounds in another language for it. To Latinise a pun, we must seek
a pun in Latin, that will answer to it; as, to give an idea of the
double endings in Hudibras, we must have recourse to a similar
practice in the old monkish doggrel. Dennis, the fiercest oppugner of
puns in ancient or modern times, professes himself highly tickled
with the "a stick" chiming to "ecclesiastic." Yet what is this but a
species of pun, a verbal consonance?
IX.--THAT THE WORST PUNS ARE THE BEST
If by worst be only meant the most far-fetched and startling, we agree
to it. A pun is not bound by the laws which limit nicer wit. It is a
pistol let off at the ear; not a feather to tickle the intellect. It
is an antic which does not stand upon manners, but comes bounding into
the presence, and does not show the less comic for being dragged in
sometimes by the head and shoulders. What though it limp a little, or
prove defective in one leg--all the better. A pun may easily be too
curious and artificial. Who has not at one time or other been at a
party of professors (himself perhaps an old offender in that line),
where, after ringing a round of the most ingenious conceits, every man
contributing his shot, and some there the most expert shooters of the
day; after making a poor _word_ run the gauntlet till it is ready to
drop; after hunting and winding it through all the possible ambages of
similar sounds; after squeezing, and hauling, and tugging at it, till
the very milk of it will not yield a drop further,--suddenly some
obscure, unthought-of fellow in a corner, who was never 'prentice
to the trade, whom the company for very pity passed over, as we
do by a known poor man when a money-subscription is going round,
no one calling upon him for his quota--has all at once come out
with something so whimsical, yet so pertinent; so brazen in its
pretensions, yet so impossible to be denied; so exquisitely good,
and so deplorably bad, at the same time,--that it has proved a Robin
Hood's shot; any thing ulterior to that is despaired of; and the party
breaks up, unanimously voting it to be the very worst (that is, best)
pun of the evening. This species of wit is the better for not being
perfect in all its parts. What it gains in completeness, it loses in
naturalness. The more exactly it satisfies the critical, the less hold
it has upon some other faculties. The puns which are most entertaining
are those which will least bear an analysis. Of this kind is the
following, recorded, with a sort of stigma, in one of Swift's
Miscellanies.
An Oxford scholar, meeting a porter who was carrying a hare through
the streets, accosts him with this extraordinary question: "Prithee,
friend, is that thy own hare, or a wig?"
There is no excusing this, and no resisting it. A man might blur ten
sides of paper in attempting a defence of it against a critic who
should be laughter-proof. The quibble in itself is not considerable.
It is only a new turn given, by a little false pronunciation, to a
very common, though not very courteous inquiry. Put by one gentleman
to another at a dinner-party, it would have been vapid; to the
mistress of the house, it would have shown much less wit than
rudeness. We must take in the totality of time, place, and person;
the pert look of the inquiring scholar, the desponding looks of the
puzzled porter; the one stopping at leisure, the other hurrying on
with his burthen; the innocent though rather abrupt tendency of
the first member of the question, with the utter and inextricable
irrelevancy of the second; the place--a public street, not favourable
to frivolous investigations; the affrontive quality of the primitive
inquiry (the common question) invidiously transferred to the
derivative (the new turn given to it) in the implied satire; namely,
that few of that tribe are expected to eat of the good things which
they carry, they being in most countries considered rather as the
temporary trustees than owners of such dainties,--which the fellow was
beginning to understand; but then the _wig_ again comes in, and he can
make nothing of it: all put together constitute a picture: Hogarth
could have made it intelligible on canvass.
Yet nine out of ten critics will pronounce this a very bad pun,
because of the defectiveness in the concluding member, which is its
very beauty, and constitutes the surprise. The same persons shall
cry up for admirable the cold quibble from Virgil about the broken
Cremona;[1] because it is made out in all its parts, and leaves
nothing to the imagination. We venture to call it cold; because of
thousands who have admired it, it would be difficult to find one who
has heartily chuckled at it. As appealing to the judgment merely
(setting the risible faculty aside,) we must pronounce it a monument
of curious felicity. But as some stories are said to be too good to be
true, it may with equal truth be asserted of this bi-verbal allusion,
that it is too good to be natural. One cannot help suspecting that the
incident was invented to fit the line. It would have been better had
it been less perfect. Like some Virgilian hemistichs, it has suffered
by filling up. The _nimium Vicina_ was enough in conscience; the
_Cremonae_ afterwards loads it. It is in fact a double pun; and we
have always observed that a superfoetation in this sort of wit is
dangerous. When a man has said a good thing, it is seldom politic to
follow it up. We do not care to be cheated a second time; or, perhaps,
the mind of man (with reverence be it spoken) is not capacious enough
to lodge two puns at a time. The impression, to be forcible, must be
simultaneous and undivided.
[Footnote 1: Swift.]
X.--THAT HANDSOME IS THAT HANDSOME DOES
Those who use this proverb can never have seen Mrs. Conrady.
The soul, if we may believe Plotinus, is a ray from the celestial
beauty. As she partakes more or less of this heavenly light, she
informs, with corresponding characters, the fleshly tenement which she
chooses, and frames to herself a suitable mansion.
All which only proves that the soul of Mrs. Conrady, in her
pre-existent state, was no great judge of architecture.
To the same effect, in a Hymn in honour of Beauty, divine Spenser,
_platonizing_, sings:--
--"Every spirit as it is more pure,
And hath in it the more of heavenly light,
So it the fairer body doth procure
To habit in, and it more fairly dight
With cheerful grace and amiable sight.
For of the soul the body form doth take:
For soul is form, and doth the body make."
But Spenser, it is clear, never saw Mrs. Conrady.
These poets, we find, are no safe guides in philosophy; for here, in
his very next stanza but one, is a saving clause, which throws us all
out again, and leaves us as much to seek as ever:--
"Yet oft it falls, that many a gentle mind
Dwells in deformed tabernacle drown'd,
Either by chance, against the course of kind,
Or through unaptness in the substance found,
Which it assumed of some stubborn ground,
That will not yield unto her form's direction,
But is perform'd with some foul imperfection."
From which it would follow, that Spenser had seen somebody like Mrs.
Conrady.
The spirit of this good lady--her previous _anima_--must have stumbled
upon one of these untoward tabernacles which he speaks of. A more
rebellious commodity of clay for a ground, as the poet calls it, no
gentle mind--and sure hers is one of the gentlest--ever had to deal
with.
Pondering upon her inexplicable visage--inexplicable, we mean, but by
this modification of the theory--we have come to a conclusion that,
if one must be plain, it is better to be plain all over, than, amidst
a tolerable residue of features, to hang out one that shall be
exceptionable. No one can say of Mrs. Conrady's countenance, that it
would be better if she had but a nose. It is impossible to pull her to
pieces in this manner. We have seen the most malicious beauties of her
own sex baffled in the attempt at a selection. The _tout ensemble_
defies particularising. It is too complete--too consistent, as we may
say--to admit of these invidious reservations. It is not as if some
Apelles had picked out here a lip--and there a chin--out of the
collected ugliness of Greece, to frame a model by. It is a symmetrical
whole. We challenge the minutest connoisseur to cavil at any part or
parcel of the countenance in question; to say that this, or that, is
improperly placed. We are convinced that true ugliness, no less than
is affirmed of true beauty, is the result of harmony. Like that too
it reigns without a competitor. No one ever saw Mrs. Conrady, without
pronouncing her to be the plainest woman that he ever met with in the
course of his life. The first time that you are indulged with a sight
of her face, is an era in your existence ever after. You are glad to
have seen it--like Stonehenge. No one can pretend to forget it. No one
ever apologised to her for meeting her in the street on such a day and
not knowing her: the pretext would be too bare. Nobody can mistake her
for another. Nobody can say of her, "I think I have seen that face
somewhere, but I cannot call to mind where." You must remember that in
such a parlour it first struck you--like a bust. You wondered where
the owner of the house had picked it up. You wondered more when it
began to move its lips--so mildly too! No one ever thought of asking
her to sit for her picture. Lockets are for remembrance; and it would
be clearly superfluous to hang an image at your heart, which, once
seen, can never be out of it. It is not a mean face either; its entire
originality precludes that. Neither is it of that order of plain faces
which improve upon acquaintance. Some very good but ordinary people,
by an unwearied perseverance in good offices, put a cheat upon our
eyes: juggle our senses out of their natural impressions; and set us
upon discovering good indications in a countenance, which at first
sight promised nothing less. We detect gentleness, which had escaped
us, lurking about an under lip. But when Mrs. Conrady has done you a
service, her face remains the same; when she has done you a thousand,
and you know that she is ready to double the number, still it is that
individual face. Neither can you say of it, that it would be a good
face if it was not marked by the small pox--a compliment which is
always more admissive than excusatory--for either Mrs. Conrady never
had the small pox; or, as we say, took it kindly. No, it stands upon
its own merits fairly. There it is. It is her mark, her token; that
which she is known by.
XI.--THAT WE MUST NOT LOOK A GIFT-HORSE IN THE MOUTH
Nor a lady's age in the parish register. We hope we have more delicacy
than to do either: but some faces spare us the trouble of these
_dental_ inquiries. And what if the beast, which my friend would force
upon my acceptance, prove, upon the face of it, a sorry Rozinante, a
lean, ill-favoured jade, whom no gentleman could think of setting up
in his stables? Must I, rather than not be obliged to my friend, make
her a companion to Eclipse or Lightfoot? A horse-giver, no more than
a horse-seller, has a right to palm his spavined article upon us for
good ware. An equivalent is expected in either case; and, with my own
good will, I would no more be cheated out of my thanks, than out of my
money. Some people have a knack of putting upon you gifts of no real
value, to engage you to substantial gratitude. We thank them for
nothing. Our friend Mitis carries this humour of never refusing a
present, to the very point of absurdity--if it were possible to couple
the ridiculous with so much mistaken delicacy, and real good-nature.
Not an apartment in his fine house (and he has a true taste in
household decorations), but is stuffed up with some preposterous print
or mirror--the worst adapted to his pannels that may be--the presents
of his friends that know his weakness; while his noble Vandykes are
displaced, to make room for a set of daubs, the work of some wretched
artist of his acquaintance, who, having had them returned upon his
hands for bad likenesses, finds his account in bestowing them here
gratis. The good creature has not the heart to mortify the painter
at the expense of an honest refusal. It is pleasant (if it did not
vex one at the same time) to see him sitting in his dining parlour,
surrounded with obscure aunts and cousins to God knows whom, while
the true Lady Marys and Lady Bettys of his own honourable family, in
favour to these adopted frights, are consigned to the staircase and
the lumber-room. In like manner his goodly shelves are one by one
stript of his favourite old authors, to give place to a collection
of presentation copies--the flower and bran of modern poetry. A
presentation copy, reader--if haply you are yet innocent of such
favours--is a copy of a book which does not sell, sent you by the
author, with his foolish autograph at the beginning of it; for which,
if a stranger, he only demands your friendship; if a brother author,
he expects from you a book of yours which does sell, in return. We
can speak to experience, having by us a tolerable assortment of these
gift-horses. Not to ride a metaphor to death--we are willing to
acknowledge, that in some gifts there is sense. A duplicate out of a
friend's library (where he has more than one copy of a rare author) is
intelligible. There are favours, short of the pecuniary--a thing not
fit to be hinted at among gentlemen--which confer as much grace upon
the acceptor as the offerer: the kind, we confess, which is most to
our palate, is of those little conciliatory missives, which for their
vehicle generally choose a hamper--little odd presents of game, fruit,
perhaps wine--though it is essential to the delicacy of the latter
that it be home-made. We love to have our friend in the country
sitting thus at our table by proxy; to apprehend his presence (though
a hundred miles may be between us) by a turkey, whose goodly aspect
reflects to us his "plump corpusculum;" to taste him in grouse or
woodcock; to feel him gliding down in the toast peculiar to the
latter; to concorporate him in a slice of Canterbury brawn. This is
indeed to have him within ourselves; to know him intimately: such
participation is methinks unitive, as the old theologians phrase it.
For these considerations we should be sorry if certain restrictive
regulations, which are thought to bear hard upon the peasantry of this
country, were entirely done away with. A hare, as the law now stands,
makes many friends. Caius conciliates Titius (knowing his _gout_) with
a leash of partridges. Titius (suspecting his partiality for them)
passes them to Lucius; who in his turn, preferring his friend's relish
to his own, makes them over to Marcius; till in their ever widening
progress, and round of unconscious circum-migration, they distribute
the seeds of harmony over half a parish. We are well disposed to
this kind of sensible remembrances; and are the less apt to be taken
by those little airy tokens--inpalpable to the palate--which, under
the names of rings, lockets, keep-sakes, amuse some people's fancy
mightily. We could never away with these indigestible trifles. They
are the very kickshaws and foppery of friendship.
XII.--THAT HOME IS HOME THOUGH IT IS NEVER SO HOMELY
Homes there are, we are sure, that are no homes: the home of the very
poor man, and another which we shall speak to presently. Crowded
places of cheap entertainment, and the benches of ale-houses, if they
could speak, might bear mournful testimony to the first. To them the
very poor man resorts for an image of the home, which he cannot find
at home. For a starved grate, and a scanty firing, that is not enough
to keep alive the natural heat in the fingers of so many shivering
children with their mother, he finds in the depth of winter always a
blazing hearth, and a hob to warm his pittance of beer by. Instead
of the clamours of a wife, made gaunt by famishing, he meets with
a cheerful attendance beyond the merits of the trifle which he can
afford to spend. He has companions which his home denies him, for the
very poor man has no visiters. He can look into the goings on of the
world, and speak a little to politics. At home there are no politics
stirring, but the domestic. All interests, real or imaginary, all
topics that should expand the mind of man, and connect him to a
sympathy with general existence, are crushed in the absorbing
consideration of food to be obtained for the family. Beyond the price
of bread, news is senseless and impertinent. At home there is no
larder. Here there is at least a show of plenty; and while he cooks
his lean scrap of butcher's meat before the common bars, or munches
his humbler cold viands, his relishing bread and cheese with an onion,
in a corner, where no one reflects upon his poverty, he has sight of
the substantial joint providing for the landlord and his family. He
takes an interest in the dressing of it; and while he assists in
removing the trivet from the fire, he feels that there is such a thing
as beef and cabbage, which he was beginning to forget at home. All
this while he deserts his wife and children. But what wife, and what
children? Prosperous men, who object to this desertion, image to
themselves some clean contented family like that which they go home
to. But look at the countenance of the poor wives who follow and
persecute their good man to the door of the public house, which he
is about to enter, when something like shame would restrain him, if
stronger misery did not induce him to pass the threshold. That face,
ground by want, in which every cheerful, every conversable lineament
has been long effaced by misery,--is that a face to stay at home with?
is it more a woman, or a wild cat? alas! it is the face of the wife
of his youth, that once smiled upon him. It can smile no longer. What
comforts can it share? what burthens can it lighten? Oh, 'tis a fine
thing to talk of the humble meal shared together! But what if there be
no bread in the cupboard? The innocent prattle of his children takes
out the sting of a man's poverty. But the children of the very poor
do not prattle. It is none of the least frightful features in that
condition, that there is no childishness in its dwellings. Poor
people, said a sensible old nurse to us once, do not bring up their
children; they drag them up. The little careless darling of the
wealthier nursery, in their hovel is transformed betimes into a
premature reflecting person. No one has time to dandle it, no one
thinks it worth while to coax it, to soothe it, to toss it up and
down, to humour it. There is none to kiss away its tears. If it cries,
it can only be beaten. It has been prettily said that "a babe is fed
with milk and praise." But the aliment of this poor babe was thin,
unnourishing; the return to its little baby-tricks, and efforts to
engage attention, bitter ceaseless objurgation. It never had a toy,
or knew what a coral meant. It grew up without the lullaby of nurses,
it was a stranger to the patient fondle, the hushing caress, the
attracting novelty, the costlier plaything, or the cheaper off-hand
contrivance to divert the child; the prattled nonsense (best sense
to it), the wise impertinences, the wholesome lies, the apt story
interposed, that puts a stop to present sufferings, and awakens the
passion of young wonder. It was never sung to--no one ever told to
it a tale of the nursery. It was dragged up, to live or to die as
it happened. It had no young dreams. It broke at once into the iron
realities of life. A child exists not for the very poor as any object
of dalliance; it is only another mouth to be fed, a pair of little
hands to be betimes inured to labour. It is the rival, till it can be
the co-operator, for food with the parent. It is never his mirth, his
diversion, his solace; it never makes him young again, with recalling
his young times. The children of the very poor have no young times.
It makes the very heart to bleed to overhear the casual street-talk
between a poor woman and her little girl, a woman of the better sort
of poor, in a condition rather above the squalid beings which we have
been contemplating. It is not of toys, of nursery books, of summer
holidays (fitting that age); of the promised sight, or play; of
praised sufficiency at school. It is of mangling and clear-starching,
of the price of coals, or of potatoes. The questions of the child,
that should be the very outpourings of curiosity in idleness, are
marked with forecast and melancholy providence. It has come to be
a woman, before it was a child. It has learned to go to market; it
chaffers, it haggles, it envies, it murmurs; it is knowing, acute,
sharpened; it never prattles. Had we not reason to say, that the home
of the very poor is no home?
There is yet another home, which we are constrained to deny to be one.
It has a larder, which the home of the poor man wants; its fireside
conveniences, of which the poor dream not. But with all this, it is no
home. It is--the house of the man that is infested with many visiters.
May we be branded for the veriest churl, if we deny our heart to the
many noble-hearted friends that at times exchange their dwelling for
our poor roof! It is not of guests that we complain, but of endless,
purposeless visitants; droppers in, as they are called. We sometimes
wonder from what sky they fall. It is the very error of the position
of our lodging; its horoscopy was ill calculated, being just situate
in a medium--a plaguy suburban mid-space--fitted to catch idlers from
town or country. We are older than we were, and age is easily put out
of its way. We have fewer sands in our glass to reckon upon, and we
cannot brook to see them drop in endlessly succeeding impertinences.
At our time of life, to be alone sometimes is as needful as sleep. It
is the refreshing sleep of the day. The growing infirmities of age
manifest themselves in nothing more strongly, than in an inveterate
dislike of interruption. The thing which we are doing, we wish to be
permitted to do. We have neither much knowledge nor devices; but there
are fewer in the place to which we hasten. We are not willingly put
out of our way, even at a game of nine-pins. While youth was, we had
vast reversions in time future; we are reduced to a present pittance,
and obliged to economise in that article. We bleed away our moments
now as hardly as our ducats. We cannot bear to have our thin wardrobe
eaten and fretted into by moths. We are willing to barter our good
time with a friend, who gives us in exchange his own. Herein is the
distinction between the genuine guest and the visitant. This latter
takes your good time, and gives you his bad in exchange. The guest
is domestic to you as your good cat, or household bird; the visitant
is your fly, that flaps in at your window, and out again, leaving
nothing but a sense of disturbance, and victuals spoiled. The inferior
functions of life begin to move heavily. We cannot concoct our food
with interruptions. Our chief meal, to be nutritive, must be solitary.
With difficulty we can eat before a guest; and never understood
what the relish of public feasting meant. Meats have no sapor, nor
digestion fair play, in a crowd. The unexpected coming in of a
visitant stops the machine. There is a punctual generation who time
their calls to the precise commencement of your dining-hour--not to
eat--but to see you eat. Our knife and fork drop instinctively, and we
feel that we have swallowed our latest morsel. Others again show their
genius, as we have said, in knocking the moment you have just sat down
to a book. They have a peculiar compassionating sneer, with which they
"hope that they do not interrupt your studies." Though they flutter
off the next moment, to carry their impertinences to the nearest
student that they can call their friend, the tone of the book is
spoiled; we shut the leaves, and, with Dante's lovers, read no
more that day. It were well if the effect of intrusion were simply
co-extensive with its presence; but it mars all the good hours
afterwards. These scratches in appearance leave an orifice that closes
not hastily. "It is a prostitution of the bravery of friendship," says
worthy Bishop Taylor, "to spend it upon impertinent people, who are,
it may be, loads to their families, but can never ease my loads." This
is the secret of their gaddings, their visits, and morning calls. They
too have homes, which are--no homes.
XIII.--THAT YOU MUST LOVE ME, AND LOVE MY DOG
"Good sir, or madam, as it may be--we most willingly embrace the offer
of your friendship. We long have known your excellent qualities. We
have wished to have you nearer to us; to hold you within the very
innermost fold of our heart. We can have no reserve towards a person
of your open and noble nature. The frankness of your humour suits
us exactly. We have been long looking for such a friend. Quick--let
us disburthen our troubles into each other's bosom--let us make our
single joys shine by reduplication--But _yap, yap, yap!_--what is
this confounded cur? he has fastened his tooth, which is none of the
bluntest, just in the fleshy part of my leg."
"It is my dog, sir. You must love him for my sake. Here,
Test--Test--Test!"
"But he has bitten me."
"Ay, that he is apt to do, till you are better acquainted with him. I
have had him three years. He never bites me."
_Yap, yap, yap!_--"He is at it again."
"Oh, sir, you must not kick him. He does not like to be kicked. I
expect my dog to be treated with all the respect due to myself."
"But do you always take him out with you, when you go a
friendship-hunting?"
"Invariably. 'Tis the sweetest, prettiest, best-conditioned animal. I
call him my _test_--the touchstone by which I try a friend. No one can
properly be said to love me, who does not love him."
"Excuse us, dear sir--or madam aforesaid--if upon further
consideration we are obliged to decline the otherwise invaluable offer
of your friendship. We do not like dogs."
"Mighty well, sir--you know the conditions--you may have worse offers.
Come along, Test."
The above dialogue is not so imaginary, but that, in the intercourse
of life, we have had frequent occasions of breaking off an agreeable
intimacy by reason of these canine appendages. They do not always
come in the shape of dogs; they sometimes wear the more plausible and
human character of kinsfolk, near acquaintances, my friend's friend,
his partner, his wife, or his children. We could never yet form a
friendship--not to speak of more delicate correspondences--however
much to our taste, without the intervention of some third anomaly,
some impertinent clog affixed to the relation--the understood _dog_
in the proverb. The good things of life are not to be had singly, but
come to us with a mixture; like a schoolboy's holiday, with a task
affixed to the tail of it. What a delightful companion is ****, if he
did not always bring his tall cousin with him! He seems to grow with
him; like some of those double births, which we remember to have read
of with such wonder and delight in the old "Athenian Oracle," where
Swift commenced author by writing Pindaric Odes (what a beginning for
him!) upon Sir William Temple. There is the picture of the brother,
with the little brother peeping out at his shoulder; a species of
fraternity, which we have no name of kin close enough to comprehend.
When **** comes, poking in his head and shoulders into your room,
as if to feel his entry, you think, surely you have now got him to
yourself--what a three hours' chat we shall have!--but, ever in the
haunch of him, and before his diffident body is well disclosed in your
apartment, appears the haunting shadow of the cousin, over-peering his
modest kinsman, and sure to over-lay the expected good talk with his
insufferable procerity of stature, and uncorresponding dwarfishness of
observation. Misfortunes seldom come alone. 'Tis hard when a blessing
comes accompanied. Cannot we like Sempronia, without sitting down to
chess with her eternal brother? or know Sulpicia, without knowing all
the round of her card-playing relations? must my friend's brethren
of necessity be mine also? must we be hand and glove with Dick Selby
the parson, or Jack Selby the calico printer, because W.S., who is
neither, but a ripe wit and a critic, has the misfortune to claim a
common parentage with them? Let him lay down his brothers; and 'tis
odds but we will cast him in a pair of ours (we have a superflux) to
balance the concession. Let F.H. lay down his garrulous uncle; and
Honorius dismiss his vapid wife, and superfluous establishment of six
boys--things between boy and manhood--too ripe for play, too raw for
conversation--that come in, impudently staring their father's old
friend out of countenance; and will neither aid, nor let alone, the
conference: that we may once more meet upon equal terms, as we were
wont to do in the disengaged state of bachelorhood.
It is well if your friend, or mistress, be content with these
canicular probations. Few young ladies but in this sense keep a dog.
But when Rutilia hounds at you her tiger aunt; or Ruspina expects you
to cherish and fondle her viper sister, whom she has preposterously
taken into her bosom, to try stinging conclusions upon your constancy;
they must not complain if the house be rather thin of suitors. Scylla
must have broken off many excellent matches in her time, if she
insisted upon all, that loved her, loving her dogs also.
An excellent story to this moral is told of Merry, of Della Cruscan
memory. In tender youth, he loved and courted a modest appanage to
the Opera, in truth a dancer, who had won him by the artless contrast
between her manners and situation. She seemed to him a native violet,
that had been transplanted by some rude accident into that exotic and
artificial hotbed. Nor, in truth, was she less genuine and sincere
than she appeared to him. He wooed and won this flower. Only for
appearance' sake, and for due honour to the bride's relations, she
craved that she might have the attendance of her friends and kindred
at the approaching solemnity. The request was too amiable not to be
conceded; and in this solicitude for conciliating the good will of
mere relations, he found a presage of her superior attentions to
himself, when the golden shaft should have "killed the flock of all
affections else." The morning came; and at the Star and Garter,
Richmond--the place appointed for the breakfasting--accompanied with
one English friend, he impatiently awaited what reinforcements the
bride should bring to grace the ceremony. A rich muster she had made.
They came in six coaches--the whole corps du ballet--French, Italian,
men and women. Monsieur de B., the famous _pirouetter_ of the day, led
his fair spouse, but craggy, from the banks of the Seine. The Prima
Donna had sent her excuse. But the first and second Buffa were there;
and Signor Sc----, and Signora Ch----, and Madame V----, with a
countless cavalcade besides of chorusers, figurantes, at the sight
of whom Merry afterwards declared, that "then for the first time it
struck him seriously, that he was about to marry--a dancer." But there
was no help for it. Besides, it was her day; these were, in fact, her
friends and kinsfolk. The assemblage, though whimsical, was all very
natural. But when the bride--handing out of the last coach a still
more extraordinary figure than the rest--presented to him as her
_father_--the gentleman that was to _give her away_--no less a person
than Signor Delpini himself--with a sort of pride, as much as to
say, See what I have brought to do us honour!--the thought of so
extraordinary a paternity quite overcame him; and slipping away under
some pretence from the bride and her motley adherents, poor Merry
took horse from the back yard to the nearest sea-coast, from which,
shipping himself to America, he shortly after consoled himself with a
more congenial match in the person of Miss Brunton; relieved from his
intended clown father, and a bevy of painted Buffas for bridemaids.
XIV.--THAT WE SHOULD RISE WITH THE LARK
At what precise minute that little airy musician doffs his night
gear, and prepares to tune up his unseasonable matins, we are not
naturalists enough to determine. But for a mere human gentleman--that
has no orchestra business to call him from his warm bed to such
preposterous exercises--We take ten, or half after ten (eleven, of
course, during this Christmas solstice), to be the very earliest hour,
at which he can begin to think of abandoning his pillow. To think of
it, we say; for to do it in earnest, requires another half hour's good
consideration. Not but there are pretty sun-risings, as we are told,
and such like gawds, abroad in the world, in summer time especially,
some hours before what we have assigned; which a gentleman may see,
as they say, only for getting up. But, having been tempted once or
twice, in earlier life, to assist at those ceremonies, we confess
our curiosity abated. We are no longer ambitious of being the sun's
courtiers, to attend at his morning levees. We hold the good hours of
the dawn too sacred to waste them upon such observances; which have
in them, besides, something Pagan and Persic. To say truth, we never
anticipated our usual hour, or got up with the sun (as 'tis called),
to go a journey, or upon a foolish whole day's pleasuring, but we
suffered for it all the long hours after in listlessness and headachs;
Nature herself sufficiently declaring her sense of our presumption,
in aspiring to regulate our frail waking courses by the measures of
that celestial and sleepless traveller. We deny not that there is
something sprightly and vigorous, at the outset especially, in these
break-of-day excursions. It is flattering to get the start of a lazy
world; to conquer death by proxy in his image. But the seeds of sleep
and mortality are in us; and we pay usually in strange qualms, before
night falls, the penalty of the unnatural inversion. Therefore, while
the busy part of mankind are fast huddling on their clothes, are
already up and about their occupations, content to have swallowed
their sleep by wholesale; we chose to linger a-bed, and digest our
dreams. It is the very time to recombine the wandering images, which
night in a confused mass presented; to snatch them from forgetfulness;
to shape, and mould them. Some people have no good of their dreams.
Like fast feeders, they gulp them too grossly, to taste them
curiously. We love to chew the cud of a foregone vision: to collect
the scattered rays of a brighter phantasm, or act over again, with
firmer nerves, the sadder nocturnal tragedies; to drag into day-light
a struggling and half-vanishing night-mare; to handle and examine
the terrors, or the airy solaces. We have too much respect for these
spiritual communications, to let them go so lightly. We are not so
stupid, or so careless, as that Imperial forgetter of his dreams, that
we should need a seer to remind us of the form of them. They seem to
us to have as much significance as our waking concerns; or rather to
import us more nearly, as more nearly we approach by years to the
shadowy world, whither we are hastening. We have shaken hands with the
world's business; we have done with it; we have discharged ourself
of it. Why should we get up? we have neither suit to solicit, nor
affairs to manage. The drama has shut in upon us at the fourth act.
We have nothing here to expect, but in a short time a sick bed, and
a dismissal. We delight to anticipate death by such shadows as night
affords. We are already half acquainted with ghosts. We were never
much in the world. Disappointment early struck a dark veil between us
and its dazzling illusions. Our spirits showed grey before our hairs.
The mighty changes of the world already appear as but the vain stuff
out of which dramas are composed. We have asked no more of life than
what the mimic images in play-houses present us with. Even those
types have waxed fainter. Our clock appears to have struck. We are
SUPERANNUATED. In this dearth of mundane satisfaction, we contract
politic alliances with shadows. It is good to have friends at court.
The abstracted media of dreams seem no ill introduction to that
spiritual presence, upon which, in no long time, we expect to be
thrown. We are trying to know a little of the usages of that colony;
to learn the language, and the faces we shall meet with there, that we
may be the less awkward at our first coming among them. We willingly
call a phantom our fellow, as knowing we shall soon be of their dark
companionship. Therefore, we cherish dreams. We try to spell in them
the alphabet of the invisible world; and think we know already, how it
shall be with us. Those uncouth shapes, which, while we clung to flesh
and blood, affrighted us, have become familiar. We feel attenuated
into their meagre essences, and have given the hand of half-way
approach to incorporeal being. We once thought life to be something;
but it has unaccountably fallen from us before its time. Therefore we
choose to dally with visions. The sun has no purposes of ours to light
us to. Why should we get up?
XV.--THAT WE SHOULD LIE DOWN WITH THE LAMB
We could never quite understand the philosophy of this arrangement,
or the wisdom of our ancestors in sending us for instruction to
these woolly bedfellows. A sheep, when it is dark, has nothing to do
but to shut his silly eyes, and sleep if he can. Man found out long
sixes.--Hail candle-light! without disparagement to sun or moon, the
kindliest luminary of the three--if we may not rather style thee their
radiant deputy, mild viceroy of the moon!--We love to read, talk, sit
silent, eat, drink, sleep, by candle-light. They are every body's sun
and moon. This is our peculiar and household planet. Wanting it, what
savage unsocial nights must our ancestors have spent, wintering in
caves and unillumined fastnesses! They must have lain about and
grumbled at one another in the dark. What repartees could have passed,
when you must have felt about for a smile, and handled a neighbour's
cheek to be sure that he understood it? This accounts for the
seriousness of the elder poetry. It has a sombre cast (try Hesiod or
Ossian), derived from the tradition of those unlantern'd nights. Jokes
came in with candles. We wonder how they saw to pick up a pin, if they
had any. How did they sup? what a melange of chance carving they must
have made of it!--here one had got a leg of a goat, when he wanted
a horse's shoulder--there another had dipt his scooped palm in a
kid-skin of wild honey, when he meditated right mare's milk. There
is neither good eating nor drinking in fresco. Who, even in these
civilised times, has never experienced this, when at some economic
table he has commenced dining after dusk, and waited for the
flavour till the lights came? The senses absolutely give and take
reciprocally. Can you tell pork from veal in the dark? or distinguish
Sherris from pure Malaga? Take away the candle from the smoking
man; by the glimmering of the left ashes, he knows that he is still
smoking, but he knows it only by an inference; till the restored
light, coming in aid of the olfactories, reveals to both senses the
full aroma. Then how he redoubles his puffs! how he burnishes!--There
is absolutely no such thing as reading, but by a candle. We have
tried the affectation of a book at noon-day in gardens, and in sultry
arbours; but it was labour thrown away. Those gay motes in the beam
come about you, hovering and teazing, like so many coquets, that will
have you all to their self, and are jealous of your abstractions. By
the midnight taper, the writer digests his meditations. By the same
light, we must approach to their perusal, if we would catch the flame,
the odour. It is a mockery, all that is reported of the influential
Phoebus. No true poem ever owed its birth to the sun's light. They are
abstracted works--
"Things that were born, when none but the still night,
And his dumb candle, saw his pinching throes."
Marry, daylight--daylight might furnish the images, the crude
material; but for the fine shapings, the true turning and filing (as
mine author hath it), they must be content to hold their inspiration
of the candle. The mild internal light, that reveals them, like fires
on the domestic hearth, goes out in the sunshine. Night and silence
call out the starry fancies, Milton's Morning Hymn on Paradise, we
would hold a good wager, was penned at midnight; and Taylor's richer
description of a sun-rise smells decidedly of the taper. Even ourself,
in these our humbler lucubrations, tune our best measured cadences
(Prose has her cadences) not unfrequently to the charm of the drowsier
watchman, "blessing the doors;" or the wild sweep of winds at
midnight. Even now a loftier speculation than we have yet attempted,
courts our endeavours. We would indite something about the Solar
System.--_Betty, bring the candles_.
XVI.--THAT A SULKY TEMPER IS A MISFORTUNE
We grant that it is, and a very serious one--to a man's friends, and
to all that have to do with him; but whether the condition of the man
himself is so much to be deplored, may admit of a question. We can
speak a little to it, being ourself but lately recovered--we whisper
it in confidence, reader--out of a long and desperate fit of the
sullens. Was the cure a blessing? The conviction which wrought it,
came too clearly to leave a scruple of the fanciful injuries--for
they were mere fancies--which had provoked the humour. But the humour
itself was too self-pleasing, while it lasted--we know how bare we
lay ourself in the confession--to be abandoned all at once with the
grounds of it. We still brood over wrongs which we know to have been
imaginary; and for our old acquaintance, N----, whom we find to
have been a truer friend than we took him for, we substitute some
phantom--a Caius or a Titius--as like him as we dare to form it, to
wreak our yet unsatisfied resentments on. It is mortifying to fall at
once from the pinnacle of neglect; to forego the idea of having been
ill-used and contumaciously treated by an old friend. The first thing
to aggrandise a man in his own conceit, is to conceive of himself as
neglected. There let him fix if he can. To undeceive him is to deprive
him of the most tickling morsel within the range of self-complacency.
No flattery can come near it. Happy is he who suspects his friend of
an injustice; but supremely blest, who thinks all his friends in a
conspiracy to depress and undervalue him. There is a pleasure (we
sing not to the profane) far beyond the reach of all that the world
counts joy--a deep, enduring satisfaction in the depths, where the
superficial seek it not, of discontent. Were we to recite one half of
this mystery, which we were let into by our late dissatisfaction, all
the world would be in love with disrespect; we should wear a slight
for a bracelet, and neglects and contumacies would be the only matter
for courtship. Unlike to that mysterious book in the Apocalypse, the
study of this mystery is unpalatable only in the commencement. The
first sting of a suspicion is grievous; but wait--out of that wound,
which to flesh and blood seemed so difficult, there is balm and honey
to be extracted. Your friend passed you on such or such a day,--having
in his company one that you conceived worse than ambiguously disposed
towards you,--passed you in the street without notice. To be sure he
is something shortsighted; and it was in your power to have accosted
_him_. But facts and sane inferences are trifles to a true adept in
the science of dissatisfaction. He must have seen you; and S----,
who was with him, must have been the cause of the contempt. It galls
you, and well it may. But have patience. Go home, and make the worst
of it, and you are a made man from this time. Shut yourself up,
and--rejecting, as an enemy to your peace, every whispering suggestion
that but insinuates there may be a mistake--reflect seriously upon the
many lesser instances which you had begun to perceive, in proof of
your friend's disaffection towards you. None of them singly was much
to the purpose, but the aggregate weight is positive; and you have
this last affront to clench them. Thus far the process is any thing
but agreeable. But now to your relief comes in the comparative
faculty. You conjure up all the kind feelings you have had for your
friend; what you have been to him, and what you would have been to
him, if he would have suffered you; how you defended him in this
or that place; and his good name--his literary reputation, and so
forth, was always dearer to you than your own! Your heart, spite of
itself, yearns towards him. You could weep tears of blood but for a
restraining pride. How say you? do you not yet begin to apprehend a
comfort? some allay of sweetness in the bitter waters? Stop not here,
nor penuriously cheat yourself of your reversions. You are on vantage
ground. Enlarge your speculations, and take in the rest of your
friends, as a spark kindles more sparks. Was there one among them, who
has not to you proved hollow, false, slippery as water? Begin to think
that the relation itself is inconsistent with mortality. That the very
idea of friendship, with its component parts, as honour, fidelity,
steadiness, exists but in your single bosom. Image yourself to
yourself, as the only possible friend in a world incapable of that
communion. Now the gloom thickens. The little star of self-love
twinkles, that is to encourage you through deeper glooms than this.
You are not yet at the half point of your elevation. You are not yet,
believe me, half sulky enough. Adverting to the world in general, (as
these circles in the mind will spread to infinity) reflect with what
strange injustice you have been treated in quarters where, (setting
gratitude and the expectation of friendly returns aside as chimeras,)
you pretended no claim beyond justice, the naked due of all men. Think
the very idea of right and fit fled from the earth, or your breast
the solitary receptacle of it, till you have swelled yourself into at
least one hemisphere; the other being the vast Arabia Stony of your
friends and the world aforesaid. To grow bigger every moment in your
own conceit, and the world to lessen: to deify yourself at the expense
of your species; to judge the world--this is the acme and supreme
point of your mystery--these the true PLEASURES of SULKINESS. We
profess no more of this grand secret than what ourself experimented
on one rainy afternoon in the last week, sulking in our study. We had
proceeded to the penultimate point, at which the true adept seldom
stops, where the consideration of benefit forgot is about to merge
in the meditation of general injustice--when a knock at the door was
followed by the entrance of the very friend, whose not seeing of us in
the morning, (for we will now confess the case our own), an accidental
oversight, had given rise to so much agreeable generalization!
To mortify us still more, and take down the whole flattering
superstructure which pride had piled upon neglect, he had brought in
his hand the identical S----, in whose favour we had suspected him of
the contumacy. Asseverations were needless, where the frank manner of
them both was convictive of the injurious nature of the suspicion. We
fancied that they perceived our embarrassment; but were too proud, or
something else, to confess to the secret of it. We had been but too
lately in the condition of the noble patient in Argos:
Qui se credebat miros audire tragoedos.
In vacuo laetus sessor plausorque theatro--
and could have exclaimed with equal reason against the friendly hands
that cured us--
Pol me occidistis, amici,
Non servastis, ait; cui sic extorta voluptas,
Et demptus per vim mentis gratissimus error.
APPENDIX
LAMB'S ESSAYS ON "THE OLD ACTORS" AS ORIGINALLY PRINTED IN THE _LONDON
MAGAZINE_. (SEE NOTE ON PAGE 444.)
ON SOME OF THE OLD ACTORS
(_London Magazine_, Feb., 1822)
Of all the actors who flourished in my time--a melancholy phrase
if taken aright, reader--Bensley had most of the swell of soul,
was greatest in the delivery of heroic conceptions, the emotions
consequent upon the presentment of a great idea to the fancy. He had
the true poetical enthusiasm--the rarest faculty among players. None
that I remember possessed even a portion of that fine madness which
he threw out in Hotspur's famous rant about glory, or the transports
of the Venetian incendiary at the vision of the fired city.[1] His
voice had the dissonance, and at times the inspiriting effect of
the trumpet. His gait was uncouth and stiff, but no way embarrassed
by affectation; and the thorough-bred gentleman was uppermost in
every movement. He seized the moment of passion with the greatest
truth; like a faithful clock never striking before the time; never
anticipating or leading you to anticipate. He was totally destitute
of trick and artifice. He seemed come upon the stage to do the poet's
message simply, and he did it with as genuine fidelity as the nuncios
in Homer deliver the errands of the gods. He let the passion or the
sentiment do its own work without prop or bolstering. He would have
scorned to mountebank it; and betrayed none of that _cleverness_ which
is the bane of serious acting. For this reason, his Iago was the only
endurable one which I remember to have seen. No spectator from his
action could divine more of his artifice than Othello was supposed to
do. His confessions in soliloquy alone put you in possession of the
mystery. There were no bye-intimations to make the audience fancy
their own discernment so much greater than that of the Moor--who
commonly stands like a great helpless mark set up for mine Ancient,
and a quantity of barren spectators, to shoot their bolts at. The Iago
of Bensley did not go to work so grossly. There was a triumphant tone
about the character, natural to a general consciousness of power; but
none of that petty vanity which chuckles and cannot contain itself
upon any little successful stroke of its knavery--which is common with
your small villains, and green probationers in mischief. It did not
clap or crow before its time. It was not a man setting his wits at a
child, and winking all the while at other children who are mightily
pleased at being let into the secret; but a consummate villain
entrapping a noble nature into toils, against which no discernment was
available, where the manner was as fathomless as the purpose seemed
dark, and without motive. The part of Malvolio, in the Twelfth Night,
was performed by Bensley, with a richness and a dignity of which (to
judge from some recent castings of that character) the very tradition
must be worn out from the stage. No manager in those days would have
dreamed of giving it to Mr. Baddeley, or Mr. Parsons: when Bensley
was occasionally absent from the theatre, John Kemble thought it
no derogation to succeed to the part. Malvolio is not essentially
ludicrous. He becomes comic but by accident. He is cold, austere,
repelling; but dignified, consistent, and, for what appears, rather of
an over-stretched morality. Maria describes him as a sort of Puritan;
and he might have worn his gold chain with honour in one of our old
round-head families, in the service of a Lambert, or a Lady Fairfax.
But his morality and his manners are misplaced in Illyria. He is
opposed to the proper _levities_ of the piece, and falls in the
unequal contest. Still his pride, or his gravity, (call it which you
will) is inherent, and native to the man, not mock or affected, which
latter only are the fit objects to excite laughter. His quality is at
the best unlovely, but neither buffoon nor contemptible. His bearing
is lofty, a little above his station, but probably not much above
his deserts. We see no reason why he should not have been brave,
honourable, accomplished. His careless committal of the ring to the
ground (which he was commissioned to restore to Cesario), bespeaks a
generosity of birth and feeling.[2] His dialect on all occasions is
that of a gentleman, and a man of education. We must not confound him
with the eternal low steward of comedy. He is master of the household
to a great Princess, a dignity probably conferred upon him for other
respects than age or length of service.[3] Olivia, at the first
indication of his supposed madness, declares that she "would not
have him miscarry for half of her dowry." Does this look as if
the character was meant to appear little or insignificant? Once,
indeed, she accuses him to his face--of what?--of being "sick of
self-love,"--but with a gentleness and considerateness which could
not have been, if she had not thought that this particular infirmity
shaded some virtues. His rebuke to the knight, and his sottish
revellers, is sensible and spirited; and when we take into
consideration the unprotected condition of his mistress, and the
strict regard with which her state of real or dissembled mourning
would draw the eyes of the world upon her house-affairs, Malvolio
might feel the honour of the family in some sort in his keeping, as
it appears not that Olivia had any more brothers, or kinsmen, to look
to it--for Sir Toby had dropped all such nice respects at the buttery
hatch. That Malvolio was meant to be represented as possessing some
estimable qualities, the expression of the Duke in his anxiety to
have him reconciled, almost infers: "Pursue him, and intreat him to
a peace." Even in his abused state of chains and darkness, a sort of
greatness seems never to desert him. He argues highly and well with
the supposed Sir Topas,[4] and philosophizes gallantly upon his straw.
There must have been some shadow of worth about the man; he must have
been something more than a mere vapour--a thing of straw, or Jack in
office--before Fabian and Maria could have ventured sending him upon a
courting errand to Olivia. There was some consonancy (as he would say)
in the undertaking, or the jest would have been too bold even for that
house of misrule. There was "example for it," said Malvolio; "the lady
of the Strachy married the yeoman of the wardrobe." Possibly too he
might remember--for it must have happened about his time--an instance
of a Duchess of Malfy (a countrywoman of Olivia's, and her equal at
least) descending from her state to court her steward--
The misery of them that are born great!
They are forced to woo, because none dare woo them.
To be sure the lady was not very tenderly handled for it by her
brothers in the sequel, but their vengeance appears to have been
whetted rather by her presumption in re-marrying at all, (when they
had meditated the keeping of her fortune in their family) than by her
choice of an inferior, of Antonio's noble merits especially, for her
husband; and, besides, Olivia's brother was just dead. Malvolio was a
man of reading, and possibly reflected upon these lines, or something
like them in his own country poetry--
--Ceremony has made many fools.
It is as easy way unto a duchess
As to a hatted dame, if her love answer:
But that by timorous honours, pale respects,
Idle degrees of fear, men make their ways
Hard of themselves.
"'Tis but fortune, all is fortune. Maria once told me, she did affect
me; and I have heard herself come thus near, that, should she fancy,
it should be one of my complexion." If here was no encouragement, the
devil is in it. I wish we could get at the private history of all
this. Between the Countess herself, serious or dissembling--for one
hardly knows how to apprehend this fantastical great lady--and the
practices of that delicious little piece of mischief, Maria--
The lime twigs laid
By Machiavel the waiting maid--
the man might well be rapt into a fool's paradise.
Bensley threw over the part an air of Spanish loftiness. He looked,
spake, and moved like an old Castilian. He was starch, spruce,
opinionated, but his superstructure of pride seemed bottomed upon a
sense of worth. There was something in it beyond the coxcomb. It was
big and swelling, but you could not be sure that it was hollow. You
might wish to see it taken down, but you felt that it was upon an
elevation. He was magnificent from the outset; but when the decent
sobrieties of the character began to give way, and the poison of
self-love in his conceit of the Countess's affection gradually to
work, you would have thought that the hero of La Mancha in person
stood before you. How he went smiling to himself! with what ineffable
carelessness would he twirl his gold chain! what a dream it was! you
were infected with the illusion, and did not wish that it should be
removed! you had no room for laughter! if an unseasonable reflection
of morality obtruded itself, it was a deep sense of the pitiable
infirmity of man's nature, that can lay him open to such frenzies--but
in truth you rather admired than pitied the lunacy while it
lasted--you felt that an hour of such mistake was worth an age with
the eyes open. Who would not wish to live but for a day in the conceit
of such a lady's love as Olivia? Why, the Duke would have given his
principality but for a quarter of a minute, sleeping or waking, to
have been so deluded. The man seemed to tread upon air, to taste
manna, to walk with his head in the clouds, to mate Hyperion. O! shake
not the castles of his pride--endure yet for a season, bright moments
of confidence--"stand still ye watches of the element," that Malvolio
may be still in fancy fair Olivia's lord--but fate and retribution say
no--I hear the mischievous titter of Maria--the witty taunts of Sir
Toby--the still more insupportable triumph of the foolish knight--the
counterfeit Sir Topas is unmasked--and "thus the whirligig of time,"
as the true clown hath it, "brings in his revenges." I confess that I
never saw the catastrophe of this character while Bensley played it
without a kind of tragic interest. There was good foolery too. Few now
remember Dodd. What an Aguecheek the stage lost in him! Lovegrove,
who came nearest to the old actors, revived the character some few
seasons ago, and made it sufficiently grotesque; but Dodd was _it_,
as it came out of nature's hands. It might be said to remain _in
puris naturalibus_. In expressing slowness of apprehension this actor
surpassed all others. You could see the first dawn of an idea stealing
slowly over his countenance, climbing up by little and little, with
a painful process, till it cleared up at last to the fulness of a
twilight conception--its highest meridian. He seemed to keep back
his intellect, as some have had the power to <DW44> their pulsation.
The balloon takes less time in filling, than it took to cover
the expansion of his broad moony face over all its quarters with
expression. A glimmer of understanding would appear in a corner of his
eye, and for lack of fuel go out again. A part of his forehead would
catch a little intelligence, and be a long time in communicating it to
the remainder.
I am ill at dates, but I think it is now better than five and twenty
years ago that walking in the gardens of Gray's Inn--they were then
far finer than they are now--the accursed Verulam Buildings had not
encroached upon all the east side of them, cutting out delicate green
crankles, and shouldering away one of two of the stately alcoves
of the terrace--the survivor stands gaping and relationless as if
it remembered its brother--they are still the best gardens of any
of the Inns of Court, my beloved Temple not forgotten--have the
gravest character, their aspect being altogether reverend and
law-breathing--Bacon has left the impress of his foot upon their
gravel walks--taking my afternoon solace on a summer day upon the
aforesaid terrace, a comely sad personage came towards me, whom from
his grave air and deportment I judged to be one of the old Benchers
of the Inn. He had a serious thoughtful forehead, and seemed to be
in meditations of mortality. As I have an instinctive awe of old
Benchers, I was passing him with that sort of subindicative token of
respect which one is apt to demonstrate towards a venerable stranger,
and which rather denotes an inclination to greet him than any
positive motion of the body to that effect--a species of humility and
will-worship which I observe nine times out of ten rather puzzles
than pleases the person it is offered to--when the face turning full
upon me strangely identified itself with that of Dodd. Upon close
inspection I was not mistaken. But could this sad thoughtful
countenance be the same vacant face of folly which I had hailed so
often under circumstances of gaiety; which I had never seen without
a smile, or recognized but as the usher of mirth; that looked out
so formally flat in Foppington, so frothily pert in Tattle, so
impotently busy in Backbite; so blankly divested of all meaning, or
resolutely expressive of none, in Acres, in Fribble, and a thousand
agreeable impertinences? Was this the face--full of thought and
carefulness--that had so often divested itself at will of every trace
of either to give me diversion, to clear my cloudy face for two or
three hours at least of its furrows? Was this the face--manly, sober,
intelligent,--which I had so often despised, made mocks at, made merry
with? The remembrance of the freedoms which I had taken with it came
upon me with a reproach of insult. I could have asked it pardon. I
thought it looked upon me with a sense of injury. There is something
strange as well as sad in seeing actors--your pleasant fellows
particularly--subjected to and suffering the common lot--their
fortunes, their casualties, their deaths, seem to belong to the scene,
their actions to be amenable to poetic justice only. We can hardly
connect them with more awful responsibilities. The death of this fine
actor took place shortly after this meeting. He had quitted the stage
some months; and, as I learned afterwards, had been in the habit of
resorting daily to these gardens almost to the day of his decease. In
these serious walks probably he was divesting himself of many scenic
and some real vanities--weaning himself from the frivolities of the
lesser and the greater theatre--doing gentle penance for a life of no
very reprehensible fooleries,--taking off by degrees the buffoon mask
which he might feel he had worn too long--and rehearsing for a more
solemn cast of part. Dying he "put on the weeds of Dominic."[5]
The elder Palmer (of stage-treading celebrity) commonly played Sir
Toby in those days; but there is a solidity of wit in the jests of
that half-Falstaff which he did not quite fill out. He was as much too
showy as Moody (who sometimes took the part) was dry and sottish. In
sock or buskin there was an air of swaggering gentility about Jack
Palmer. He was a _gentleman_ with a slight infusion of _the footman_.
His brother Bob (of recenter memory) who was his shadow in every thing
while he lived, and dwindled into less than a shadow afterwards--was
a _gentleman_ with a little stronger infusion of the _latter
ingredient_; that was all. It is amazing how a little of the more or
less makes a difference in these things. When you saw Bobby in the
Duke's Servant,[6] you said, what a pity such a pretty fellow was only
a servant. When you saw Jack figuring in Captain Absolute, you thought
you could trace his promotion to some lady of quality who fancied the
handsome fellow in his top-knot, and had bought him a commission.
Therefore Jack in Dick Amlet was insuperable.
Jack had two voices,--both plausible, hypocritical, and insinuating;
but his secondary or supplemental voice still more decisively
histrionic than his common one. It was reserved for the spectator; and
the dramatis personae were supposed to know nothing at all about it.
The _lies_ of young Wilding, and the _sentiments_ in Joseph Surface,
were thus marked out in a sort of italics to the audience. This secret
correspondence with the company before the curtain (which is the
bane and death of tragedy) has an extremely happy effect in some
kinds of comedy, in the more highly artificial comedy of Congreve
or of Sheridan especially, where the absolute sense of reality (so
indispensable to scenes of interest) is not required, or would rather
interfere to diminish your pleasure. The fact is, you do not believe
in such characters as Surface--the villain of artificial comedy--even
while you read or see them. If you did, they would shock and not
divert you. When Ben, in Love for Love, returns from sea, the
following exquisite dialogue occurs at his first meeting with his
father--
_Sir Sampson_. Thou hast been many a weary league, Ben, since I saw
thee.
_Ben_. Ey, ey, been! Been far enough, an that be all--Well father, and
how do all at home? how does brother Dick, and brother Val?
_Sir Sampson_. Dick! body o' me, Dick has been dead these two years. I
writ you word when you were at Leghorn.
_Ben_. Mess, that's true; Marry, I had forgot. Dick's dead, as you
say--Well, and how?--I have a many questions to ask you--
Here is an instance of insensibility which in real life would be
revolting, or rather in real life could not have co-existed with the
warm-hearted temperament of the character. But when you read it in the
spirit with which such playful selections and specious combinations
rather than strict _metaphrases_ of nature should be taken, or when
you saw Bannister play it, it neither did, nor does wound the moral
sense at all. For what is Ben--the pleasant sailor which Bannister
gave us--but a piece of a satire--a creation of Congreve's fancy--a
dreamy combination of all the accidents of a sailor's character--his
contempt of money--his credulity to women--with that necessary
estrangement from home which it is just within the verge of
credibility to suppose _might_ produce such an hallucination as is
here described. We never think the worse of Ben for it, or feel it
as a stain upon his character. But when an actor comes, and instead
of the delightful phantom--the creature dear to half-belief--which
Bannister exhibited--displays before our eyes a downright concretion
of a Wapping sailor--a jolly warm-hearted Jack Tar--and nothing
else--when instead of investing it with a delicious confusedness of
the head, and a veering undirected goodness of purpose--he gives to
it a downright daylight understanding, and a full consciousness of its
actions; thrusting forward the sensibilities of the character with a
pretence as if it stood upon nothing else, and was to be judged by
them alone--we feel the discord of the thing; the scene is disturbed;
a real man has got in among the dramatis personae, and puts them out.
We want the sailor turned out. We feel that his true place is not
behind the curtain, but in the first or second gallery.
(_To be resumed occasionally_.)
ELIA.
[Footnote 1:
How lovelily the Adriatic whore
Dress'd in her flames will shine--devouring flames--
Such as will burn her to her wat'ry bottom,
And hiss in her foundation.
_Pierre, in Venice Preserved._]
[Footnote 2: _Viola_. She took the ring from me; I'll none of it.
_Mal_. Come, Sir, you peevishly threw it to her; and her will is, it
should be so returned. If it be worth stooping for, there it lies in
your eye; if not, be it his that finds it.]
[Footnote 3: Mrs. Inchbald seems to have fallen into the common
mistake of the character in some sensible observations, otherwise,
upon this Comedy. "It might be asked," she says, "whether this
credulous steward was much deceived in imputing a degraded taste, in
the sentiments of love, to his fair lady Olivia, as she actually did
fall in love with a domestic; and one, who from his extreme youth,
was perhaps a greater reproach to her discretion, than had she cast a
tender regard upon her old and faithful servant." But where does she
gather the fact of his age? Neither Maria nor Fabian ever cast that
reproach upon him.]
[Footnote 4: _Clown._ What is the opinion of Pythagoras concerning
wild fowl?
_Mal._ That the soul of our grandam might haply inhabit a bird.
_Clown._ What thinkest thou of his opinion?
_Mal._ I think nobly of the soul, and no way approve of his opinion.]
[Footnote 5: Dodd was a man of reading, and left at his death a choice
collection of old English literature. I should judge him to have been
a man of wit. I know one instance of an impromptu which no length of
study could have bettered. My merry friend, Jem White, had seen him
one evening in Aguecheek, and recognizing Dodd the next day in Fleet
Street, was irresistibly impelled to take off his hat and salute him
as the identical Knight of the preceding evening with a "Save you,
_Sir Andrew_." Dodd, not at all disconcerted at this unusual address
from a stranger, with a courteous half-rebuking wave of the hand, put
him off with an "Away, _Fool_."]
[Footnote 6: High Life Below Stairs.]
THE OLD ACTORS
(_London Magazine_, April, 1822)
The artificial Comedy, or Comedy of manners, is quite extinct on our
stage. Congreve and Farquhar show their heads once in seven years only
to be exploded and put down instantly. The times cannot bear them. Is
it for a few wild speeches, an occasional licence of dialogue? I think
not altogether. The business of their dramatic characters will not
stand the moral test. We screw every thing up to that. Idle gallantry
in a fiction, a dream, the passing pageant of an evening, startles us
in the same way as the alarming indications of profligacy in a son or
ward in real life should startle a parent or guardian. We have no such
middle emotions as dramatic interests left. We see a stage libertine
playing his loose pranks of two hours' duration, and of no after
consequence, with the severe eyes which inspect real vices with their
bearings upon two worlds. We are spectators to a plot or intrigue (not
reducible in life to the point of strict morality) and take it all
for truth. We substitute a real for a dramatic person, and judge him
accordingly. We try him in our courts, from which there is no appeal
to the _dramatis personae_, his peers. We have been spoiled with--not
sentimental comedy--but a tyrant far more pernicious to our pleasures
which has succeeded to it, the exclusive and all-devouring drama of
common life; where the moral point is everything; where, instead of
the fictitious half-believed personages of the stage (the phantoms of
old comedy) we recognise ourselves, our brothers, aunts, kinsfolk,
allies, patrons, enemies,--the same as in life,--with an interest in
what is going on so hearty and substantial, that we cannot afford our
moral judgment, in its deepest and most vital results, to compromise
or slumber for a moment. What is _there_ transacting, by no
modification is made to affect us in any other manner than the same
events or characters would do in our relationships of life. We carry
our fire-side concerns to the theatre with us. We do not go thither,
like our ancestors, to escape from the pressure of reality, so much as
to confirm our experience of it; to make assurance double, and take a
bond of fate. We must live our toilsome lives twice over, as it was
the mournful privilege of Ulysses to descend twice to the shades. All
that neutral ground of character which stood between vice and virtue;
or which, in fact, was indifferent to neither, where neither properly
was called in question--that happy breathing-place from the burden
of a perpetual moral questioning--the sanctuary and quiet Alsatia
of hunted casuistry--is broken up and disfranchised as injurious to
the interests of society. The privileges of the place are taken away
by law. We dare not dally with images or names of wrong. We bark
like foolish dogs at shadows. We dread infection from the scenic
representation of disorder; and fear a painted pustule. In our anxiety
that our morality should not take cold, we wrap it up in a great
blanket surtout of precaution against the breeze and sunshine.
I confess for myself that (with no great delinquencies to answer for)
I am glad for a season to take an airing beyond the diocese of the
strict conscience,--not to live always in the precincts of the law
courts,--but now and then, for a dream-while or so, to imagine a world
with no meddling restrictions--to get into recesses, whither the
hunter cannot follow me--
--Secret shades
Of woody Ida's inmost grove,
While yet there was no fear of Jove--
I come back to my cage and my restraint the fresher and more healthy
for it. I wear my shackles more contentedly for having respired the
breath of an imaginary freedom. I do not know how it is with
others, but I feel the better always for the perusal of one of
Congreve's--nay, why should I not add even of Wycherley's--comedies. I
am the gayer at least for it; and I could never connect those sports
of a witty fancy in any shape with any result to be drawn from them to
imitation in real life. They are a world of themselves almost as much
as a fairyland. Take one of their characters, male or female (with
few exceptions they are alike), and place it in a modern play, and
my virtuous indignation shall rise against the profligate wretch as
warmly as the Catos of the pit could desire; because in a modern play
I am to judge of right and wrong, and the standard of _police_ is
the measure of _poetical justice_. The atmosphere will blight it.
It cannot thrive here. It is got into a moral world where it has
no business; from which it must needs fall head-long; as dizzy and
incapable of keeping its stand, as a Swedenborgian bad spirit that has
wandered unawares within the sphere of one of his good men or angels.
But in its own world do we feel the creature is so very bad?
The Fainalls and the Mirabels, the Dorimants, and Lady Touchwoods, in
their own sphere do not offend my moral sense--or, in fact, appeal
to it at all. They seem engaged in their proper element. They break
through no laws, or conscientious restraints. They know of none. They
have got out of Christendom into the land--what shall I call it?--of
cuckoldry--the Utopia of gallantry, where pleasure is duty, and the
manners perfect freedom. It is altogether a speculative scene of
things, which has no reference whatever to the world that is. No good
person can be justly offended as a spectator, because no good person
suffers on the stage. Judged morally, every character in these
plays--the few exceptions only are _mistakes_--is alike essentially
vain and worthless. The great art of Congreve is especially shown in
this, that he has entirely excluded from his scenes,--some little
generosities in the part of Angelica perhaps excepted,--not only any
thing like a faultless character, but any pretensions to goodness
or good feelings whatsoever. Whether he did this designedly, or
instinctively, the effect is as happy, as the design (if design) was
bold. I used to wonder at the strange power which his Way of the World
in particular possesses of interesting you all along in the pursuits
of characters, for whom you absolutely care nothing--for you neither
hate nor love his personages--and I think it is owing to this very
indifference for any, that you endure the whole. He has spread a
privation of moral light, I will call it, rather than by the ugly name
of palpable darkness, over his creations; and his shadows flit before
you without distinction or preference. Had he introduced a good
character, a single gush of moral feeling, a revulsion of the judgment
to actual life and actual duties, the impertinent Goshen would have
only lighted to the discovery of deformities, which now are none,
because we think them none.
Translated into real life, the characters of his, and his friend
Wycherley's dramas, are profligates and strumpets,--the business of
their brief existence, the undivided pursuit of lawless gallantry. No
other spring of action, or possible motive of conduct, is recognised;
principles which universally acted upon must reduce this frame of
things to a chaos. But we do them wrong in so translating them. No
such effects are produced in _their_ world. When we are among them, we
are amongst a chaotic people. We are not to judge them by our usages.
No reverend institutions are insulted by their proceedings,--for
they have none among them. No peace of families is violated,--for
no family ties exist among them. No purity of the marriage bed is
stained,--for none is supposed to have a being. No deep affections
are disquieted,--no holy wedlock bands are snapped asunder,--for
affection's depth and wedded faith are not of the growth of that soil.
There is neither right nor wrong,--gratitude or its opposite,--claim
or duty,--paternity or sonship. Of what consequence is it to virtue,
or how is she at all concerned about it, whether Sir Simon, or
Dapperwit, steal away Miss Martha; or who is the father of Lord
Froth's, or Sir Paul Pliant's children?
The whole is a passing pageant, where we should sit as unconcerned at
the issues, for life or death, as at a battle of the frogs and mice.
But like Don Quixote, we take part against the puppets, and quite as
impertinently. We dare not contemplate an Atlantis, a scheme, out of
which our coxcombical moral sense is for a little transitory ease
excluded. We have not the courage to imagine a state of things for
which there is neither reward nor punishment. We cling to the painful
necessities of shame and blame. We would indict our very dreams.
Amidst the mortifying circumstances attendant upon growing old, it
is something to have seen the School for Scandal in its glory. This
comedy grew out of Congreve and Wycherley, but gathered some allays of
the sentimental comedy which followed theirs. It is impossible that
it should be now acted, though it continues, at long intervals, to be
announced in the bills. Its hero, when Palmer played it at least, was
Joseph Surface. When I remember the gay boldness, the graceful solemn
plausibility, the measured step, the insinuating voice--to express it
in a word--the downright _acted_ villany of the part, so different
from the pressure of conscious actual wickedness,--the hypocritical
assumption of hypocrisy,--which made Jack so deservedly a favourite
in that character, I must needs conclude the present generation of
playgoers more virtuous than myself, or more dense. I freely confess
that he divided the palm with me with his better brother; that, in
fact, I liked him quite as well. Not but there are passages,--like
that, for instance, where Joseph is made to refuse a pittance to a
poor relation,--incongruities which Sheridan was forced upon by the
attempt to join the artificial with the sentimental comedy, either
of which must destroy the other--but over these obstructions Jack's
manner floated him so lightly, that a refusal from him no more shocked
you, than the easy compliance of Charles gave you in reality any
pleasure; you got over the paltry question as quickly as you could, to
get back into the regions of pure comedy, where no cold moral reigns.
The highly artificial manner of Palmer in this character counteracted
every disagreeable impression which you might have received from the
contrast, supposing them real, between the two brothers. You did
not believe in Joseph with the same faith with which you believed
in Charles. The latter was a pleasant reality, the former a no less
pleasant poetical foil to it. The comedy, I have said, is incongruous;
a mixture of Congreve with sentimental incompatibilities; the gaity
upon the whole is buoyant; but it required the consummate art of
Palmer to reconcile the discordant elements.
A player with Jack's talents, if we had one now, would not dare to do
the part in the same manner. He would instinctively avoid every
turn which might tend to unrealize, and so to make the character
fascinating. He must take his cue from his spectators, who would
expect a bad man and a good man as rigidly opposed to each other, as
the death-beds of those geniuses are contrasted in the prints, which
I am sorry to see have disappeared from the windows of my old friend
Carrington Bowles, of St. Paul's Churchyard memory--(an exhibition as
venerable as the adjacent cathedral, and almost coeval) of the bad
and good man at the hour of death; where the ghastly apprehensions
of the former,--and truly the grim phantom with his reality of a
toasting fork is not to be despised,--so finely contrast with the
meek complacent kissing of the rod,--taking it in like honey and
butter,--with which the latter submits to the scythe of the gentle
bleeder, Time, who wields his lancet with the apprehensive finger of
a popular young ladies' surgeon. What flesh, like loving grass, would
not covet to meet half-way the stroke of such a delicate mower?--John
Palmer was twice an actor in this exquisite part. He was playing to
you all the while that he was playing upon Sir Peter and his lady. You
had the first intimation of a sentiment before it was on his lips.
His altered voice was meant to you, and you were to suppose that his
fictitious co-flutterers on the stage perceived nothing at all of it.
What was it to you if that half-reality, the husband, was over-reached
by the puppetry--or the thin thing (Lady Teazle's reputation) was
persuaded it was dying of a plethory? The fortunes of Othello and
Desdemona were not concerned in it. Poor Jack has passed from
the stage--in good time, that he did not live to this our age of
seriousness. The fidgety pleasant old Teazle _King_ too is gone in
good time. His manner would scarce have passed current in our day.
We must love or hate--acquit or condemn--censure or pity--exert our
detestable coxcombry of moral judgment upon every thing. Joseph
Surface, to go down now, must be a downright revolting villain--no
compromise--his first appearance must shock and give horror--his
specious plausibilities, which the pleasurable faculties of our
fathers welcomed with such hearty greetings, knowing that no harm
(dramatic harm even) could come, or was meant to come of them, must
inspire a cold and killing aversion. Charles (the real canting person
of the scene--for the hypocrisy of Joseph has its ulterior legitimate
ends, but his brother's professions of a good heart centre in
down-right self-satisfaction) must be _loved_, and Joseph _hated_. To
balance one disagreeable reality with another, Sir Peter Teazle must
be no longer the comic idea of a fretful old bachelor bridegroom,
whose teazings (while King acted it) were evidently as much played off
at you, as they were meant to concern any body on the stage,--he must
be a real person, capable in law of sustaining an injury--a person
towards whom duties are to be acknowledged--the genuine crim-con
antagonist of the villainous seducer, Joseph. To realize him more,
his sufferings under his unfortunate match must have the downright
pungency of life--must (or should) make you not mirthful but
uncomfortable, just as the same predicament would move you in a
neighbour or old friend. The delicious scenes which give the play its
name and zest, must affect you in the same serious manner as if you
heard the reputation of a dear female friend attacked in your real
presence. Crabtree, and Sir Benjamin--those poor snakes that lived
but in the sunshine of your mirth--must be ripened by this hot-bed
process of realization into asps or amphisbaenas; and Mrs. Candour--O
frightful! become a hooded serpent. Oh who that remembers Parsons and
Dodd--the wasp and butterfly of the School for Scandal--in those two
characters; and charming natural Miss Pope, the perfect gentlewoman as
distinguished from the fine lady of comedy, in this latter part--would
forego the true scenic delight--the escape from life--the oblivion of
consequences--the holiday barring out of the pedant Reflection--those
Saturnalia of two or three brief hours, well won from the world--to
sit instead at one of our modern plays--to have his coward conscience
(that forsooth must not be left for a moment) stimulated with
perpetual appeals--dulled rather, and blunted, as a faculty without
repose must be--and his moral vanity pampered with images of notional
justice, notional beneficence, lives saved without the spectators'
risk, and fortunes given away that cost the author nothing?
No piece was, perhaps, ever so completely cast in all its parts as
this _manager's comedy_. Miss Farren had succeeded to Mrs. Abingdon
in Lady Teazle; and Smith, the original Charles, had retired, when I
first saw it. The rest of the characters, with very slight exceptions,
remained. I remember it was then the fashion to cry down John Kemble,
who took the part of Charles after Smith; but, I thought, very
unjustly. Smith, I fancy, was more airy, and took the eye with a
certain gaiety of person. He brought with him no sombre recollections
of tragedy. He had not to expiate the fault of having pleased
beforehand in lofty declamation. He had no sins of Hamlet or of
Richard to atone for. His failure in these parts was a passport to
success in one of so opposite a tendency. But as far as I could judge,
the weighty sense of Kemble made up for more personal incapacity than
he had to answer for. His harshest tones in this part came steeped
and dulcified in good humour. He made his defects a grace. His exact
declamatory manner, as he managed it, only served to convey the points
of his dialogue with more precision. It seemed to head the shafts to
carry them deeper. Not one of his sparkling sentences was lost. I
remember minutely how he delivered each in succession, and cannot by
any effort imagine how any of them could be altered for the better. No
man could deliver brilliant dialogue--the dialogue of Congreve or of
Wycherley--because none understood it--half so well as John Kemble.
His Valentine, in Love for Love, was, to my recollection, faultless.
He flagged sometimes in the intervals of tragic passion. He would
slumber over the level parts of an heroic character. His Macbeth has
been known to nod. But he always seemed to me to be particularly alive
to pointed and witty dialogue. The relaxing levities of tragedy have
not been touched by any since him--the playful court-bred spirit in
which he condescended to the players in Hamlet--the sportive relief,
which he threw into the darker shades of Richard--disappeared with
him. Tragedy is become a uniform dead weight. They have fastened lead
to her buskins. She never pulls them off for the ease of a moment.
To invert a commonplace from Niobe, she never forgets herself to
liquefaction. John had his sluggish moods, his torpors--but they were
the halting stones and resting places of his tragedy--politic savings,
and fetches of the breath--husbandry of the lungs, where nature
pointed him to be an economist--rather, I think, than errors of
the judgment. They were, at worst, less painful than the eternal
tormenting unappeasable vigilance, the "lidless dragon eyes," of
present fashionable tragedy. The story of his swallowing opium pills
to keep him lively upon the first night of a certain tragedy, we may
presume to be a piece of retaliatory pleasantry on the part of the
suffering author. But, indeed, John had the art of diffusing a
complacent equable dulness (which you knew not where to quarrel with)
over a piece which he did not like, beyond any of his contemporaries.
John Kemble had made up his mind early, that all the good tragedies,
which could be written, had been written; and he resented any new
attempt. His shelves were full. The old standards were scope enough
for his ambition. He ranged in them absolute--and "fair in Otway, full
in Shakspeare shone." He succeeded to the old lawful thrones, and did
not care to adventure bottomry with a Sir Edward Mortimer, or any
casual speculator that offered. I remember, too acutely for my peace,
the deadly extinguisher which he put upon my friend G.'s "Antonio."
G., satiate with visions of political justice (possibly not to be
realized in our time), or willing to let the sceptical worldlings see,
that his anticipations of the future did not preclude a warm sympathy
for men as they are and have been--wrote a tragedy. He chose a
story, affecting, romantic, Spanish--the plot simple, without being
naked--the incidents uncommon, without being overstrained. Antonio,
who gives the name to the piece, is a sensitive young Castilian, who,
in a fit of his country honour, immolates his sister--
But I must not anticipate the catastrophe--the play, reader, is
extant in choice English--and you will employ a spare half crown not
injudiciously in the quest of it.
The conception was bold, and the denouement--the time and place in
which the hero of it existed, considered--not much out of keeping; yet
it must be confessed, that it required a delicacy of handling both
from the author and the performer, so as not much to shock the
prejudices of a modern English audience. G., in my opinion, had done
his part.
John, who was in familiar habits with the philosopher, had undertaken
to play Antonio. Great expectations were formed. A philosopher's first
play was a new era. The night arrived. I was favoured with a seat in
an advantageous box, between the author and his friend M----. G. sate
cheerful and confident. In his friend M.'s looks, who had perused the
manuscript, I read some terror. Antonio in the person of John Philip
Kemble at length appeared, starched out in a ruff which no one could
dispute, and in most irreproachable mustachios. John always dressed
most provokingly correct on these occasions. The first act swept
by, solemn and silent. It went off, as G. assured M., exactly as
the opening act of a piece--the protasis--should do. The cue of
the spectators was to be mute. The characters were but in their
introduction. The passions and the incidents would be developed
hereafter. Applause hitherto would be impertinent. Silent attention
was the effect all-desirable. Poor M. acquiesced--but in his honest
friendly face I could discern a working which told how much more
acceptable the plaudit of a single hand (however misplaced) would
have been than all this reasoning. The second act (as in duty bound)
rose a little in interest; but still John kept his forces under--in
policy, as G. would have it--and the audience were most complacently
attentive. The protasis, in fact, was scarcely unfolded. The
interest would warm in the next act, against which a special
incident was provided. M. wiped his cheek, flushed with a friendly
perspiration--'tis M.'s way of showing his zeal--"from every pore of
him a perfume falls--." I honour it above Alexander's. He had once or
twice during this act joined his palms in a feeble endeavour to elicit
a sound--they emitted a solitary noise without an echo--there was no
deep to answer to his deep. G. repeatedly begged him to be quiet.
The third act at length brought on the scene which was to warm the
piece progressively to the final flaming forth of the catastrophe. A
philosophic calm settled upon the clear brow of G. as it approached.
The lips of M. quivered. A challenge was held forth upon the stage,
and there was promise of a fight. The pit roused themselves on this
extraordinary occasion, and, as their manner is, seemed disposed to
make a ring,--when suddenly Antonio, who was the challenged, turning
the tables upon the hot challenger, Don Gusman (who by the way should
have had his sister) baulks his humour, and the pit's reasonable
expectation at the same time, with some speeches out of the
new philosophy against duelling. The audience were here fairly
caught--their courage was up, and on the alert--a few blows, _ding
dong_, as R----s the dramatist afterwards expressed it to me, might
have done the business--when their most exquisite moral sense was
suddenly called in to assist in the mortifying negation of their own
pleasure. They could not applaud, for disappointment; they would
not condemn, for morality's sake. The interest stood stone still;
and John's manner was not at all calculated to unpetrify it. It
was Christmas time, and the atmosphere furnished some pretext for
asthmatic affections. One began to cough--his neighbour sympathised
with him--till a cough became epidemical. But when, from being
half-artificial in the pit, the cough got frightfully naturalised
among the fictitious persons of the drama; and Antonio himself (albeit
it was not set down in the stage directions) seemed more intent
upon relieving his own lungs than the distresses of the author and
his friends,--then G. "first knew fear;" and mildly turning to M.,
intimated that he had not been aware that Mr. K. laboured under a
cold; and that the performance might possibly have been postponed
with advantage for some nights further--still keeping the same serene
countenance, while M. sweat like a bull. It would be invidious to
pursue the fates of this ill-starred evening. In vain did the plot
thicken in the scenes that followed, in vain the dialogue wax more
passionate and stirring, and the progress of the sentiment point more
and more clearly to the arduous developement which impended. In vain
the action was accelerated, while the acting stood still. From the
beginning, John had taken his stand; had wound himself up to an even
tenor of stately declamation, from which no exigence of dialogue or
person could make him swerve for an instant. To dream of his rising
with the scene (the common trick of tragedians) was preposterous;
for from the onset he had planted himself, as upon a terrace, on an
eminence vastly above the audience, and he kept that sublime level
to the end. He looked from his throne of elevated sentiment upon the
under-world of spectators with a most sovran and becoming contempt.
There was excellent pathos delivered out to them: an they would
receive it, so; an they would not receive it, so. There was no offence
against decorum in all this; nothing to condemn, to damn. Not an
irreverent symptom of a sound was to be heard. The procession of
verbiage stalked on through four and five acts, no one venturing to
predict what would come of it, when towards the winding up of the
latter, Antonio, with an irrelevancy that seemed to stagger Elvira
herself--for she had been coolly arguing the point of honour with
him--suddenly whips out a poniard, and stabs his sister to the heart.
The effect was, as if a murder had been committed in cold blood. The
whole house rose up in clamorous indignation demanding justice. The
feeling rose far above hisses. I believe at that instant, if they
could have got him, they would have torn the unfortunate author to
pieces. Not that the act itself was so exorbitant, or of a complexion
different from what they themselves would have applauded upon another
occasion in a Brutus, or an Appius--but for want of attending to
Antonio's _words_, which palpably led to the expectation of no less
dire an event, instead of being seduced by his _manner_, which
seemed to promise a sleep of a less alarming nature than it was his
cue to inflict upon Elvira, they found themselves betrayed into an
accompliceship of murder, a perfect misprision of parricide, while
they dreamed of nothing less. M., I believe, was the only person
who suffered acutely from the failure; for G. thenceforward, with
a serenity unattainable but by the true philosophy, abandoning a
precarious popularity, retired into his fast hold of speculation,--the
drama in which the world was to be his tiring room, and remote
posterity his applauding spectators at once, and actors.
ELIA.
THE OLD ACTORS
(_London Magazine_, October, 1822)
I do not know a more mortifying thing than to be conscious of a
foregone delight, with a total oblivion of the person and manner
which conveyed it. In dreams I often stretch and strain after the
countenance of Edwin, whom I once saw in Peeping Tom. I cannot catch a
feature of him. He is no more to me than Nokes or Pinkethman. Parsons,
and still more Dodd, were near being lost to me, till I was refreshed
with their portraits (fine treat) the other day at Mr. Mathews's
gallery at Highgate; which, with the exception of the Hogarth
pictures, a few years since exhibited in Pall Mall, was the most
delightful collection I ever gained admission to. There hang the
players, in their single persons, and in grouped scenes, from the
Restoration--Bettertons, Booths, Garricks, justifying the prejudices
which we entertain for them--the Bracegirdles, the Mountforts, and the
Oldfields, fresh as Cibber has described them--the Woffington (a true
Hogarth) upon a couch, dallying and dangerous--the Screen Scene in
Brinsley's famous comedy, with Smith and Mrs. Abingdon, whom I have
not seen, and the rest, whom having seen, I see still there. There is
Henderson, unrivalled in Comus, whom I saw at second hand in the elder
Harley--Harley, the rival of Holman, in Horatio--Holman, with the
bright glittering teeth in Lothario, and the deep paviour's sighs in
Romeo--the jolliest person ("our son is fat") of any Hamlet I have
yet seen, with the most laudable attempts (for a personable man) at
looking melancholy--and Pope, the abdicated monarch of tragedy and
comedy, in Harry the Eighth and Lord Townley. There hang the two
Aickins, brethren in mediocrity--Wroughton, who in Kitely seemed to
have forgotten that in prouder days he had personated Alexander--the
specious form of John Palmer, with the special effrontery of
Bobby--Bensley, with the trumpet-tongue, and little Quick (the retired
Dioclesian of Islington) with his squeak like a Bart'lemew fiddle.
There are fixed, cold as in life, the immovable features of Moody,
who, afraid of o'erstepping nature, sometimes stopped short of
her--and the restless fidgetiness of Lewis, who, with no such fears,
not seldom leaped o' the other side. There hang Farren and Whitfield,
and Burton and Phillimore, names of small account in those times, but
which, remembered now, or casually recalled by the sight of an old
play-bill, with their associated recordations, can "drown an eye
unused to flow." There too hangs (not far removed from them in death)
the graceful plainness of the first Mrs. Pope, with a voice unstrung
by age, but which, in her better days, must have competed with the
silver tones of Barry himself, so enchanting in decay do I remember
it--of all her lady parts exceeding herself in the Lady Quakeress
(there earth touched heaven!) of O'Keefe, when she played it to
the "merry cousin" of Lewis--and Mrs. Mattocks, the sensiblest
of viragos--and Miss Pope, a gentlewoman ever, to the verge of
ungentility, with Churchill's compliment still burnishing upon her gay
Honeycomb lips. There are the two Bannisters, and Sedgwick, and Kelly,
and Dignum (Diggy), and the bygone features of Mrs. Ward, matchless in
Lady Loverule; and the collective majesty of the whole Kemble family,
and (Shakspeare's woman) Dora Jordan; and, by her, _two Antics_, who
in former and in latter days have chiefly beguiled us of our griefs;
whose portraits we shall strive to recall, for the sympathy of those
who may not have had the benefit of viewing the matchless Highgate
Collection.
MR. SUETT
O for a "slip-shod muse," to celebrate in numbers, loose and shambling
as himself, the merits and the person of Mr. Richard Suett, comedian!
Richard, or rather Dicky Suett--for so in his lifetime he was best
pleased to be called, and time hath ratified the appellation--lieth
buried on the north side of the cemetery of Holy Paul, to whose
service his nonage and tender years were set apart and dedicated.
There are who do yet remember him at that period--his pipe clear and
harmonious. He would often speak of his chorister days, when he was
"cherub Dicky."
What clipped his wings, or made it expedient that he should exchange
the holy for the profane state; whether he had lost his good voice
(his best recommendation to that office), like Sir John, "with
hallooing and singing of anthems;" or whether he was adjudged to lack
something, even in those early years, of the gravity indispensable
to an occupation which professeth to "commerce with the skies"--I
could never rightly learn; but we find him, after the probation of a
twelvemonth or so, reverting to a secular condition, and become one of
us.
I think he was not altogether of that timber, out of which cathedral
seats and sounding boards are hewed. But if a glad heart--kind and
therefore glad--be any part of sanctity, then might the robe of
Motley, with which he invested himself with so much humility after
his deprivation, and which he wore so long with so much blameless
satisfaction to himself and to the public, be accepted for a
surplice--his white stole, and _albe_.
The first fruits of his secularization was an engagement upon the
boards of Old Drury, at which theatre he commenced, as I have been
told, with adopting the manner of Parsons in old men's characters. At
the period in which most of us knew him, he was no more an imitator
than he was in any true sense himself imitable.
He was the Robin Good-Fellow of the stage. He came in to trouble all
things with a welcome perplexity, himself no whit troubled for the
matter. He was known, like Puck, by his note--_Ha! Ha! Ha!_--sometimes
deepening to _Ho! Ho! Ho!_ with an irresistible accession, derived
perhaps remotely from his ecclesiastical education, foreign to
his prototype, of--_O La!_ Thousands of hearts yet respond to the
chuckling _O La!_ of Dicky Suett, brought back to their remembrance by
the faithful transcript of his friend Mathews's mimicry. The "force of
nature could no further go." He drolled upon the stock of these two
syllables richer than the cuckoo.
Care, that troubles all the world, was forgotten in his composition.
Had he had but two grains (nay, half a grain) of it, he could never
have supported himself upon those two spider's strings, which served
him (in the latter part of his unmixed existence) as legs. A doubt or
a scruple must have made him totter, a sigh have puffed him down;
the weight of a frown had staggered him, a wrinkle made him lose his
balance. But on he went, scrambling upon those airy stilts of his,
with Robin Good-Fellow, "thorough brake, thorough briar," reckless of
a scratched face or a torn doublet.
Shakspeare foresaw him, when he framed his fools and jesters. They
have all the true Suett stamp, a loose gait, a slippery tongue, this
last the ready midwife to a without-pain-delivered jest; in words
light as air, venting truths deep as the centre; with idlest rhymes
tagging conceit when busiest, singing with Lear in the tempest, or Sir
Toby at the buttery hatch.
Jack Bannister and he had the fortune to be more of personal
favourites with the town than any actors before or after. The
difference, I take it, was this:--Jack was more _beloved_ for his
sweet, good-natured, moral, pretensions. Dicky was more _liked_ for
his sweet, good-natured, no pretensions at all. Your whole conscience
stirred with Bannister's performance of Walter in the Children in the
Wood--how dearly beautiful it was!--but Dicky seemed like a thing, as
Shakspeare says of Love, too young to know what conscience is. He put
us into Vesta's days. Evil fled before him--not as from Jack, as from
an antagonist,--but because it could not touch him, any more than a
cannon-ball a fly. He was delivered from the burthen of that death;
and, when Death came himself, not in metaphor, to fetch Dicky, it is
recorded of him by Robert Palmer, who kindly watched his exit, that he
received the last stroke, neither varying his accustomed tranquillity,
nor tune, with the simple exclamation, worthy to have been recorded in
his epitaph--_O La!--O La! Bobby!_
MR. MUNDEN
Not many nights ago we had come home from seeing this extraordinary
performer in Cockletop; and when we retired to our pillow, his
whimsical image still stuck by us, in a manner as to threaten sleep.
In vain we tried to divest ourselves of it by conjuring up the most
opposite associations. We resolved to be serious. We raised up the
gravest topics of life; private misery, public calamity. All would not
do.
--There the antic sate
Mocking our state--
his queer visnomy--his bewildering costume--all the strange things
which he had raked together--his serpentine rod swagging about in his
pocket--Cleopatra's tear, and the rest of his relics--O'Keefe's wild
farce, and _his_ wilder commentary--till the passion of laughter, like
grief in excess, relieved itself by its own weight, inviting the sleep
which in the first instance it had driven away.
But we were not to escape so easily. No sooner did we fall into
slumbers, than the same image, only more perplexing, assailed us in
the shape of dreams. Not one Munden, but five hundred, were dancing
before us, like the faces which, whether you will or no, come when
you have been taking opium--all the strange combinations, which this
strangest of all strange mortals ever shot his proper countenance
into, from the day he came commissioned to dry up the tears of the
town for the loss of the now almost forgotten Edwin. O for the power
of the pencil to have fixed them when we awoke! A season or two since
there was exhibited a Hogarth gallery. We do not see why there should
not be a Munden gallery. In richness and variety the latter would not
fall far short of the former.
There is one face of Farley, one face of Knight, one face (but what a
one it is!) of Liston; but Munden has none that you can properly pin
down, and call _his_. When you think he has exhausted his battery of
looks, in unaccountable warfare with your gravity, suddenly he sprouts
out an entirely new set of features, like Hydra. He is not one, but
legion. Not so much a comedian, as a company. If his name could be
multiplied like his countenance, it might fill a play-bill. He, and
he alone, literally _makes faces_: applied to any other person, the
phrase is a mere figure, denoting certain modifications of the human
countenance. Out of some invisible wardrobe he dips for faces, as his
friend Suett used for wigs, and fetches them out as easily. We should
not be surprised to see him some day put out the head of a
river horse; or come forth a pewit, or lapwing, some feathered
metamorphosis.
We have seen this gifted actor in Sir Christopher Curry--in Old
Dornton--diffuse a glow of sentiment which has made the pulse of a
crowded theatre beat like that of one man; when he has come in aid of
the pulpit, doing good to the moral heart of a people. We have seen
some faint approaches to this sort of excellence in other players.
But in what has been truly denominated "the sublime of farce," Munden
stands out as single and unaccompanied as Hogarth. Hogarth, strange to
tell, had no followers. The school of Munden began, and must end, with
himself.
Can any man _wonder_, like him? can any man _see ghosts_, like
him? or _fight with his own shadow_--sessa--as he does in that
strangely-neglected thing, the Cobler of Preston--where his
alternations from the Cobler to the Magnifico, and from the Magnifico
to the Cobler, keep the brain of the spectator in as wild a ferment,
as if some Arabian Night were being acted before him, or as if Thalaba
were no tale! Who like him can throw, or ever attempted to throw, a
supernatural interest over the commonest daily-life objects? A table,
or a joint stool, in his conception, rises into a dignity equivalent
to Cassiopeia's chair. It is invested with constellatory importance.
You could not speak of it with more deference, if it were mounted into
the firmament. A beggar in the hands of Michael Angelo, says Fuseli,
rose the Patriarch of Poverty. So the gusto of Munden antiquates and
ennobles what it touches. His pots and his ladles are as grand and
primal as the seething-pots and hooks seen in old prophetic vision.
A tub of butter, contemplated by him, amounts to a Platonic idea. He
understands a leg of mutton in its quiddity. He stands wondering, amid
the commonplace materials of life, like primaeval man, with the sun and
stars about him.
ELIA.
NOTES
ELIA
Lamb took the name of Elia, which should, he said, be pronounced
Ellia, from an old clerk, an Italian, at the South-Sea House in Lamb's
time: that is, in 1791-1792. Writing to John Taylor in July, 1821,
just after he had taken over the magazine (see below), Lamb says,
referring to the South-Sea House essay, "having a brother now there,
and doubting how he might relish certain descriptions in it, I clapt
down the name of Elia to it, which passed off pretty well, for Elia
himself added the function of an author to that of a scrivener, like
myself. I went the other day (not having seen him [Elia] for a year)
to laugh over with him at my usurpation of his name, and found him,
alas! no more than a name, for he died of consumption eleven months
ago, and I knew not of it. So the name has fairly devolved to me, I
think; and 'tis all he has left me."
In the library at Welbeck is a copy of a pamphlet, in French, entitled
_Considerations sur l'etat actuel de la France au mois de Juin 1815,
par un Anglais_, which was presented to the Duke of Portland by the
author, F.A. Elia. This was probably Lamb's Elia. The pamphlet is
reprinted, together with other interesting matter remotely connected
with Lamb, in _Letters from the Originals at Welbeck Abbey_, privately
printed, 1909.
_Elia. Essays which have appeared under that signature in the London
Magazine_, was published early in 1823. Lamb's original intention was
to furnish the book with a whimsical preface, as we learn from the
following letter to John Taylor, dated December 7, 1822:--
"DEAR SIR,--I should like the enclosed Dedication to be printed,
unless you dislike it. I like it. It is in the olden style. But if
you object to it, put forth the book as it is; only pray don't let
the printer mistake the word _curt_ for _curst_.
"C.L.
"DEDICATION.
"TO THE FRIENDLY AND JUDICIOUS READER,
who will take these Papers, as they were meant; not understanding
every thing perversely in its absolute and literal sense, but
giving fair construction, as to an after-dinner conversation;
allowing for the rashness and necessary incompleteness of first
thoughts; and not remembering, for the purpose of an after taunt,
words spoken peradventure after the fourth glass, the Author
wishes (what he would will for himself) plenty of good friends to
stand by him, good books to solace him, prosperous events to all
his honest undertakings, and a candid interpretation to his most
hasty words and actions. The other sort (and he hopes many of them
will purchase his book too) he greets with the curt invitation of
Timon, 'Uncover, dogs, and lap:' or he dismisses them with the
confident security of the philosopher,--'you beat but on the case
of Elia.'
"On better consideration, pray omit that Dedication. The Essays
want no Preface: they are _all Preface_. A Preface is nothing but
a talk with the reader; and they do nothing else. Pray omit it.
"There will be a sort of Preface in the next Magazine, which may
act as an advertisement, but not proper for the volume.
"Let ELIA come forth bare as he was born.
"C.L.
"N.B.--_No_ Preface."
The "sort of Preface in the next number" was the character sketch of
the late Elia on page 171.
_Elia_ did not reach a second edition in Lamb's lifetime--that is to
say, during a period of twelve years--although the editions into which
it has passed between his death and the present day are legion. Why,
considering the popularity of the essays as they appeared in the
_London Magazine_, the book should have found so few purchasers is a
problem difficult of solution. Lamb himself seems to have attributed
some of the cause to Southey's objection, in the _Quarterly Review_,
that _Elia_ "wanted a sounder religious feeling;" but more probably
the book was too dear: it was published at 9s. 6d.
Ordinary reviewers do not seem to have perceived at all that a rare
humorist, humanist and master of prose had arisen, although among the
finer intellects who had any inclination to search for excellence for
excellence's sake Lamb made his way. William Hazlitt, for example,
drew attention to the rich quality of _Elia_; as also did Leigh Hunt;
and William Hone, who cannot, however, as a critic be mentioned with
these, was tireless in advocating the book. Among strangers to Lamb
who from the first extolled his genius was Miss Mitford. But _Elia_
did not sell.
Ten years passed before Lamb collected his essays again, and then
in 1833 was published _The Last Essays of Elia_, with Edward
Moxon's imprint. The mass of minor essays in the _London Magazine_
and elsewhere, which Lamb disregarded when he compiled his two
collections, will be found in Vol. I. of the present edition. _The
Last Essays of Elia_ had little, if any, better reception than the
first; and Lamb had the mortification of being asked by the Norris
family to suppress the exquisite and kindly little memoir of Randal
Norris, entitled "A Death-Bed" (see page 279), which was held to be
too personal. When, in 1835, after Lamb's death, a new edition of
_Elia_ and _The Last Essays of Elia_ was issued, the "Confessions of
a Drunkard" took its place (see Vol. I.).
Meanwhile a Philadelphian firm had been beforehand with Lamb, and
had issued in 1828 a second series of _Elia_. The American edition
of _Elia_ had been the same as the English except for a slightly
different arrangement of the essays. But when in 1828 the American
second series was issued, it was found to contain three pieces not
by Lamb at all. A trick of writing superficially like Lamb had been
growing in the _London Magazine_ ever since the beginning; hence the
confusion of the American editor. The three articles not by Lamb, as
he pointed out to N.P. Willis (see _Pencillings by the Way_), are
"Twelfth Night," "The Nuns and Ale of Caverswell," and "Valentine's
Day." Of these Allan Cunningham wrote the second, and B.W. Procter
(Barry Cornwall) the other two. The volume contained only eleven
essays which Lamb himself selected for _The Last Essays of Elia_: it
was eked out with the three spurious pieces above referred to, with
several pieces never collected by Lamb, and with four of the humorous
articles in the _Works_, 1818. Bernard Barton's sonnet "To Elia" stood
as introduction. Altogether it was a very interesting book, as books
lacking authority often are.
In the notes that follow reference is often made to Lamb's Key. This
is a paper explaining certain initials and blanks in _Elia_, which
Lamb drew up for R.B. Pitman, a fellow clerk at the East India House.
I give it here in full, merely remarking that the first numerals refer
to the pages of the original edition of _Elia_ and those in brackets
to the present volume:--
M. . . . Page 13 [7] Maynard, hang'd himself.
G.D. . . " 21 [11] George Dyer, Poet.
H. . . . " 32 [16] Hodges.
W. . . . " 45 [23]
Dr. T----e . " 46 [24] Dr. Trollope.
Th. . . " 47 [24] Thornton.
S. . . " 47 [24] Scott, died in Bedlam.
M. . . " 47 [24] Maunde, dismiss'd school.
C.V. le G. . " 48 [25] Chs. Valentine le Grice.
F. . . . " 49 [25] Favell; left Camb'rg because he was
asham'd of his father, who was a
house-painter there.
Fr. . . " 50 [26] Franklin, Gramr. Mast., Hertford.
T. . . " 50 [26] Marmaduke Thompson.
K. . . " 59 [30] Kenney, Dramatist. Author of
_Raising Wind_, &c.
S.T.C. . . " 60 [31] Samuel Taylor Coleridge. [Not in
Lamb's autograph.]
Alice W----n . " 63 [32] Feigned (Winterton).
*** . . " 64 [32] No Meaning.
**** . . " 64 [32] No Meaning.
*** . . " 64 [32] No Meaning.
Mrs. S. . . " 87 [44] Mrs. Spinkes.
R. . . . " 98 [50] Ramsay, London Library, Ludg. St.;
now extinct.
Granville S. . " 98 [50] Granville Sharp. [Not in Lamb's
autograph.]
E.B. . . " 130 [65] Edward Burney, half-brother of Miss
Burney.
B. . . . " 141 [71] Braham, now a Xtian.
*********** . " 170 [85] Distrest Sailors.
J----ll. . " 195 [97] Jekyll.
Susan P. . " 198 [99] Susan Peirson.
R.N. . . " 206 [103] Randal Norris, Subtreasr, Inner Temple.
C. . . . " 216 [108] Coleridge.
F. . . . " 222 [111] Field.
B.F. . . " 238 [118] Baron Field, brother of Frank.
Lord C. . " 243 [121] Lord Camelford.
Sally W----r . " 248 [123] Sally Winter.
J.W. . . " 248 [123] Jas. White, author of _Falstaff's
Letters_.
St. L. . . " 268 [133] No meaning.
B., Rector of ---- " 268 [133] No meaning.
The _London Magazine_, with John Scott (1783-1821) as its editor was
founded in 1820 by Baldwin, Cradock & Joy. Its first number was dated
January, 1820, and Lamb's first contribution was in the number for
August, 1820. Lamb had known Scott as editor of _The Champion_ in
1814, but, according to Talfourd, it was Hazlitt who introduced Lamb
to the _London Magazine_.
John Scott, who was the author of two interesting books of travel,
_A Visit to Paris in 1814_ and _Paris Re-visited_ in 1815, was an
admirable editor, and all was going exceedingly well until he plunged
into a feud with _Blackwood's Magazine_ in general, and John Gibson
Lockhart in particular, the story of which in full may be read in
Mr. Lang's _Life and Letters of Lockhart_, 1896. In the duel which
resulted Scott was shot above the hip. The wound was at first thought
lightly of, but Scott died on February 27, 1821--an able man much
regretted.
The magazine did not at first show signs of Scott's loss; it continued
to bear the imprint of its original publishers and its quality
remained very high. With Lamb and Hazlitt writing regularly this
could hardly be otherwise. But four months after the death of Scott
and eighteen months after its establishment the _London Magazine_
passed into the hands of the publishers Taylor & Hessey, the first
number with their imprint being dated August, 1821. Although for a
while no diminution of merit was perceptible and rather an access
of gaiety--for Taylor brought Hood with him and John Hamilton
Reynolds--yet the high editorial standards of Scott ceased to be
applied. Thenceforward the decline of the magazine was steady.
John Taylor (1781-1864), senior partner in the firm of Taylor &
Hessey, was known as the identifier of Sir Philip Francis with the
author of "Junius," on which subject he had issued three books.
Although unfitted for the post, he acted as editor of the _London
Magazine_ until it was again sold in 1825.
With the beginning of 1825 Taylor made a change in the magazine. He
started a new series, and increased the size and the price. But the
experiment did not answer; the spirit had evaporated; and in the
autumn he sold it to Henry Southern (1799-1853), who had founded
the _Retrospective Review_ in 1820. The last number of the _London
Magazine_ to bear Taylor & Hessey's name, and (in my opinion) to
contain anything by Lamb, was August, 1825. We have no definite
information on the matter, but there is every indication in Lamb's
_Letters_ that Taylor was penurious and not clever in his relations
with contributors. Scott Lamb seems to have admired and liked; but
even in Scott's day payment does not seem to have been prompt. Lamb
was paid, according to Barry Cornwall, two or three times the amount
of other writers, who received for prose a pound a page. But Lamb
himself says that the rate for him was twenty guineas a sheet, a sheet
being sixteen pages; and he told Moore that he had received L170 for
two years' Elia. In a letter to Barton in January, 1823, Lamb remarks:
"B---- [Baldwin] who first engaged me as 'Elia' has not paid me up yet
(nor any of us without repeated mortifying appeals)."
The following references to the _London_ in Lamb's letters to Barton
tell the story of its decadence quite clearly enough. In May,
1823:--"I cannot but think _the London_ drags heavily. I miss Janus
[Wainewright]. And O how it misses Hazlitt--Procter, too, is affronted
(as Janus has been) with their abominable curtailment of his things."
Again, a little later, in September:--"The 'London' I fear falls
off.--I linger among its creaking rafters, like the last rat. It will
topple down, if they don't get some Buttresses. They have pulled down
three, W. Hazlitt, Procter, and their best stay, kind light-hearted
Wainwright, their Janus."
In January, 1824, at the beginning of his eight months' silence:--"The
London must do without me for a time, a time, and half a time, for I
have lost all interest about it."
Again, in December, 1824:--"Taylor & Hessey finding their magazine
goes off very heavily at 2s. 6d., are prudently going to raise their
price another shilling; and having already more authors than they
want, intend to increase the number of them. If they set up against
the New Monthly, they must change their present hands. It is not tying
the dead carcase of a Review to a half-dead Magazine will do their
business."
In January, 1825 (to Sarah Hutchinson):--"You ask about the editor of
the Lond. I know of none. This first specimen [of a new series] is
flat and pert enough to justify subscribers, who grudge at t'other
shilling."
Next month Lamb writes, again to Barton:--"Our second Number [of the
new series] is all trash. What are T. & H. about? It is whip syllabub,
'thin sown with aught of profit or delight'. Thin sown! not a germ of
fruit or corn. Why did poor Scott die! There was comfort in writing
with such associates as were his little band of scribblers, some gone
away, some affronted away, and I am left as the solitary widow [in one
of Barton's poems] looking for watercresses."
Finally, in August, 1825:--"Taylor has dropt the 'London'. It was
indeed a dead weight. It was Job in the Slough of Despond. I shuffle
off my part of the pack, and stand like Christian with light and merry
shoulders."
In addition to Lamb and Hazlitt the _London Magazine_ had more or
less regular contributions, in its best days, from De Quincey, Allan
Cunningham (Nalla), T.G. Wainewright, afterwards the poisoner, but
in those days an amusing weaver of gay artificial prose, John Clare,
Bernard Barton, H.F. Cary, Richard Ayton, George Darley, Thomas Hood,
John Hamilton Reynolds, Sir John Bowring, John Poole, B.W. Procter;
while among occasional writers for it were Thomas Carlyle, Landor and
Julius Hare.
The essay, "Stage Illusion," in the number for August, 1825, was,
I believe, the last that Lamb contributed. (In this connection see
Mr. Bertram Dobell's _Sidelights on Charles Lamb_, 1903.) Lamb then
passed over to Colburn's _New Monthly Magazine_, where the "Popular
Fallacies" appeared, together with certain other of his later essays.
His last contribution to that magazine was dated September, 1826. In
1827 he was chiefly occupied in selecting Garrick play extracts for
Hone's _Table Book_, at the British Museum, and for a while after that
he seems to have been more interested in writing acrostics and album
verses than prose. In 1831, however, Moxon's _Englishman's Magazine_
offered harbourage for anything Lamb cared to give it, and a brief
revival of Elia (under the name of Peter) resulted. With its death in
October, 1831, Lamb's writing career practically ceased.
* * * * *
Page 1. THE SOUTH-SEA HOUSE.
_London Magazine_, August, 1820.
Although the "Bachelor's Complaint of the Behaviour of Married
People," "Valentine's Day," and "On the Acting of Munden," were all
written before this essay, it is none the less the first of the
essays of Elia. I have remarked, in the notes to a small edition of
_Elia_, that it is probably unique in literature for an author to
find himself, as Lamb did, in his forty-fourth year, by recording
impressions gathered in his seventeenth; but I think now that Lamb
probably visited his brother at the South-Sea House from time to time
in later years, and gathered other impressions then. I am led to this
conclusion partly by the fact that Thomas Tame was not appointed
Deputy-Accountant until four or five years after Lamb had left.
We do not know exactly what Lamb's duties were at the South-Sea
House or how long he was there: probably only for the twenty-three
weeks--from September, 1791--mentioned in the receipt below,
discovered by Mr. J.A. Rutter in a little exhibition of documents
illustrative of the South Sea Bubble in the Albert Museum at Exeter:--
Rec'd 8th feby 1792 of the Honble South Sea Company by the hands
of their Secretary Twelve pounds 1s. 6d. for 23 weeks attendance
in the Examiners Office.
L12 1 6. CHAS. LAMB.
This shows that Lamb's salary was half a guinea weekly, paid
half-yearly. His brother John was already in the service of the
Company, where he remained till his death, rising to Accountant. It
has been conjectured that it was through his influence that Charles
was admitted, with the view of picking up book-keeping; but the real
patron and introducer was Joseph Pake, one of the directors, whom we
meet on page 92. Whether Lamb had ideas of remaining, or whether he
merely filled a temporary gap in the Examiners' Office, we cannot
tell. He passed to the East India House in the spring of 1792.
The South Sea Company was incorporated in 1710. The year of the Bubble
was 1720. The South-Sea House, remodelled, is now a congeries of
offices.
Page 2, line 11. _Forty years ago_. To be accurate, twenty-eight to
thirty.
Page 3, line 1. _Accounts ... puzzle me_. Here Elia begins his
"matter-of-lie" career. Lamb was at this time in the Accountants'
Office of the India House, living among figures all day.
Page 3, line 7 from foot. _Evans_. William Evans. The Directories of
those days printed lists of the chief officials in some of the public
offices, and it is possible to trace the careers of the clerks whom
Lamb names. All are genuine. Evans, whose name is given one year as
Evan Evans, was appointed cashier (or deputy-cashier) in 1792.
Page 4, line 4. _Ready to imagine himself one_. Lamb was fond of this
conceit. See his little essay "The Last Peach" (Vol. I.), and the
mischievous letter to Bernard Barton, after Fauntleroy's trial,
warning him against peculation.
Page 4, line 7. _Anderton's_. Either the coffee-shop in Fleet Street,
now Anderton's Hotel, or a city offshoot of it. The portrait, if it
ever was in existence, is no longer known there.
Page 5, line 17. _John Tipp_. John Lamb succeeded Tipp as Accountant
somewhen about 1806.
Page 5, line 27. _I know not, etc._ This parenthesis was not in the
_London Magazine_, but the following footnote was appended to the
sentence:--
"I have since been informed, that the present tenant of them is
a Mr. Lamb, a gentleman who is happy in the possession of some
choice pictures, and among them a rare portrait of Milton, which
I mean to do myself the pleasure of going to see, and at the same
time to refresh my memory with the sight of old scenes. Mr.
Lamb has the character of a right courteous and communicative
collector."
Mr. Lamb was, of course, John Lamb, or James Elia (see the essay "My
Relations"), then (in 1820) Accountant of the South-Sea House. He left
the Milton to his brother. It is now in America.
Page 6, line 5 from foot. _Henry Man_. This was Henry Man (1747-1790),
deputy-secretary of the South-Sea House from 1776, and an author
of light trifles in the papers, and of one or two books. The
_Miscellaneous Works in Verse and Prose of the late Henry Man_ was
published in 1802, among the subscribers being three of the officials
named in this essay--John Evans, R. Plumer, and Mr. Tipp, and also
Thomas Maynard, who, though assigned to the Stock Exchange, is
probably the "childlike, pastoral M----" of a later paragraph. Small
politics are for the most part kept out of Man's volumes, which are
high-spirited rather than witty, but this punning epigram (of which
Lamb was an admirer) on Lord Spencer and Lord Sandwich may be
quoted:--
Two Lords whose names if I should quote,
Some folks might call me sinner:
The one invented _half a coat_,
The other _half a dinner_.
Such lords as these are useful men,
Heaven sends them to console one;
Because there's now not one in ten,
That can procure a _whole one_.
Page 7, line 13. _Plumer_. Richard Plumer (spelled Plomer in the
directories), deputy-secretary after Man. Lamb was peculiarly
interested in the Plumers from the fact that his grandmother, Mrs.
Field, had been housekeeper of their mansion at Blakesware, near Ware
(see notes to "Dream-Children" and "Blakesmoor in H----shire"). The
fine old Whig was William Plumer, who had been her employer, and was
now living at Gilston. He died in 1821.
The following passage from the memoir of Edward Cave (1691-1754),
which Dr. Johnson wrote for the _Gentleman's Magazine_ (which Cave
established) in 1754, shows that Lamb was mistaken about Plumer:--
He [Cave] was afterwards raised to the office of clerk of the
franks, in which he acted with great spirit and firmness; and
often stopped franks which were given by members of parliament to
their friends; because he thought such extension of a peculiar
right illegal. This raised many complaints, and having stopped,
among others, a frank given to the old dutchess of _Marlborough_
by Mr. _Walter Plummer_, he was cited before the house, as for
breach of privilege, and accused, I suppose very unjustly,
of opening letters to detect them. He was treated with great
harshness and severity, but declining their questions by pleading
his oath of secrecy, was at last dismissed. And it must be
recorded to his honour, that when he was ejected from his office,
he did not think himself discharged from his trust, but continued
to refuse to his nearest friends any information about the
management of the office.
I borrow from Canon Ainger an interesting note on Walter Plumer,
written in the eighteen-eighties, showing that Lamb was mistaken on
other matters too:--
The present Mr. Plumer, of Allerton, Totness, a grandson of
Richard Plumer of the South-Sea House, by no means acquiesces in
the tradition here recorded as to his grandfather's origin. He
believes that though the links are missing, Richard Plumer was
descended in regular line from the Baronet, Sir Walter Plumer,
who died at the end of the seventeenth century. Lamb's memory
has failed him here in one respect. The "Bachelor Uncle," Walter
Plumer, uncle of William Plumer of Blakesware, was most certainly
not a bachelor (see the pedigree of the family in Cussans'
_Hertfordshire_).
Page 7, line 10 from foot. M----. According to the Key to the initials
and blanks in some of the essays, which Lamb filled in for a curious
correspondent, M---- stood for one Maynard. "Maynard, hang'd himself"
is Lamb's entry. He was chief clerk in the Old Annuities and Three Per
Cents, 1788-1793.
* * * * *
Page 8. OXFORD IN THE VACATION.
_London Magazine_, October, 1820, where it is dated at the end,
"August 5, 1820. From my rooms facing the Bodleian." My own belief
is that Lamb wrote the essay at Cambridge, under the influence of
Cambridge, where he spent a few weeks in the summers of 1819 and 1820,
and transferred the scene to Oxford by way of mystification. He knew
Oxford, of course, but he had not been there for some years, and it
was at Cambridge that he met Dyer and saw the Milton MSS.
Concerning a visit to Oxford (in 1810), Hazlitt had written, in his
_Table Talk_ essay "On the Conversation of Authors," in the preceding
(the September) number of the _London Magazine_:--
L---- [that is, Lamb] once came down into the country to see us.
He was "like the most capricious poet Ovid among the Goths." The
country people thought him an oddity, and did not understand his
jokes. It would be strange if they had; for he did not make any
while he staid. But when we crossed the country to Oxford, then he
spoke a little. He and the old colleges were hail-fellow well-met;
and in the quadrangles, he "walked gowned."
The quotation is a reference to Lamb's sonnet, "I was not Trained in
Academic Bowers," written at Cambridge in 1819:--
Yet can I fancy, wandering 'mid thy towers,
Myself a nursling, Granta, of thy lap;
My brow seems tightening with the Doctor's cap,
And I walk _gowned_.
Page 8, line 6 from foot. _Agnize_. Lamb was fond of this word. I
have seen it stated ingeniously that it was of his own coinage--from
_agnus_, a lamb--but the derivation is _ad gnoscere_, to acknowledge,
to recognise, and the word is to be found in other places--in
"Othello," for example (Act I., Scene 3, line 232):--
I do agnise
A natural and prompt alacrity.
Page 9, middle. _Red-letter days_. See note on page 351. The holidays
at the India House, which are given in the London directories of
Lamb's early time there, make a considerable list. But in 1820 the
Accountants' Office, where Lamb was, kept only five days in the year.
Page 10, line 11. _I can here ... enact the student._ Lamb had
distilled the matter of this paragraph into his sonnet, "I was not
Trained in Academic Bowers," written at Cambridge in August of the
preceding year (see above and Vol. IV.).
Page 11, line 12 from foot. _Unsettle my faith._ At this point, in the
_London Magazine_, Lamb appended the footnote:--
"There is something to me repugnant, at any time, in written hand.
The text never seems determinate. Print settles it. I had thought
of the Lycidas as of a full-grown beauty--as springing up with all
its parts absolute--till, in evil hour, I was shown the original
written copy of it, together with the other minor poems of its
author, in the Library of Trinity, kept like some treasure to be
proud of. I wish they had thrown them in the Cam, or sent them,
after the latter cantos of Spenser, into the Irish Channel. How
it staggered me to see the fine things in their ore! interlined,
corrected! as if their words were mortal, alterable, displaceable
at pleasure! as if they might have been otherwise, and just
as good! as if inspirations were made up of parts, and those
fluctuating, successive, indifferent! I will never go into the
work-shop of any great artist again, nor desire a sight of his
picture, till it is fairly off the easel; no, not if Raphael were
to be alive again, and painting another Galatea."
In the Appendix to Vol. I., page 428, I have printed a passage from
the original MS. of _Comus_, which there is reason to believe was
contributed to the _London Magazine_ by Lamb.
Page 11, line 9 from foot. _G.D._ George Dyer (1755-1841), Lamb's
friend for many years. This is the first mention of him in the essays;
but we shall meet him again, particularly in "Amicus Redivivus."
George Dyer was educated at Christ's Hospital long before Lamb's
time there, and, becoming a Grecian, had entered Emmanuel College,
Cambridge. He became at first an usher in Essex, then a private tutor
to the children of Robert Robinson, the Unitarian, whose life he
afterwards excellently wrote, then an usher again, at Northampton, one
of his colleagues being John Clarke, father of Lamb's friend, Charles
Cowden Clarke. In 1792 he settled in Clifford's Inn as a hack; wrote
poems, made indexes, examined libraries for a great bibliographical
work (never published), and contributed "all that was original" to
Valpy's classics in 141 volumes. Under this work his sight gave way;
and he once showed Hazlitt two fingers the use of which he had lost
in copying out MSS. of Procrus and Plotinus in a fine Greek hand.
Fortunately a good woman took him under her wing; they were married in
1825; and Dyer's last days were happy. His best books were his _Life
of Robert Robinson_ and his _History of the University and Colleges
of Cambridge_. Lamb and his friends laughed at him and loved him. In
addition to the stories told by Lamb in his letters and essays, there
are amusing characteristics of Dyer in Crabb Robinson's diary, in
Leigh Hunt, in Hazlitt, in Talfourd, and in other places. All bear
upon his gentleness, his untidiness and his want of humour. One of
the most famous stories tells of Dyer's criticism of Williams, the
terrible Ratcliffe Highway murderer. Dyer, who would never say an ill
word of any one, was asked his opinion of this cold-blooded assassin
of two families. "He must," he replied after due thought, "be rather
an eccentric character."
Page 12, line 10. _Injustice to him._ In the _London Magazine_ the
following footnote came here, almost certainly by Lamb:--
"Violence or injustice certainly none, Mr. Elia. But you will
acknowledge that the charming unsuspectingness of our friend has
sometimes laid him open to attacks, which, though savouring (we
hope) more of waggery than malice--such is our unfeigned respect
for G.D.--might, we think, much better have been omitted. Such was
that silly joke of L[amb], who, at the time the question of the
Scotch Novels was first agitated, gravely assured our friend--who
as gravely went about repeating it in all companies--that Lord
Castlereagh had acknowledged himself to be the author of Waverly!
_Note--not by Elia."_
Page 12, line 11. _"Strike an abstract idea."_ I do not find this
quotation--if it be one; but when John Lamb once knocked Hazlitt down,
during an argument on pigments, Hazlitt refrained from striking back,
remarking that he was a metaphysician and dealt not in blows but in
ideas. Lamb may be slyly remembering this.
Page 12, line 15. C----. Cambridge. Dyer added a work on _Privileges
of the University if Cambridge_ to his _History_.
Page 12, line 8 from foot. _Our friend M.'s._ Basil Montagu, Q.C.
(1770-1851), legal writer, philanthropist, editor of Bacon, and the
friend of Wordsworth and Coleridge. The Mrs. M. here referred to was
Montagu's third wife, a Mrs. Skepper. It was she who was called by
Edward Irving "the noble lady," and to whom Carlyle addressed some
early letters. A.S. was Anne Skepper, afterwards Mrs. Bryan Waller
Procter, a fascinating lady who lived to a great age and died as
recently as 1888. The Montagus then lived at 25 Bedford Square.
Page 13, line 17. _Starts like a thing surprised._ Here we have an
interesting example of Lamb's gift of fused quotation. Wordsworth's
line in the "Ode on Intimations of Immortality,"
Tremble like a guilty thing surprised,
and Shakespeare's phrase in "Hamlet" (Act I., Scene 1, line 148),
Started like a guilty thing,
were probably both in his mind as he wrote.
Page 13, line 24. _Obtruded personal presence._ In the _London
Magazine_ the following passage came here:--
"D. commenced life, after a course of hard study in the 'House of
pure Emanuel,' as usher to a knavish fanatic schoolmaster at ***,
at a salary of eight pounds per annum, with board and lodging.
Of this poor stipend, he never received above half in all the
laborious years he served this man. He tells a pleasant anecdote,
that when poverty, staring out at his ragged knees, has sometimes
compelled him, against the modesty of his nature, to hint at
arrears, Dr. *** would take no immediate notice, but, after
supper, when the school was called together to even-song, he would
never fail to introduce some instructive homily against riches,
and the corruption of the heart occasioned through the desire
of them--ending with 'Lord, keep thy servants, above all things
from the heinous sin of avarice. Having food and raiment,
us therewithal be content. Give me Agar's wish,'--and the
like;--which to the little auditory, sounded like a doctrine
full of Christian prudence and simplicity,--but to poor D. was a
receipt in full for that quarter's demands at least.
"And D. has been under-working for himself ever since;--drudging
at low rates for unappreciating booksellers,--wasting his fine
erudition in silent corrections of the classics, and in those
unostentatious but solid services to learning, which commonly fall
to the lot of laborious scholars, who have not the art to sell
themselves to the best advantage. He has published poems, which
do not sell, because their character is inobtrusive like his
own,--and because he has been too much absorbed in ancient
literature, to know what the popular mark in poetry is, even if he
could have hit it. And, therefore, his verses are properly, what
he terms them, _crotchets;_ voluntaries; odes to Liberty, and
Spring; effusions; little tributes, and offerings, left behind
him, upon tables and window-seats, at parting from friends'
houses; and from all the inns of hospitality, where he has been
courteously (or but tolerably) received in his pilgrimage. If his
muse of kindness halt a little behind the strong lines, in fashion
in this excitement-craving age, his prose is the best of the
sort in the world, and exhibits a faithful transcript of his own
healthy natural mind, and cheerful innocent tone of conversation."
The foregoing passage called forth a protest from one W.K.
necessitating the following reply from Lamb, which was printed in the
_London Magazine_, under the "Lion's Head," for December, 1820:--
"Elia requests the Editor to inform W.K. that in his article on
Oxford, under the initials G.D., it is his ambition to make more
familiar to the public, a character, which, for integrity and
single-heartedness, he has long been accustomed to rank among the
best patterns of his species. That, if he has failed in the end
which he proposed, it was an error of judgment merely. That, if
in pursuance of his purpose, he has drawn forth some personal
peculiarities of his friend into notice, it was only from the
conviction that the public, in living subjects especially, do not
endure pure panegyric. That the anecdotes, which he produced,
were no more than he conceived necessary to awaken attention to
character, and were meant solely to illustrate it. That it is an
entire mistake to suppose, that he undertook the character to
set off his own wit or ingenuity. That, he conceives, a candid
interpreter might find something intended, beyond a heartless
jest. That G.D., however, having thought it necessary to disclaim
the anecdote respecting Dr. ----, it becomes him, who never for
a moment can doubt the veracity of his friend, to account for
it from an imperfect remembrance of some story he heard long
ago, and which, happening to tally with his argument, he set
too hastily to the account of G.D. That, from G.D.'s strong
affirmations and proofs to the contrary, he is bound to believe
it belongs to no part of G.D.'s biography. That the transaction,
supposing it true, must have taken place more than forty years
ago. That, in consequence, it is not likely to 'meet the eye of
many who might be justly offended.'
"Finally, that what he has said of the Booksellers, referred to a
period of many years, in which he has had the happiness of G.D.'s
acquaintance; and can have nothing to do with any present or
prospective engagements of G.D., with those gentlemen, to the
nature of which he professes himself an entire stranger."
The result of the protest was that Lamb omitted the passage objected
to when he collected _Elia_ in 1823. It might well be restored now;
but I have preferred to print everything in the body of this edition
as Lamb arranged it for press.
* * * * *
Page 14. CHRIST'S HOSPITAL FIVE AND THIRTY YEARS AGO.
_London Magazine_, November, 1820.
This essay, which is based upon the "Recollections of Christ's
Hospital" in Vol. I., is a curious blend of Lamb's own experiences at
school with those of Coleridge. Both boys entered at the same time--on
July 17, 1782: Coleridge was then nearly ten, Lamb was seven and a
half. Coleridge was "clothed" on July 18 and went to Hertford for
a while; Lamb was clothed on October 9. Lamb left the school in
November, 1789, Coleridge in September, 1791.
The school which Lamb knew is now no more. The boys are now all in new
buildings in the midst of green fields near Horsham, many miles from
Lamb's city and its roar.
Page 14, line 15. _The worthy sub-treasurer._ Randal Norris (see note
to "A Death-Bed"). I have not been able to discover the cause of his
influence.
Page 14, lines 18, 19. _Crug ... piggins._ Crug is still current
slang. In the school museum one of these piggins is preserved.
Page 14, line 25. _Three banyan days._ Three vegetarian days.
Coleridge complains (in a letter to Poole) that he was never
sufficiently fed except on Wednesdays. He gives the following table of
food:--
Our diet was very scanty. Every morning a bit of dry bread and
some bad small beer. Every evening a larger piece of bread, and
cheese or butter, whichever we liked. For dinner,--on Sunday,
boiled beef and broth; Monday, bread and butter, and milk and
water; Tuesday, roast mutton; Wednesday, bread and butter, and
rice milk; Thursday, boiled beef and broth; Friday, boiled mutton
and broth; Saturday, bread and butter, and pease-porridge. Our
food was portioned; and, excepting on Wednesdays, I never had a
bellyfull. Our appetites were damped, never satisfied; and we had
no vegetables.
Page 14, line 8 from foot. _Caro equina._ Horseflesh. Mr. Pearce's
chapter on food at the school in his excellent _Annals of Christ's
Hospital_ is very interesting, and records great changes.
Rotten-roasted or rare, _i.e._, over-roasted or under-done.
Page 15, line 3. _The good old relative._ Aunt Hetty, or more
properly, Sarah Lamb. Compare the "Lines written on the Day of my
Aunt's Funeral," Vol. IV.:--
I have not forgot
How thou didst love thy Charles, when he was yet
A prating schoolboy: I have not forgot
The busy joy on that important day,
When, childlike, the poor wanderer was content
To leave the bosom of parental love,
His childhood's play-place, and his early home,
For the rude fosterings of a stranger's hand,
Hard, uncouth tasks, and schoolboys' scanty fare.
How did thine eyes peruse him round and round
And hardly knew him in his yellow coats,
Red leathern belt, and gown of russet blue.
Page 15, line 13. _I was a poor friendless boy._ Here Lamb speaks as
Coleridge, who came all the way from Ottery St. Mary, in Devonshire
(not Calne, in Wiltshire), and had no London friends. In _John
Woodvil_ Lamb borrowed St. Mary Ottery again (see Vol. IV.). Coleridge
has recorded how unhappy he was in his early days at school.
Page 15, line 12 from foot. _Whole-day-leaves._ In this connection
the following passage from Trollope's _History of Christ's Hospital_,
1834, is interesting:--
Those days, on which _leave_ is given to be absent from the Hospital
during the whole day, are called _whole-day leaves_.... A _ticket_ is
a small oval medal attached to the button-hole, without which, except
on leaves, no boy is allowed to pass the gates. Subjoined is a list of
the holidays, which have been hitherto kept at Christ's Hospital; but
it is in contemplation to abridge them materially. Of the policy of
such a measure great doubts may fairly be entertained, inasmuch as the
vacations are so short as to give sufficient respite neither to master
nor scholar; and these occasional breaks, in the arduous duties of the
former more especially, enable him to repair the exhausted energies of
body and mind by necessary relaxation. If those days, which are marked
with an asterisk, fall on a Sunday, they are kept on the Monday
following; and likewise the state holidays.
HOLIDAYS KEPT AT CHRIST'S HOSPITAL
Jan. 25. St. Paul's conversion.
*30. King Charles's martyrdom.
Feb. 2. Candlemas Day.
24. St. Matthias.
Shrove Tuesday.
Ash Wednesday.
March 25. Lady Day.
April 23. St. George.
25. St. Mark.
May 1. St. Philip and St. James.
*29. Restoration of King
Charles II.
Ascension Day.
Whit Monday.
Whit Tuesday.
June 11. St. Barnabas.
24. St. John Baptist.
29. St. Peter.
July 25. St. James.
Thursday after St.
James. (Nurses' Holiday.)
Aug. 24. St. Bartholomew.
Sept. *2. London burnt.
*21. St. Matthew.
29. St. Michael.
Oct. 18. St. Luke.
*23. King Edward VI. born.
28. St. Simon and St. Jude.
Nov. 1. All Saints.
*5. Gunpowder Plot.
*9. Lord Mayor's Day.
*17. Queen Elizabeth's birthday.
30. St. Andrew.
Dec. 21. St. Thomas.
Also the birthdays of the King and Queen, and the Prince and Princess
of Wales: and the King's accession, proclamation, and coronation.
In addition to the generous allowance of holidays above given the boys
had every alternate Wednesday for a whole day; eleven days at Easter,
four weeks in the summer, and fifteen days at Christmas. In 1837 the
holiday system was remodelled. Compare Lamb's other remarks on his
whole-day rambles in "Recollections of Christ's Hospital" (Vol. I.)
and in the essays in the present volume entitled "Amicus Redivivus"
and "Newspapers."
Page 16, line 14. _The Tower_. Blue-coat boys still have this right
of free entrance to the Tower; but the lions are no more. They were
transferred to the Zoological Gardens in 1831.
Page 16, line 16. _L.'s governor_. Meaning Samuel Salt, M.P.; but it
was actually his friend Mr. Timothy Yeats who signed Lamb's paper.
More accurately, Lamb's father lived under Salt's roof.
Page 16, line 7 from foot. _H----_. According to Lamb's Key this was
Hodges; but in the British Museum copy of _Elia_, first edition, some
one has written Huggins. It is immaterial. Nevis and St. Kitt's (St.
Christopher's) are islands in the British West Indies. Tobin would
be James Webbe Tobin, of Nevis, who died in 1814, the brother of the
playwright John Tobin, author of "The Honeymoon."
Page 17, line 2. _A young ass_. The general opinion at Christ's
Hospital is that Lamb invented this incident; and yet it has the air
of being true.
Page 17, line 18. _L.'s admired Perry_. John Perry, steward from 1761
to 1785, mentioned in Lamb's earlier essay.
Page 17, foot. _Gags_. Still current slang.
Page 17, foot. ----. No name in the Key. The quotation is an
adaptation of:--
It is reported thou didst eat strange flesh
Which some did die to look on.
"Antony and Cleopatra," Act I., Scene 4, lines 67-68.
It is perhaps worth remarking that in _David Copperfield_ Dickens has
a school incident of a similar character.
Page 18, line 14 from foot. _Mr. Hathaway_. Matthias Hathaway, steward
from 1790 to 1813.
Page 19, line 8. _I was a hypochondriac lad_. Here Lamb drops the
Coleridge mask and speaks as himself.
Page 20, line 15. _Bamber Gascoigne, and Peter Aubert_. Bamber
Gascoigne, M.P. (1725-1791), of Bifrons, in Essex. Of Peter Aubert
I can find nothing, except that the assistant secretary of the East
India Company at the time Lamb wrote this essay was Peter Auber,
afterwards full secretary. His name here may be a joke.
Page 20, line 6 from foot. _Matthew Field_. The Rev. Matthew Feilde,
also vicar of Ugley and curate of Berden. For the Rev. James Boyer see
below.
Page 21, line 18. _"Peter Wilkins," etc. The Adventures of Peter
Wilkins_, by Robert Paltock, 1751, is still read; but _The Voyages and
Adventures of Captain Robert Boyle_, 1736, has had its day. It was a
blend of unconvincing travel and some rather free narrative: a piece
of sheer hackwork to meet a certain market. See Lamb's sonnet to
Stothard, Vol. IV. _The Fortunate Blue-Coat Boy_ I have not seen.
Canon Ainger describes it as a rather foolish romance, showing how a
Blue-coat boy marries a rich lady of rank. The sub-title is "Memoirs
of the Life and Happy Adventures of Mr. Benjamin Templeman; formerly a
Scholar in Christ's Hospital. By an Orphanotropian," 1770.
Page 22, footnote. I have not discovered a copy of Matthew Feilde's
play.
Page 23, line 17 from foot. _Squinting W----_. Not identifiable.
Page 23, line 7 from foot. _Coleridge, in his literary life_.
Coleridge speaks in the _Biographia Literaria_ of having had the
"inestimable advantage of a very sensible, though at the same time a
very severe master, the Reverend James Bowyer [Boyer]," and goes on to
attribute to that master's discrimination and thoroughness much of his
own classical knowledge and early interest in poetry and criticism.
Coleridge gives this example of Boyer's impatient humour:--
In our own English compositions (at least for the last three years
of our school education), he showed no mercy to phrase, metaphor,
or image, unsupported by a sound sense, or where the same sense
might have been conveyed with equal force and dignity in plainer
words. _Lute, harp_ and _lyre, Muse, Muses_ and _inspirations,
Pegasus, Parnassus_ and _Hippocrene_, were all an abomination to
him. In fancy I can almost hear him now exclaiming, "Harp? Harp?
Lyre? Pen and ink, boy, you mean! Muse, boy, muse? Your nurse's
daughter, you mean! Pierian spring? Oh, aye! the cloister pump, I
suppose!"
Touching Boyer's cruelty, Coleridge adds that his "severities, even
now, not seldom furnish the dreams by which the blind fancy would fain
interpret to the mind the painful sensations of distempered sleep."
In _Table Talk_ Coleridge tells another story of Boyer. "The
discipline at Christ's Hospital in my time," he says, "was
ultra-Spartan; all domestic ties were to be put aside. 'Boy!' I
remember Bowyer saying to me once when I was crying the first day of
my return after the holidays, 'Boy! the school is your father! Boy!
the school is your mother! Boy! the school is your brother! the school
is your sister! the school is your first cousin, and your second
cousin, and all the rest of your relations! Let's have no more
crying!'"
Leigh Hunt in his autobiography also has reminiscences of Boyer and
Feilde.
James Boyer or Bowyer was born in 1736, was admitted to the school in
1744, and passed to Balliol. He resigned his Upper Grammar Mastership
in 1799, and probably retired to the rectory of Gainscolne to which
he had been appointed by the school committee six years earlier. They
also gave him L500 and a staff.
Page 23, line 6 from foot. _Author of the Country Spectator_. Thomas
Fanshaw Middleton (1769-1822), afterwards Bishop of Calcutta, who was
at school with Lamb and Coleridge. In the little statuette group which
is called the Coleridge Memorial, subscribed for in 1872, on the
centenary of Coleridge's birth, and held in rotation by the ward in
which most prizes have been gained in the year, Middleton is the
tallest figure. It is reproduced in my large edition. The story which
it celebrates is to the effect that Middleton found Coleridge reading
Virgil in the playground and asked him if he were learning a lesson.
Coleridge replied that he was "reading for pleasure," an answer which
Middleton reported to Boyer, and which led to Boyer taking special
notice of him. The _Country Spectator_ was a magazine conducted by
Middleton in 1792-1793.
Page 23, line 3 from foot. _C----_. Coleridge again.
Page 24, line 4. _Lancelot Pepys Stevens_. Rightly spelled Stephens,
afterwards Under Grammar Master at the school.
Page 24, line 6. _Dr. T----e_. Arthur William Trollope (1768-1827),
who succeeded Boyer as Upper Grammar Master. He resigned in 1826.
Page 24, line 21. _Th----_. Sir Edward Thornton (1766-1852),
diplomatist, who was sent as Envoy Extraordinary and Minister
Plenipotentiary to Lower Saxony, to Sweden, to Denmark and other
courts, afterwards becoming minister to Portugal.
Page 24, line 23. _Middleton_. See note above. The treatise was _The
Doctrine of the Greek Article as applied to the Criticism and the
Illustration of the New Testament_, 1808. It was directed chiefly
against Granville Sharpe. Middleton was the first Bishop of Calcutta.
Page 24, line 8 from foot. _Richards_. This was George Richards
(1767-1837). His poem on "Aboriginal Britons," which won a prize
given in 1791 by Earl Harcourt, is mentioned favourably in Byron's
_English Bards and Scotch Reviewers_. Richards became vicar of St.
Martin's-in-the-Fields and a Governor of Christ's Hospital. He founded
a gold medal for Latin hexameters.
Page 24, foot. _S---- ... M----_. According to the Key "Scott, died in
Bedlam," and "Maunde, dismiss'd school."
Page 24, foot. "_Finding some of Edward's race._" From Prior's Carmen
Seculare for 1700:--
Finding some of Stuart's race
Unhappy, pass their annals by.
Lamb alters Stuart to Edward because Edward VI. founded Christ's
Hospital.
Page 25, line 12. _C.V. Le G----_. Charles Valentine Le Grice
(1773-1858), whom we meet also in the essay on "Grace Before Meat."
Le Grice, in his description of Lamb as a schoolboy in Talfourd's
_Memorials_, remarked: "I never heard his name mentioned without
the addition of Charles, although, as there was no other boy of the
name of Lamb, the addition was unnecessary; but there was an implied
kindness in it, and it was a proof that his gentle manners excited
that kindness."
Page 25, line 20. _Allen_. Robert Allen, whom we meet again in the
essay on "Newspapers." After a varied and not fortunate career he died
of apoplexy in 1805.
Page 25, line 8 from foot. _The junior Le G----_. Samuel Le Grice
became a soldier and died in the West Indies. Lamb wrote of him to
Coleridge in 1796, after the tragedy at his home, at a time when
friends were badly needed, "Sam Le Grice who was then in town was with
me the first 3 or 4 days, and was as a brother to me, gave up every
hour of his time to the very hurting of his health and spirits, in
constant attendance and humouring my poor father."
Page 25, line 8 from foot. _F----_. Joseph Favell, afterwards Captain,
who had a commission from the Duke of York--as had Sam Le Grice--and
was killed in the Peninsula, at Salamanca, 1812. Lamb states in the
essay on "Poor Relations," where Favell figures as "W.," that he met
his death at St. Sebastian. Both Sam Le Grice and Favell were to have
accompanied Coleridge and Southey to the Susquehanna as Pantisocrats.
Page 26, line 1. _Fr----_. Frederick William Franklin, master of the
Hertford branch of the school from 1801 to 1827. He died in 1836.
Page 26, line 2. _Marmaduke T----_. Marmaduke Thompson, to whom Lamb
dedicated _Rosamund Gray_ in 1798.
Page 26, line 3. _Catalogue of Grecians_. Lamb was at Christ's
Hospital from 1782 to 1789, and his list is not quite complete.
He himself never was a Grecian; that is to say, one of the picked
scholars on the grammar side of the school, two of whom were sent
up to Cambridge with a hospital exhibition every year, on the
understanding that they should take orders. Lamb was one of the
Deputy-Grecians from whom the Grecians were chosen, but his stammer
standing in his way and a Church career being out of the question, he
never became a full Grecian. Writing to George Dyer, who had been a
Grecian, in 1831, Lamb says: "I don't know how it is, but I keep my
rank in fancy still since school days. I can never forget I was a
deputy Grecian!... Alas! what am I now? What is a Leadenhall clerk, or
India pensioner, to a deputy Grecian? How art thou fallen, O Lucifer!"
Lamb's memory is preserved at Christ's Hospital by a medal which is
given for the best English essays. It was first struck in 1875, the
centenary of his birth.
* * * * *
Page 26. THE TWO RACES OF MEN.
_London Magazine_, December, 1820.
Writing to Wordsworth in April of 1816, Lamb says:--"I have not bound
the poems yet. I wait till people have done borrowing them. I think
I shall get a chain and chain them to my shelves, _more Bodleiano_,
and people may come and read them at chain's length. For of those who
borrow, some read slow; some mean to read but don't read; and some
neither read nor meant to read, but borrow to leave you an opinion of
their sagacity. I must do my money-borrowing friends the justice to
say that there is nothing of this caprice or wantonness of alienation
in them. When they borrow my money they never fail to make use of it."
Probably the germ of the essay is to be found in this passage, as Lamb
never forgot his thoughts.
Page 26, line 17 of essay. _Brinsley_. Richard Brinsley Sheridan, the
dramatist and a great spendthrift. He died in 1816. Lamb knew him
slightly.
Page 26, line 9 from foot. _Beyond Tooke_. That is, beyond the
philological theories of _The Diversions of Purley_ by John Home Tooke
(1736-1812).
Page 27, line 22. _Ralph Bigod_. John Fenwick, an unlucky friend of
the Lambs, an anticipatory Micawber, of whom we know too little,
and seem likely to find out little more. Lamb mentions him again in
the essay on "Chimney Sweepers," and in that on "Newspapers," in
his capacity as editor of _The Albion_, for which Lamb wrote its
extinguishing epigram in the summer of 1801. There are references to
the Fenwicks in Mary Lamb's letters to Sarah Stoddart and in Lamb's
letters; but nothing very informing. After financial embarrassments in
England they emigrated to America.
Page 29, line 12. _Comberbatch_. Coleridge, who had enlisted as a
young man in the 15th Light Dragoons as Silas Titus Comberback.
Page 29, line 16. _Bloomsbury_. Lamb was then in rooms at 20 Great
Russell Street (now Russell Street), Covent Garden, which is not in
Bloomsbury.
Page 29, line 27. _Should he go on acting_. The _Letters_ contain
references to this habit of Coleridge's. Writing to him in 1809 Lamb
says, referring among other loans to the volume of Dodsley with
Vittoria Corombona ("The White Devil," by John Webster) in it:--"While
I think on it, Coleridge, I fetch'd away my books which you had at the
_Courier_ Office, and found all but a third volume of the old plays,
containing the 'White Devil, 'Green's 'Tu Quoque,' and the 'Honest
Whore,' perhaps the most valuable volume of them all--_that_ I could
not find. Pray, if you can, remember what you did with it, or where
you took it out with you a walking perhaps; send me word, for, to use
the old plea, it spoils a set. I found two other volumes (you had
three), the _Arcadia_ and _Daniel_, enriched with manuscript notes. I
wish every book I have were so noted. They have thoroughly converted
me to relish _Daniel_, or to say I relish him, for after all, I
believe I did relish him."
And several years later (probably in 1820) we find him addressing
Coleridge with reference to Luther's _Table Talk:_--"Why will you make
your visits, which should give pleasure, matter of regret to your
friends? You never come but you take away some folio, that is part of
my existence. With a great deal of difficulty I was made to comprehend
the extent of my loss. My maid, Becky, brought me a dirty bit of
paper, which contained her description of some book which Mr.
Coleridge had taken away. It was _Luster's Tables_, which, for some
time, I could not make out. 'What! has he carried away any of the
_tables_, Becky?' 'No, it wasn't any tables, but it was a book that he
called _Luster's Tables_.' I was obliged to search personally among my
shelves, and a huge fissure suddenly disclosed to me the true nature
of the damage I had sustained."
Allsop tells us that Lamb once said of Coleridge: "He sets his mark
upon whatever he reads; it is henceforth sacred. His spirit seems to
have breathed upon it; and, if not for its author, yet for his sake,
we admire it."
Page 30, line 1. _John Buncle_. Most of Lamb's books are in America;
Lamb's copy of _John Buncle_, with an introductory note written in by
Coleridge, was sold, with other books from his library, in New York
in 1848. _The Life of John Buncle, Esq_., a book highly praised by
Hazlitt, was by Thomas Amory (1691?-1788), published, Part I. in 1756
and Part II. in 1766. A condensed reprint was issued in 1823 entitled
_The Spirit of Buncle_, in which, Mr. W.C. Hazlitt suggests, Lamb may
have had a hand with William Hazlitt.
Page 30, line 19. _Spiteful K._ James Kenney (1780-1849), the
dramatist, then resident at Versailles, where Lamb and his sister
visited him in 1822. He married Louisa Mercier, daughter of Louis
Sebastian Mercier, the French critic, and widow of Lamb's earlier
friend, Thomas Holcroft. One of their two sons was named Charles Lamb
Kenney (1821-1881). Lamb recovered Margaret of Newcastle's _Letters_
(folio, 1664), which is among the books in America, as is also the
Fulke Greville (small folio, 1633).
Page 31, line 4. _S.T.C.... annotations_. Lamb's copy of Daniel's
_Poetical Works_, two volumes, 1718, and of Browne's _Enquiries
into Vulgar and Common Errors_, folio, 1658, both with marginalia
by himself and Coleridge, are in existence, but I cannot say where:
probably in America. Lamb's copy of Beaumont and Fletcher, with
Coleridge's notes (see "Old China"), is, however, safe in the British
Museum. His Fulke Greville, as I have said, is in America, but I
fancy it has nothing of Coleridge in it, nor has his Burton--quarto,
1621--which still exists.
Coleridge's notes in the Beaumont and Fletcher folio are not numerous,
but usually ample and seriously critical. At the foot of a page of the
"Siege of Corinth," on which he had written two notes (one, "O flat!
flat! flat! Sole! Flounder! Place! all stinking! stinkingly flat!"),
he added:--
_N.B._--I shall not be long here, Charles!--I gone, you will not
mind my having spoiled a book in order to leave a Relic.
S.T.C.
Octr. 1811.
Underneath the initials S.T.C. are the initials W.W. which suggest
that Wordsworth was present.
The Museum also has Lamb's Milton, with annotations by himself and
Coleridge.
In the _Descriptive Catalogue of the Library of Charles Lamb_,
privately issued by the New York Dibdin Club in 1897, is a list
of five of Lamb's books now in America containing valuable and
unpublished marginalia by Coleridge: _The Life of John Buncle_,
Donne's _Poems_ ("I shall die soon, my dear Charles Lamb, and then you
will not be vexed that I have scribbled your book. S.T.C., 2d May,
1811"), Reynolds' _God's Revenge against ... Murder_, 1651 ("O what
a beautiful _concordia discordantium_ is an unthinking good man's
soul!"), _The History of Philip de Commines_ in English, and Petwin's
_Letters Concerning the Mind_.
* * * * *
Page 31. NEW YEAR'S EVE.
_London Magazine_, January, 1821.
The melancholy pessimism of this essay led to some remonstrance from
robuster readers of the _London Magazine_. In addition to the letter
from "A Father" referred to below, the essay produced, seven months
later, in the August number of the _London Magazine_, a long poetical
"Epistle to Elia," signed "Olen," in which very simply and touchingly
Lamb was reminded that the grave is not the end, was asked to consider
the promises of the Christian faith, and finally was offered a glimpse
of some of the friends he would meet in heaven--among them Ulysses,
Shakespeare and Alice W----n. Taylor, the publisher and editor of the
magazine, sent Lamb a copy. He replied, acknowledging the kindness of
the author, and adding:--"Poor Elia ... does not pretend to so very
clear revelations of a future state of being as 'Olen' seems gifted
with. He stumbles about dark mountains at best; but he knows at least
how to be thankful for this life, and is too thankful, indeed, for
certain relationships lent him here, not to tremble for a possible
resumption of the gift. He is too apt to express himself lightly, and
cannot be sorry for the present occasion, as it has called forth a
reproof so Christian-like."
Lamb thought the poet to be James Montgomery, but it was in reality
Charles Abraham Elton. The poem was reprinted in a volume entitled
_Boyhood and other Poems_, in 1835.
It is conceivable that Lamb was reasoned with privately upon the
sentiments expressed in this essay; and perhaps we may take the
following sonnet which he contributed over his own name to, the
_London Magazine_ for April, 1821, as a kind of defiant postscript
thereto, a further challenge to those who reproached him for his
remarks concerning death, and who suggested that he did not really
mean them:--
They talk of time, and of time's galling yoke,
That like a millstone on man's mind doth press,
Which only works and business can redress:
Of divine Leisure such foul lies are spoke,
Wounding her fair gifts with calumnious stroke.
But might I, fed with silent meditation,
Assoiled live from that fiend Occupation--
_Improbus labor_, which my spirits hath broke--
I'd drink of time's rich cup, and never surfeit--
Fling in more days than went to make the gem
That crowned the white top of Methusalem--
Yea on my weak neck take, and never forfeit,
Like Atlas bearing up the dainty sky,
The heaven-sweet burthen of eternity.
It was also probably the present essay which led to Lamb's difference
with Southey and the famous letter of remonstrance. Southey accused
_Elia_ of wanting "a sounder religious feeling," and Lamb suggests in
his reply that "New Year's Eve" was the chief offender. See Vol. I.
for Lamb's amplification of one of its passages.
It may be interesting here to quote Coleridge's description of Lamb
as "one hovering between heaven and earth, neither hoping much nor
fearing anything."
Page 31, line 10 from foot. _Bells_. The music of bells seems always
to have exerted fascination over Lamb. See the reference in the story
of the "First Going to Church," in _Mrs. Leicester's School_, Vol.
III.; in his poem "Sabbath Bells," Vol. IV.; and his "John Woodvil,"
Vol. IV.
Page 31, foot. "_I saw the skirts of the departing Year_." From
Coleridge's "Ode to the Departing Year," as printed in 1796 and
1797. Lamb was greatly taken by this line. He wrote to Coleridge on
January 2, 1797, in a letter of which only a small portion has been
printed:--"The opening [of the Ode] is in the spirit of the sublimest
allegory. The idea of the 'skirts of the departing year, seen far
onwards, waving in the wind,' is one of those noble Hints at which
the Reader's imagination is apt to kindle into grand conceptions."
Afterwards Coleridge altered "skirts" to "train."
Page 32, line 21. _Seven.... years_. See note to "Dream-Children."
Alice W--n is identified with Ann Simmons, who lived near Blakesware
when Lamb was a youth, and of whom he wrote his love sonnets.
According to the Key the name is "feigned."
Page 32, line 25. _Old Dorrell_. See the poem "Going or Gone,"
Vol. IV. There seems really to have been such an enemy of the Lamb
fortunes. He was one of the witnesses to the will of John Lamb, the
father--William Dorrell.
Page 33, line 5. _Small-pox at five_. There is no other evidence than
this casual mention that Lamb ever suffered from this complaint.
Possibly he did not. He went to Christ's Hospital at the age of seven.
Page 33, line 13. _From what have I not fallen_. Lamb had had this
idea many years before. In 1796 he wrote this sonnet (text of 1818):--
We were two pretty babes, the youngest she,
The youngest, and the loveliest far, I ween,
And Innocence her name. The time has been
We two did love each other's company;
Time was, we two had wept to have been apart:
But when by show of seeming good beguil'd,
I left the garb and manners of a child,
And my first love for man's society,
Defiling with the world my virgin heart--
My loved companion dropp'd a tear, and fled,
And hid in deepest shades her awful head.
Beloved, who shall tell me where thou art--
In what delicious Eden to be found--
That I may seek thee the wide world around?
Page 33, line 27. _Phantom cloud of Elia_. The speculations in the
paragraph that ends with these words were fantastical at any rate to
one reader, who, under the signature "A Father," contributed to the
March number of the _London Magazine_ a eulogy of paternity, in which
Elia was reasoned with and rebuked. "Ah! Elia! hadst thou possessed
'offspring of thine own to dally with,' thou wouldst never have made
the melancholy avowal that thou hast 'almost ceased to hope!'" Lamb
did not reply.
Page 33, line 7 from foot. _Not childhood alone ..._ The passage
between these words and "freezing days of December" was taken by
Charles Lloyd, Lamb's early friend, as the motto of a poem, in his
_Poems_, 1823, entitled "Stanzas on the Difficulty with which, in
Youth, we Bring Home to our Habitual Consciousness the Idea of Death."
Page 34, line 15 from foot. _Midnight darlings_. Leigh Hunt
records, in his essay "My Books," that he once saw Lamb kiss an old
folio--Chapman's _Homer_.
Page 34, line 8 from foot. "_Sweet assurance of a look_." A favourite
quotation of Lamb's (here adapted) from Matthew Roydon's elegy on Sir
Philip Sidney:--
A sweet attractive kind of grace,
A full assurance given by looks.
A portion of the poem is quoted in the Elia essay on "Some Sonnets of
Sir Philip Sidney."
* * * * *
Page 37. MRS. BATTLE'S OPINIONS ON WHIST.
_London Magazine_, February, 1821.
Mrs. Battle was probably, in real life, to a large extent Sarah
Burney, the wife of Rear-Admiral James Burney, Lamb's friend, and the
centre of the whist-playing set to which he belonged. The theory that
Lamb's grandmother, Mrs. Field, was the original Mrs. Battle, does
not, I think, commend itself, although that lady may have lent a trait
or two. It has possibly arisen from the relation of the passage in the
essay on Blakesware, where Mrs. Battle is said to have died in the
haunted room, to that in "Dream-Children," where Lamb says that Mrs.
Field occupied this room.
The fact that Mrs. Battle and Mrs. Burney were both Sarahs is a small
piece of evidence towards their fusion, but there is something more
conclusive in the correspondence. Writing in March, 1830, concerning
the old whist days, to William Ayrton, one of the old whist-playing
company, and the neighbour of the Burneys in Little James Street,
Pimlico, Lamb makes use of an elision which, I think, may be taken as
more than support of the theory that Mrs. Battle and Mrs. Burney were
largely the same--practically proof. "Your letter, which was only
not so pleasant as your appearance would have been, has revived some
old images; Phillips (not the Colonel), with his few hairs bristling
up at the charge of a revoke, which he declares impossible; the old
Captain's significant nod over the right shoulder (was it not?);
Mrs. B----'s determined questioning of the score, after the game was
absolutely gone to the d----l." Lamb, I think, would have written out
Mrs. Burney in full had he not wished to suggest Mrs. Battle too.
This conjecture is borne out by the testimony of the late Mrs.
Lefroy, in her youth a friend of the Burneys and the Lambs, who
told Canon Ainger that though Mrs. Battle had many differing points
she was undoubtedly Mrs. Burney. But of course there are the usual
cross-trails--the reference to the pictures at Sandham; to Walter
Plumer; to the legacy to Lamb; and so forth. Perhaps among the
Blakesware portraits was one which Lamb chose as Mrs. Battle's
presentment; perhaps Mrs. Field had told him of an ancient dame who
had certain of Mrs. Battle's characteristics, and he superimposed Mrs.
Burney upon this foundation.
For further particulars concerning the Burney whist parties see the
notes to the "Letter to Southey," Vol. I.
Admiral Burney (1750-1821), a son of Dr. Burney, the historian of
music, and friend of Johnson and Reynolds, was the brother of Fanny
Burney, afterwards Madame d'Arblay. See also "The Wedding," page 275
of this volume, for another glimpse of Lamb's old friend. Admiral
Burney wrote _An Essay on the Game of Whist_, which was published in
1821. As he lived until November, 1821, he probably read the present
essay. Writing to Wordsworth, March 20, 1822, Lamb says: "There's
Capt. Burney gone!--what fun has whist now; what matters it what you
lead, if you can no longer fancy him looking over you?"
Page 37, line 1 of essay. "_A clean hearth_." To this, in the _London
Magazine_, Lamb put the footnote:--
"This was before the introduction of rugs, reader. You must remember
the intolerable crash of the unswept cinder, betwixt your foot and the
marble."
Page 37, line 8 of essay. _Win one game, and lose another_. To this,
in the _London Magazine_, Lamb put the note:--
"As if a sportsman should tell you he liked to kill a fox one day,
and lose him the next."
Page 38, line 26. _Mr. Bowles_. The Rev. William Lisle Bowles
(1762-1850), whose sonnets had so influenced Coleridge's early
poetical career. His edition of Pope was published in 1806. I have
tried in vain to discover if Mr. Bowles' MS. and notes for this
edition are still in existence. If so, they might contain Lamb's
contribution. But it is rather more likely, I fear, that Lamb invented
the story. The game of ombre is in Canto III. of _The Rape of the
Lock_.
The only writing on cards which we know Lamb to have done, apart from
this essay, is the elementary rules of whist which he made out for
Mrs. Badams quite late in his life as a kind of introduction to the
reading of Admiral Burney's treatise. This letter is in America and
has never been printed except privately; nor, if its owner can help
it, will it.
Page 40, line 26. _Old Walter Plumer_. See the essay on "The South-Sea
House."
Page 42, line 18 from foot. _Bad passions_. Here came in the _London
Magazine_, in parenthesis, "(dropping for a while the speaking mask of
old Sarah Battle)."
Page 43, line 2. _Bridget Elia_. This is Lamb's first reference in
the essays to Mary Lamb under this name. See "Mackery End" and "Old
China."
A little essay on card playing in the _Every-Day Book_, the authorship
of which is unknown, but which may be Hone's, ends with the following
pleasant passage:--
Cousin Bridget and the gentle Elia seem beings of that age wherein
lived Pamela, whom, with "old Sarah Battle," we may imagine
entering their room, and sitting down with them to a _square_
game. Yet Bridget and Elia live in our own times: she, full of
kindness to all, and of soothings to Elia especially;--he, no less
kind and consoling to Bridget, in all simplicity holding converse
with the world, and, ever and anon, giving us scenes that Metzu
and De Foe would admire, and portraits that Deuner and Hogarth
would rise from their graves to paint.
* * * * *
Page 43. A CHAPTER ON EARS.
_London Magazine_, March, 1821.
Lamb was not so utterly without ear as he states. Crabb Robinson in
his diary records more than once that Lamb hummed tunes, and Barron
Field, in the memoir of Lamb contributed by him to the _Annual
Biography and Obituary_ for 1836, mentions his love for certain
beautiful airs, among them Kent's "O that I had wings like a dove"
(mentioned in this essay), and Handel's "From mighty kings." Lamb says
that it was Braham who awakened a love of music in him. Compare Lamb's
lines to Clara Novello, Vol. IV., page 101, and also Mary Lamb's
postscript to his "Free Thoughts on Eminent Composers," same volume.
Page 43, foot. _I was never ... in the pillory_. This sentence led
to an amusing article in the _London Magazine_ for the next month,
April, 1821, entitled "The Confessions of H.F.V.H. Delamore, Esq.,"
unmistakably, I think, by Lamb, which will be found in Vol. I. of this
edition, wherein Lamb confesses to a brief sojourn in the stocks at
Barnet for brawling on Sunday, an incident for the broad truth of
which we have the testimony of his friend Brook Pulham.
Page 44, lines 6 and 7. "_Water parted from the sea_," "_In Infancy_."
Songs by Arne in "Artaxerxes," Lamb's "First Play" (see page 113).
Page 44, line 11. _Mrs. S----_. The Key gives "Mrs. Spinkes." We meet
a Will Weatherall in "Distant Correspondents," page 120; but I have
not been able to discover more concerning either.
Page 44, line 17. _Alice W----n_. See note to "Dream Children."
Page 44, line 26. _My friend A._ Probably William Ayrton (1777-1818),
the musical critic, one of the Burneys' whist-playing set, and a
friend and correspondent of Lamb's. See the musical rhyming letter to
him from Lamb, May 17, 1817.
Page 47, line 5. _My friend, Nov----_. Vincent Novello (1781-1861),
the organist, the father of Mrs. Cowden Clarke, and a great friend of
Lamb.
Page 47, footnote. Another friend of Vincent Novello's uses the same
couplet (from Watt's _Divine Songs for Children_, Song XXVIII.,
"For the Lord's Day, Evening") in the description of glees by the
old cricketers at the Bat and Ball on Broad Halfpenny Down, near
Hambledon--I refer to John Nyren, author of _The Young Cricketer's
Tutor_, 1833. There is no evidence that Lamb and Nyren ever met, but
one feels that they ought to have done so, in Novello's hospitable
rooms.
Page 48, line 3. _Lutheran beer_. Edmund Ollier, the son of Charles
Ollier, the publisher of Lamb's _Works_, 1818, in his reminiscences of
Lamb, prefixed to one edition of _Elia_, tells this story: "Once at a
musical party at Leigh Hunt's, being oppressed with what to him was
nothing but a prolonged noise ... he said--'If one only had a pot of
porter, one might get through this.' It was procured for him and he
weathered the Mozartian storm."
In the _London Magazine_ this essay had the following postscript:--
"P.S.--A writer, whose real name, it seems, is _Boldero_, but who
has been entertaining the town for the last twelve months, with
some very pleasant lucubrations, under the assumed signature of
_Leigh Hunt_[1], in his Indicator, of the 31st January last, has
thought fit to insinuate, that I _Elia_ do not write the little
sketches which bear my signature, in this Magazine; but that the
true author of them is a Mr. L----b. Observe the critical period
at which he has chosen to impute the calumny!--on the very
eve of the publication of our last number--affording no scope
for explanation for a full month--during which time, I must
needs lie writhing and tossing, under the cruel imputation of
nonentity.--Good heavens! that a plain man must not be allowed
_to be_--
"They call this an age of personality: but surely this spirit of
anti-personality (if I may so express it) is something worse.
"Take away my moral reputation: I may live to discredit that
calumny.
"Injure my literary fame,--I may write that up again--
"But when a gentleman is robbed of his identity, where is he?
"Other murderers stab but at our existence, a frail and perishing
trifle at the best. But here is an assassin who aims at our very
essence; who not only forbids us _to be_ any longer, but _to have
been_ at all. Let our ancestors look to it--
"Is the parish register nothing? Is the house in Princes-street,
Cavendish-square, where we saw the light six-and-forty years
ago, nothing? Were our progenitors from stately Genoa, where we
flourished four centuries back, before the barbarous name of
Boldero[2] was known to a European mouth, nothing? Was the goodly
scion of our name, transplanted into England, in the reign of the
seventh Henry, nothing? Are the archives of the steel yard, in
succeeding reigns (if haply they survive the fury of our envious
enemies) showing that we flourished in prime repute, as merchants,
down to the period of the commonwealth, nothing?
"Why then the world, and all that's in't is nothing--
The covering sky is nothing, Bohemia is nothing.--
"I am ashamed that this trifling writer should have power to move
me so."
Leigh Hunt, in _The Indicator_, January 31 and February 7, 1821, had
reprinted from _The Examiner_ a review of Lamb's _Works_, with a few
prefatory remarks in which it was stated: "We believe we are taking no
greater liberty with him [Charles Lamb] than our motives will warrant,
when we add that he sometimes writes in the _London Magazine_ under
the signature of Elia."
In _The Indicator_ of March 7, 1821, Leigh Hunt replied to Elia. Leigh
Hunt was no match for Lamb in this kind of raillery, and the first
portion of the reply is rather cumbersome. At the end, however, he
says: "There _was_, by the bye, a family of the name of Elia who came
from Italy,--Jews; which may account for this boast about Genoa. See
also in his last article in the London Magazine [the essay on "Ears"]
some remarkable fancies of conscience in reference to the Papal
religion. They further corroborate what we have heard; _viz._ that the
family were obliged to fly from Genoa for saying that the Pope was
the author of Rabelais; and that Elia is not an anagram, as some have
thought it, but the Judaico-Christian name of the writer before us,
whose surname, we find, is not Lamb, but Lomb;--Elia Lomb! What a
name! He told a friend of ours so in company, and would have palmed
himself upon him for a Scotchman, but that his countenance betrayed
him."
It is amusing to note that Maginn, writing the text to accompany the
Maclise portrait of Lamb in _Fraser's Magazine_ in 1835, gravely
states that Lamb's name was really Lomb, and that he was of Jewish
extraction.
The subject of Lamb's birth reopened a little while later. In
the "Lion's Head," which was the title of the pages given to
correspondence in the _London Magazine_, in the number for November,
1821, was the following short article from Lamb's pen:--
"ELIA TO HIS CORRESPONDENTS.--A Correspondent, who writes himself
Peter Ball, or Bell,--for his hand-writing is as ragged as his
manners--admonishes me of the old saying, that some people (under
a courteous periphrasis I slur his less ceremonious epithet) had
need have good memories. In my 'Old Benchers of the Inner Temple,'
I have delivered myself, and truly, a Templar born. Bell clamours
upon this, and thinketh that he hath caught a fox. It seems that
in a former paper, retorting upon a weekly scribbler who had
called my good identity in question, (see P.S. to my 'Chapter on
Ears,') I profess myself a native of some spot near Cavendish
Square, deducing my remoter origin from Italy. But who does not
see, except this tinkling cymbal, that in that idle fiction
of Genoese ancestry I was answering a fool according to his
folly--that Elia there expresseth himself ironically, as to an
approved slanderer, who hath no right to the truth, and can be
no fit recipient of it? Such a one it is usual to leave to his
delusions; or, leading him from error still to contradictory
error, to plunge him (as we say) deeper in the mire, and give
him line till he suspend himself. No understanding reader could
be imposed upon by such obvious rhodomontade to suspect me
for an alien, or believe me other than English.--To a second
Correspondent, who signs himself 'a Wiltshire man,' and claims me
for a countryman upon the strength of an equivocal phrase in my
'Christ's Hospital,' a more mannerly reply is due. Passing over
the Genoese fable, which Bell makes such a ring about, he nicely
detects a more subtle discrepancy, which Bell was too obtuse to
strike upon. Referring to the passage (in page 484 of our second
volume[3]), I must confess, that the term 'native town,' applied
to Calne, _prima facie_ seems to bear out the construction which
my friendly Correspondent is willing to put upon it. The context
too, I am afraid, a little favours it. But where the words of
an author, taken literally, compared with some other passage
in his writings, admitted to be authentic, involve a palpable
contradiction, it hath been the custom of the ingenuous
commentator to smooth the difficulty by the supposition, that
in the one case an allegorical or tropical sense was chiefly
intended. So by the word 'native,' I may be supposed to mean a
town where I might have been born; or where it might be desirable
that I should have been born, as being situate in wholesome air,
upon a dry chalky soil, in which I delight; or a town, with the
inhabitants of which I passed some weeks, a summer or two ago,
so agreeably, that they and it became in a manner native to me.
Without some such latitude of interpretation in the present case,
I see not how we can avoid falling into a gross error in physics,
as to conceive that a gentleman may be born in two places, from
which all modern and ancient testimony is alike abhorrent. Bacchus
cometh the nearest to it, whom I remember Ovid to have honoured
with the epithet 'Twice born.'[4] But not to mention that he is so
called (we conceive) in reference to the places _whence_ rather
than the places _where_ he was delivered,--for by either birth
he may probably be challenged for a Theban--in a strict way of
speaking, he was a _filius femoris_ by no means in the same sense
as he had been before a _filius alvi_, for that latter was but
a secondary and tralatitious way of being born, and he but a
denizen of the second house of his geniture. Thus much by way of
explanation was thought due to the courteous 'Wiltshire man.'--To
'Indagator,' 'Investigator,' 'Incertus,' and the rest of the pack,
that are so importunate about the true localities of his birth--as
if, forsooth, Elia were presently about to be passed to his
parish--to all such churchwarden critics he answereth, that, any
explanation here given notwithstanding, he hath not so fixed his
nativity (like a rusty vane) to one dull spot, but that, if he
seeth occasion, or the argument shall demand it, he will be born
again, in future papers, in whatever place, and at whatever
period, shall seem good unto him.
"Modo me Thebis--modo Athenis.
"ELIA."
[Footnote 1: "Clearly a fictitious appellation; for if we admit the
latter of these names to be in a manner English, what is _Leigh_?
Christian nomenclature knows no such."]
[Footnote 2: "It is clearly of transatlantic origin."]
[Footnote 3: See page 15 of this volume.]
[Footnote 4:
"Imperfectus adhuc infans genetricis ab alvo
Eripitur, patrioque tener (si credere dignum est)
Insuitur femori--
Tutaque bis geniti sunt incunabula Bacchi.
"_Metamorph._ lib. iii., 310."]
* * * * *
Page 48. ALL FOOLS' DAY.
_London Magazine_, April, 1821.
Page 49, line 1. _Empedocles_. Lamb appended this footnote in the
_London Magazine_:--
He who, to be deem'd
A god, leap'd fondly into Etna's flames.
_Paradise Lost_, III., lines 470-471 [should be 469-470].
Page 49, line 5. _Cleombrotus_. Lamb's _London Magazine_ footnote:--
He who, to enjoy
Plato's Elysium, leap'd into the sea.
_Paradise Lost_, III., lines 471-472.
Page 49, line 8. _Plasterers at Babel_. Lamb's _London Magazine_
note:--
The builders next of Babel on the plain
Of Sennaar.
_Paradise Lost_, III., lines 466-467.
Page 49, line 10. _My right hand_. Lamb, it is probably unnecessary to
remind the reader, stammered too.
Page 49, line 13 from foot. _Duns_, Duns Scotus (1265?-1308?),
metaphysician, author of _De modis significandi sive Grammatica
Speculativa_ and other philosophic works. Known as Doctor Subtilis.
There was nothing of Duns in the _London Magazine_; the sentence ran:
"Mr. Hazlitt, I cannot indulge you in your definitions." This was at a
time when Lamb and Hazlitt were not on good terms.
Page 49, last line. _Honest R----_. Lamb's Key gives "Ramsay, London
Library, Ludgate Street; now extinct." I have tried in vain to find
out more about Ramsay. The London Library was established at 5 Ludgate
Street in 1785. Later, the books were lodged at Charles Taylor's house
in Hatton Garden, and were finally removed to the present London
Institute in Finsbury Circus.
Page 50, line 6. _Good Granville S----_. Lamb's Key gives Granville
Sharp. This was the eccentric Granville Sharp, the Quaker abolitionist
(1735-1813).
* * * * *
Page 51. A QUAKER'S MEETING.
_London Magazine_, April, 1821.
Lamb's connection with Quakers was somewhat intimate throughout
his life. In early days he was friendly with the Birmingham
Lloyds--Charles, Robert and Priscilla, of the younger generation,
and their father, Charles Lloyd, the banker and translator of Horace
and Homer (see _Charles Lamb and the Lloyds_, 1898); and later with
Bernard Barton, the Quaker poet of Woodbridge. Also he had loved from
afar Hester Savory, the subject of his poem "Hester" (see Vol. IV.). A
passage from a letter written in February, 1797, to Coleridge, bears
upon this essay:--"Tell Lloyd I have had thoughts of turning Quaker,
and have been reading, or am rather just beginning to read, a most
capital book, good thoughts in good language, William Penn's 'No
Cross, No Crown,' I like it immensely. Unluckily I went to one of his
meetings, tell him, in St. John Street [Clerkenwell] yesterday, and
saw a man under all the agitations and workings of a fanatic, who
believed himself under the influence of some 'inevitable presence.'
This cured me of Quakerism; I love it in the books of Penn and
Woolman, but I detest the vanity of a man thinking he speaks by the
Spirit...."
Both Forster and Hood tell us that Lamb in outward appearance
resembled a Quaker.
Page 52, line 13. _The uncommunicating muteness of fishes_. Lamb had
in mind this thought on the silence of fishes when he was at work on
_John Woodvil_. Simon remarks, in the exquisite passage (Vol. IV.) in
reply to the question, "What is it you love?"
The fish in th' other element
That knows no touch of eloquence.
Page 53, second quotation. "_How reverend ..._" An adaptation of
Congreve's description of York Minster in "The Mourning Bride" (Mary
Lamb's "first play"), Act I., Scene 1:--
How reverend is the face of this tall pile ...
Looking tranquillity!
Page 53, middle. _Fox and Dewesbury_. George Fox (1624-1691) founded
the Society of Friends. William Dewesbury was one of Fox's first
colleagues, and a famous preacher. William Penn (1644-1718), the
founder of Pennsylvania, was the most illustrious of the early
converts to Quakerism. Lamb refers to him again, before his judges, in
the essay on "Imperfect Sympathies," page 73. George Fox's _Journal_
was lent to Lamb by a friend of Bernard Barton's in 1823. On returning
it, Lamb remarked (February 17, 1823):--"I have quoted G.F. in my
'Quaker's Meeting' as having said he was 'lifted up in spirit' (which
I felt at the time to be not a Quaker phrase),' and the Judge and Jury
were as dead men under his feet.' I find no such words in his Journal,
and I did not get them from Sewell, and the latter sentence I am sure
I did not mean to invent. I must have put some other Quaker's words
into his mouth."
Sewel was a Dutchman--William Sewel (1654-1720). His title runs:
_History of the Rise, Increase and Progress of the Christian People
called Quakers, written originally in Low Dutch by W. Sewel, and by
himself translated into English_, 1722. James Naylor (1617-1660) was
one of the early Quaker martyrs--"my favourite" Lamb calls him in a
letter. John Woolman (1720-1772) was an American Friend. His principal
writings are to be found in _A Journal of the Life, Gospel Labours,
and Christian Experiences of that faithful minister of Jesus Christ,
John Woolman, late of Mount Holly in the Province of Jersey, North
America_, 1795. Modern editions are obtainable.
* * * * *
Page 56. THE OLD AND THE NEW SCHOOLMASTER.
_London Magazine_, May, 1821.
Page 56, line 9. _Ortelius ... Arrowsmith_. Abraham Ortellius
(1527-1598), the Dutch geographer and the author of _Theatrum
Orbis Terrae_, 1570. Aaron Arrowsmith (1750-1823) was a well-known
cartographer at the beginning of the nineteenth century. Lamb would
perhaps have known something of his _Atlas of Southern India_, a very
useful work at the East India House.
Page 56, line 13. _A very dear friend_. Barren Field (see the essay on
"Distant Correspondents").
Page 56, line 10 from foot. _My friend M_. Thomas Manning (1772-1840),
the mathematician and traveller, and Lamb's correspondent.
Page 56, last line. "_On Devon's leafy shores_." From Wordsworth's
_Excursion_, III.
Page 57, line 16. _Daily jaunts_. Though Lamb was then (1821) living
at 20 Great Russell Street, Covent Garden, he rented rooms at 14
Kingsland Row, Dalston, in which to take holidays and do his literary
work undisturbed. At that time Dalston, which adjoins Shackleton, was
the country and Kingsland Green an open space opposite Lamb's lodging.
Page 58, line 23. _The North Pole Expedition_. This would probably
be Sir John Franklin's expedition which set out in 1819 and ended in
disaster, the subject of Franklin's book, _Narrative of a Journey to
the Shores of the Polar Sea in the years 1819, 20, 21, 22_ (1823). Sir
John Ross made an expedition in 1818, and Sir William Edward Parry in
1819, and again in 1821-1823 with Lyon. The panorama was possibly
at Burford's Panorama in the Strand, afterwards moved to Leicester
Square.
Page 60, line 17. _Tractate on Education_. Milton's _Tractate on
Education_, addressed to his friend, Samuel Hartlib, was published in
1644. The quotation above is from that work. This paragraph of Lamb's
essay was afterwards humorously expanded in his "Letter to an Old
Gentleman whose Education has been Neglected" (see Vol. I.).
Page 60, last line. _Mr. Bartley's Orrery._ George Bartley
(1782?-1858), the comedian, lectured on astronomy and poetry at the
Lyceum during Lent at this time. An orrery is a working model of the
solar system. The Panopticon was, I assume, a forerunner of the famous
Panopticon in Leicester Square.
Page 61, line 8. "_Plaything for an hour_." A quotation, from Charles
and Mary Lamb's _Poetry for Children_--"Parental Recollections":--
A child's a plaything for an hour.
Page 63, end of essay. "_Can I reproach her for it_." After these
words, in the _London Magazine_, came:--
"These kind of complaints are not often drawn from me. I am aware
that I am a fortunate, I mean a prosperous man. My feelings
prevent me from transcribing any further."
* * * * *
Page 63. VALENTINE'S DAY.
This essay first appeared in _The Examiner_, February 14 and 15, 1819,
and again in _The Indicator_, February 14, 1821. Signed ***
Page 64, line 18. _Twopenny postman._ Hone computed, in his _Every-Day
Book_, Vol. I., 1825, that "two hundred thousand letters beyond the
usual daily average annually pass through the two-penny post-office in
London on Valentine's Day." The Bishop's vogue is now (1911) almost
over.
Page 65, line 15 from foot. E.B. Lamb's Key gives "Edward Burney, half
brother of Miss Burney." This was Edward Francis Burney (1760-1848),
who illustrated many old authors, among them Richardson.
* * * * *
Page 66. IMPERFECT SYMPATHIES.
_London Magazine_, August, 1821, where the title ran: "Jews, Quakers,
Scotchmen, and other Imperfect Sympathies."
Page 69, line 18 from foot. _A print ... after Leonardo._ The Virgin
of the Rocks. See Vol. IV. for Lamb's and his sister's verses on this
picture. Crabb Robinson's MS. diary tells us that the Scotchman was
one Smith, a friend of Godwin. His exact reply to Lamb's remark about
"my beauty" was: "Why, sir, from all I have heard of you, as well
as from what I have myself seen, I certainly entertain a very high
opinion of your abilities, but I confess that I have not formed any
opinion concerning your personal pretensions."
Page 70, line 10. _The poetry of Burns._ "Burns was the god of my
idolatry," Lamb wrote to Coleridge in 1796. Coleridge's lines on
Burns, "To a Friend who had declared his intention of writing no more
poetry," were addressed to Lamb. Barry Cornwall records seeing Lamb
kiss his copy of the poet.
Page 70, line 17. _You can admire him_. In the _London Magazine_ Lamb
added:--
"I have a great mind to give up Burns. There is certainly
a bragging spirit of generosity, a swaggering assertion of
independence, and _all that_, in his writings."
Page 70, line 18. _Smollett_. Tobias George Smollett (1721-1771), the
novelist, came of a Dumbartonshire family. Rory was Roderick Random's
schoolboy name. His companion was Strap. See _Roderick Random_,
Chapter XIII., for the passage in question. Smollett continued the
_History of England_ of David Hume (1711-1776), also a Scotchman, and
one of the authors whom Lamb could not read (see "Detached Thoughts on
Books and Reading," page 196).
Lamb's criticism of Scotchmen did not pass without comment. The
pleasantest remark made upon it was that of Christopher North
(John Wilson) some dozen years later (after he had met Lamb), in a
_Blackwood_ paper entitled "Twaddle on Tweedside" (May, 1833), wherein
he wrote:--
Charles Lamb ought really not to abuse Scotland in the pleasant
way he so often does in the sylvan shades of Enfield; for Scotland
loves Charles Lamb; but he is wayward and wilful in his wisdom,
and conceits that many a Cockney is a better man even than
Christopher North. But what will not Christopher forgive to Genius
and Goodness? Even Lamb bleating libels on his native land. Nay,
he learns lessons of humanity, even from the mild malice of Elia,
and breathes a blessing on him and his household in their Bower of
Rest.
Coleridge was much pleased by this little reference to his friend. He
described it as "very sweet indeed" (see his _Table Talk_, May 14,
1833).
Page 70, line 14 from foot. _Hugh of Lincoln_. Hugh was a small
Lincoln boy who, tradition states, was tortured to death by the Jews.
His dead body being touched by a blind woman, she received sight.
Many years earlier Lamb had spoken of the Jew in English society with
equal frankness (see his note to the "Jew of Malta" in the _Dramatic
Specimens_).
Page 71, line 18. _B----_. John Braham, _nee_ Abraham (1774?-1856),
the great tenor. Writing to Manning in 1808, Lamb says:--"Do you like
Braham's singing? The little Jew has bewitched me. I follow him like
as the boys followed Tom the Piper. He cures me of melancholy as
David cured Saul.... I was insensible to music till he gave me a new
sense.... Braham's singing, when it is impassioned, is finer than Mrs.
Siddons's or Mr. Kemble's acting! and when it is not impassioned it is
as good as hearing a person of fine sense talking. The brave little
Jew!"
Two years later Lamb tells Manning of Braham's absence from London,
adding: "He was a rare composition of the Jew, the gentleman, and the
angel; yet all these elements mixed up so kindly in him that you could
not tell which preponderated." In this essay Lamb refers to Braham's
singing in Handel's oratorio "Israel in Egypt." Concerning Braham's
abandonment of the Jewish faith see Lamb's sarcastic essay "The
Religion of Actors," Vol. I., page 338.
Page 73, line 17 from foot. _I was travelling_. Lamb did not really
take part in this story. It was told him by Sir Anthony Carlisle
(1768-1840), the surgeon, as he confessed to his Quaker friend,
Bernard Barton (March 11, 1823), who seemed to miss its point. Lamb
described Carlisle as "the best story-teller I ever heard."
* * * * *
Page 74. WITCHES, AND OTHER NIGHT-FEARS.
_London Magazine_, October, 1821.
Compare with this essay Maria Howe's story of "The Witch Aunt," in
_Mrs. Leicester's School_ (see Vol. III.), which Lamb had written
thirteen years earlier.
Page 75, line 12 from foot. _History of the Bible, by Stackhouse_.
Thomas Stackhouse (1677-1752) was rector of Boldon, in Durham; his
_New History of the Holy Bible from the Beginning of the World to the
Establishment of Christianity_--the work in question--was published in
1737.
Page 75, line 6 from foot. _The Witch raising up Samuel_. This
paragraph was the third place in which Lamb recorded his terror of
this picture of the Witch of Endor in Stackhouse's _Bible_, but the
first occasion in which he took it to himself. In one draft of _John
Woodvil_ (see Vol. IV.), the hero says:--
I can remember when a child the maids
Would place me on their lap, as they undrest me,
As silly women use, and tell me stories
Of Witches--make me read "Glanvil on Witchcraft,"
And in conclusion show me in the Bible,
The old Family Bible, with the pictures in it,
The 'graving of the Witch raising up Samuel,
Which so possest my fancy, being a child,
That nightly in my dreams an old Hag came
And sat upon my pillow.
Then again, in _Mrs. Leicester's School_, in the story of Maria Howe,
called "The Witch Aunt," one of the three stories in that book which
Lamb wrote, Stackhouse's _Bible_ is found once more. In my large
edition I give a reproduction of the terrible picture. Page 77, foot.
_Dear little T.H._ This was the unlucky passage which gave Southey his
chief text in his criticism of _Elia_ as a book wanting "a sounder
religious feeling," and which led to Lamb's expostulatory "Letter"
(see Vol. I.). Southey commented thus:--
This poor child, instead of being trained up in the way in which
he should go, had been bred in the ways of modern philosophy; he
had systematically been prevented from knowing anything of that
Saviour who said, "Suffer little children to come unto Me, and
forbid them not; for of such is the Kingdom of Heaven;" care had
been taken that he should not pray to God, nor lie down at night
in reliance upon His good Providence!
T.H. was Thornton Hunt, Leigh Hunt's eldest son and Lamb's "favourite
child" (see verses to him in Vol. IV.).
Page 79, line 18 from foot. _Barry Cornwall_. Bryan Waller Procter
(1787-1874), Lamb's friend. The reference is to "A Dream," a poem in
Barry Cornwall's _Dramatic Scenes_, 1819, which Lamb greatly admired.
See his sonnet to the poet in Vol. IV., where it is mentioned again.
Page 80, last paragraph of essay. In the original MS. of this essay
(now in the Dyce and Forster collection at South Kensington) the last
paragraph ran thus:--
"When I awoke I came to a determination to write prose all the
rest of my life; and with submission to some of our young writers,
who are yet diffident of their powers, and balancing perhaps
between verse and prose, they might not do unwisely to decide the
preference by the texture of their natural dreams. If these are
prosaic, they may depend upon it they have not much to expect in
a creative way from their artificial ones. What dreams must not
Spenser have had!"
* * * * *
Page 80. MY RELATIONS.
_London Magazine_, June, 1821.
Page 80, beginning. _At that point of life_. Lamb was forty-six on
February 10, 1821.
Page 80, line 12 of essay. _I had an aunt_. Aunt Hetty, who died in
1797 (see the essay on "Christ's Hospital").
Page 81, line 6. _The chapel in Essex-street_. The headquarters of
"that heresy," Unitarianism. Lamb was at first a Unitarian, but
afterwards dropped away from all sects.
Page 81, line 23. _Brother, or sister, I never had any--to know them_.
Lamb is writing strictly as the imagined Elia, Elia being Lamb in mind
rather than Lamb in fact. It amused him to present his brother John
and his sister Mary as his cousins James and Bridget Elia. We have
here an excellent example of his whimsical blending of truth and
invention: brothers and sisters he denies, yet admits one sister,
Elizabeth, who died in both their infancies. Lamb had in reality two
sisters named Elizabeth, the former of whom he never knew. She was
born in 1762. The second Elizabeth, his parents' fifth child, was born
in 1768, seven years before Charles. Altogether the Lambs had seven
children, of whom only John (born 1763), Mary Anne (born 1764) and
Charles (born 1775) grew up. Again Lamb confesses to several cousins
in Hertfordshire, and to two others. The two others were fictitious,
but it was true that he had Hertfordshire relations (see the essay
"Mackery End, in Hertfordshire").
John Lamb's character is perhaps sufficiently described in this essay
and in "Dream-Children." He was a well-to-do official in the South-Sea
House, succeeding John Tipp as accountant. Crabb Robinson found him
too bluff and noisy to be bearable; and he once knocked Hazlitt down
in a dispute about painting. He died on October 26, 1821, to his
brother's great grief, leaving Charles everything. He married late in
life a Mrs. Dowden. Probably she had her own money and needed none of
her second husband's. Hence the peculiarity of the will. Mrs. John
Lamb died in 1826.
John Lamb's sympathy with animals led him to write in 1810 a pamphlet
entitled _A Letter to the Right Hon. William Windham, on his
opposition to Lord Erskine's Bill for the Prevention of Cruelty to
Animals_--Mr. Windham having expressed it as his opinion that the
subject was not one for legislation. Lamb sent the pamphlet to Crabb
Robinson on February 7, 1810, saying:--"My Brother whom you have met
at my rooms (a plump good looking man of seven and forty!) has written
a book about humanity, which I transmit to you herewith. Wilson the
Publisher has put it in his head that you can get it Reviewed for him.
I dare say it is not in the scope of your Review--but if you could
put it into any likely train, he would rejoyce. For alas! our boasted
Humanity partakes of Vanity. As it is, he teazes me to death with
chusing to suppose that I could get it into all the Reviews at a
moment's notice.--I!! who have been set up as a mark for them to throw
at and would willingly consign them all to Hell flames and Megaera's
snaky locks.
"But here's the Book--and don't shew it Mrs. Collier, for I remember
she makes excellent Eel soup, and the leading points of the Book are
directed against that very process."
This is the passage--one red-hot sentence--concerning eels:--
"If an eel had the wisdom of Solomon, he could not help himself in
the ill-usage that befalls him; but if he had, and were told, that
it was necessary for our subsistence that he should be eaten, that
he must be skinned first, and then broiled; if ignorant of man's
usual practice, he would conclude that the cook would so far use
her reason as to cut off his head first, which is not fit for
food, as then he might be skinned and broiled without harm; for
however the other parts of his body might be convulsed during the
culinary operations, there could be no feeling of consciousness
therein, the communication with the brain being cut off; but if
the woman were immediately to stick a fork into his eye, skin
him alive, coil him up in a skewer, head and all, so that in the
extremest agony he could not move, and forthwith broil him to
death: then were the same Almighty Power that formed man from the
dust, and breathed into his nostrils the breath of life, to call
the eel into a new existence, with a knowledge of the treatment he
had undergone, and he found that the instinctive disposition which
man has in common with other carnivorous animals, which inclines
him to cruelty, was not the sole cause of his torments; but that
men did not attend to consider whether the sufferings of such
insignificant creatures could be lessened: that eels were not the
only sufferers; that lobsters and other shell fish were put into
cold water and boiled to death by slow degrees in many parts of
the sea coast; that these, and many other such wanton atrocities,
were the consequence of carelessness occasioned by the pride of
mankind despising their low estate, and of the general opinion
that there is no punishable sin in the ill-treatment of animals
designed for our use; that, therefore, the woman did not bestow
so much thought on him as to cut his head off first, and that
she would have laughed at any considerate person who should have
desired such a thing; with what fearful indignation might he
inveigh against the unfeeling metaphysician that, like a cruel
spirit alarmed at the appearance of a dawning of mercy upon
animals, could not rest satisfied with opposing the Cruelty
Prevention Bill by the plea of possible inconvenience to mankind,
highly magnified and emblazoned, but had set forth to the vulgar
and unthinking of all ranks, in the jargon of proud learning, that
man's obligations of morality towards the creatures subjected to
his use are imperfect obligations!"
The poem "The Beggar-Man," in _Poetry for Children_, 1809 (see Vol.
III.), was also from John Lamb's pen.
Page 85, asterisks. _Society for the Relief of_--Distrest Sailors,
says Lamb's Key.
Page 86, last line of essay. "_Through the green plains of pleasant
Hertfordshire_." This line occurs in a sonnet of Lamb's written many
years before the essay (see Vol. IV.). Probably, however, Lamb did
not invent it, for (the late W.J. Craig pointed out) in Leland's
_Itinerary_, which Lamb must have known, if only on account of the
antiquary's remarks on Hertfordshire, is quoted a poem by William
Vallans (_fl._ 1578-1590), "The Tale of the Two Swans," containing
the line--
The fruitful fields of pleasant Hertfordshire--
which one can easily understand would have lingered in Lamb's mind
very graciously.
In the _London Magazine_ the essay ended with the words, "Till then,
Farewell."
* * * * *
Page 86. MACKERY END, IN HERTFORDSHIRE.
_London Magazine_, July, 1821. Reprinted in _Elia_, 1823, as written,
save for the omission of italics from many passages.
Bridget Elia, who is met also in "Mrs. Battle," in "My Relations," and
in "Old China," was, of course, Mary Lamb.
Page 86, line 11 from foot. _She must have a story_. Thomas Westwood,
in his reminiscences of the Lambs in later years, printed in _Notes
and Queries_, speaks of Mary Lamb's passion for novel-reading in the
Enfield days, when he was a boy.
Page 87, line 6. _Margaret Newcastle_. Lamb's devotion to this lady is
expressed again in the essay on "The Two Races of Men," in the essay
on Beggars, and in "Detached Thoughts on Books and Reading."
Page 87, line 8. _Free-thinkers_ ... William Godwin, perhaps alone
among Lamb's friends, quite answers to the description of leader
of novel philosophies and systems; but there had been also Thomas
Holcroft and John Thelwall among the Lambs' acquaintance. And Hazlitt
and Leigh Hunt would come within this description.
Page 87, foot. _Good old English reading_. The reference is to Samuel
Salt's library in the Temple (see note to "The Old Benchers of the
Inner Temple").
Page 88, line 14. _Mackery End_. The farmhouse still stands, although
new front rooms have been added. At the end of the present hall, one
passes through what was in Lamb's time the front door, and thereafter
the house is exactly as it used to be save that its south windows have
been filled in. By kind invitation of Mr. Dolphin Smith, the farmer,
who had been there over forty years, I spent in 1902 some time in the
same parlour in which the Lambs had been entertained. Harpenden, on
the north-west, has grown immensely since Lamb's day, and the houses
at the Folly, between Wheathampstead and the Cherry Trees, are new;
but Mackery End, or Mackrye End as the farmer's waggons have it,
remains unencroached upon. Near by is the fine old mansion which is
Mackery End house proper; Lamb's Mackery End was the farm.
Lamb's first visit there must have been when he was a very little
boy--somewhere about 1780. Probably we may see recollections of it in
Mary Lamb's story "The Farmhouse" in _Mrs. Leicester's School_ (see
Vol. III. of this edition).
Page 88, line 18. _A great-aunt_. Mary Field, Lamb's grandmother, was
Mary Bruton, whose sister married, as he says, a Gladman, and was the
great-aunt mentioned. The present occupier of the farm is neither
Gladman nor Bruton; but both names are still to be found in the
county. A Miss Sarah Bruton, a direct descendant of Lamb's great-aunt,
was living at Wheathampstead in 1902. She had on her walls two
charming oval portraits of ancestresses, possibly--for she was
uncertain as to their identity--two of the handsome sisters whom Lamb
extols.
Writing to Manning, May 28, 1819, Lamb says:--"How are my cousins,
the Gladmans of Wheathampstead, and farmer Bruton? Mrs. Bruton is a
glorious woman.
"Hail, Mackery End!
"This is a fragment of a blank verse poem which I once meditated, but
got no further."
Page 89, verse. "_But thou, that didst appear so fair ..._" From
Wordsworth's "Yarrow Visited," Stanza 6. Writing to Wordsworth in
1815, Lamb said of this stanza that he thought "no lovelier" could be
found in "the wide world of poetry." From a letter to Taylor, of the
_London Magazine_, belonging to the summer of 1821, we gather that the
proof-reader had altered the last word of the third line to "air" to
make it rhyme to "fair." Lamb says: "_Day_ is the right reading, and
_I implore you to restore it_."
Page 90, line 4. _B.F._ Barron Field (see note to "Distant
Correspondents"), then living in Sydney, where he composed, and had
printed for private circulation in 1819, a volume of poems reviewed by
Lamb (see Vol. I.), in 1819, one of which was entitled "The Kangaroo."
It was the first book printed in Australia. Field edited Heywood for
the old Shakespeare Society. Although a Field, he was no kinsman of
Lamb's.
* * * * *
Page 90. MODERN GALLANTRY.
_London Magazine_, November, 1822.
De Quincey writes in "London Reminiscences" concerning the present
essay:--
Among the prominent characteristics of Lamb, I know not how it is
that I have omitted to notice the peculiar emphasis and depth of
his courtesy. This quality was in him a really chivalrous feeling,
springing from his heart, and cherished with the sanctity of a
duty. He says somewhere in speaking of himself[?] under the mask
of a third person, whose character he is describing, that, in
passing a servant girl, even at a street-crossing, he used to take
off his hat. Now, the _spirit_ of Lamb's gallantry would have
prompted some such expression of homage, though the customs of
the country would not allow it to be _literally_ fulfilled, for
the very reason that would prompt it--_viz_., in order to pay
respect--since the girl would, in such a case, suppose a man
laughing at her. But the instinct of his heart was to think
highly of female nature, and to pay a real homage (not the hollow
demonstration of outward honour which a Frenchman calls his
"homage," and which is really a mask for contempt) to the sacred
_idea_ of pure and virtuous womanhood.
Barry Cornwall has the following story in his Memoir of Lamb:--
Lamb, one day, encountered a small urchin loaded with a too heavy
package of grocery. It caused him to tremble and stop. Charles
inquired where he was going, took (although weak) the load upon
his own shoulder, and managed to carry it to Islington, the place
of destination. Finding that the purchaser of the grocery was a
female, he went with the urchin before her, and expressed a hope
that she would intercede with the poor boy's master, in order to
prevent his being over-weighted in future. "Sir," said the dame,
after the manner of Tisiphone, frowning upon him, "I buy my sugar
and have nothing to do with the man's manner of sending it." Lamb
at once perceived the character of the purchaser, and taking off
his hat, said, humbly, "Then I hope, ma'am, you'll give me a drink
of small beer." This was of course refused. He afterwards called
upon the grocer, on the boy's behalf. With what effect I do not
know.
Page 90, line 2 of essay. _Upon the point of gallantry_. Here, in the
_London Magazine_, came the words:--
"as upon a thing altogether unknown to the old classic ages.
This has been defined to consist in a certain obsequiousness, or
deferential respect, paid to females, as females."
Page 92, line 3. _Joseph Paice_. Joseph Paice was, as Lamb pointed out
to Barton in a letter in January, 1830, a real person, and all that
Lamb records. According to Miss Anne Manning's _Family Pictures_,
1860, Joseph Paice, who was a friend of Thomas Coventry, took Lamb
into his office at 27 Bread Street Hill somewhere in 1789 or 1790
to learn book-keeping and business habits. He passed thence to the
South-Sea House and thence to the East India House. Miss Manning (who
was the author of _Flemish Interiors_) helps to fill out Lamb's sketch
into a full-length portrait. She tells us that Mr. Paice's life was
one long series of gentle altruisms and the truest Christianities.
Charles Lamb speaks of his holding an umbrella over a
market-woman's fruit-basket, lest her store should be spoilt by a
sudden shower; and his uncovering his head to a servant-girl who
was requesting him to direct her on her way. These traits are
quite in keeping with many that can still be authenticated:--his
carrying presents of game _himself_, for instance, to humble
friends, who might ill have spared a shilling to a servant; and
his offering a seat in his hackney-coach to some poor, forlorn,
draggled beings, who were picking their way along on a rainy
day. Sometimes these chance guests have proved such uncongenial
companions, that the kind old man has himself faced the bad
weather rather than prolong the acquaintance, paying the
hackney-coachman for setting down the stranger at the end of his
fare. At lottery times, he used to be troubled with begging visits
from certain improvident hangers-on, who had risked their all in
buying shares of an unlucky number. About the time the numbers
were being drawn, there would be a ring at the gate-bell, perhaps
at dinner time. His spectacles would be elevated, an anxious
expression would steal over his face, as he half raised himself
from his seat, to obtain a glance at the intruder--"Ah, I thought
so, I expected as much," he would gently say. "I expected I should
soon have a visit from poor Mrs. ---- or Mrs. ----. Will you
excuse me, my dear madam," (to my grandmother) "for a moment,
while I just tell her it is quite out of my power to help her?"
counting silver into his hand all the time. Then, a parley would
ensue at the hall-door--complainant telling her tale in a doleful
voice: "My good woman, I really cannot," etc.; and at last the
hall-door would be shut. "Well, sir," my grandmother used to say,
as Mr. Paice returned to his seat, "I do not think you have sent
Mrs. ---- away quite penniless." "Merely enough for a joint of
meat, my good madam--just a trifle to buy her a joint of meat."
_Family Pictures_ should be consulted by any one who would know more
of this gentleman and of Susan Winstanly.
Page 92, line 5. _Edwards_. Thomas Edwards (1699-1757), author of
_Canons of Criticism_, 1748. The sonnet in question, which was
modelled on that addressed by Milton to Cyriack Skinner, was addressed
to Paice, as the author's nephew, bidding him carry on the family
line. Paice, however, as Lamb tells us, did not marry.
* * * * *
Page 94. THE OLD BENCHERS OF THE INNER TEMPLE.
_London Magazine_, September, 1821.
Lamb's connection with the Temple was fairly continuous until 1817,
when he was thirty-eight. He was born at No. 2 Crown Office Row in
1775, and he did not leave it, except for visits to Hertfordshire,
until 1782, when he entered Christ's Hospital. There he remained, save
for holidays, until 1789, returning then to Crown Office Row for the
brief period between leaving school and the death of Samuel Salt,
under whose roof the Lambs dwelt, in February, 1792. The 7 Little
Queen Street, the 45 and 36 Chapel Street, Pentonville, and the first
34 Southampton Buildings (with Gutch) periods, followed; but in 1801
Lamb and his sister were back in the Temple again, at 16 Mitre Court
Buildings, since rebuilt. They moved from there, after a brief return
to 34 Southampton Buildings, to 4 Inner Temple Lane (since rebuilt and
now called Johnson's Buildings) in 1809, where they remained until the
move to 20 Great Russell Street in 1817. With each change after that
(except for another and briefer sojourn in Southampton Buildings
in 1830), Lamb's home became less urban. His last link with the
Temple may be said to have snapped with the death of Randal Morris,
sub-treasurer of the Inner Temple, in 1827 (see "A Death-Bed"),
although now and then he slept at Crabb Robinson's chambers.
The Worshipful Masters of the Bench of the Hon. Society of the Inner
Temple--to give the Benchers their full title--have the government of
the Inner Temple in their hands.
Page 97, line 12 from foot, _J----ll_. Joseph Jekyll, great-nephew of
Joseph Jekyll, Master of the Rolls, well known as a wit and diner-out.
He became a Bencher in 1795, and was made a Master in Chancery in
1815, through the influence of the Prince Regent. Under his direction
the hall of the Inner Temple and the Temple Church were restored, and
he compiled a little book entitled _Facts and Observations relating to
the Temple Church and the Monuments contained in it_, 1811. He became
a K.C. in 1805, and died in 1837, aged eighty-five. Jekyll was a
friend of George Dyer, and was interested in Lamb's other friends, the
Norrises. & letter from him, thanking Lamb for a copy of the _Last
Essays of Elia_, is printed in Mr. W.C. Hazlitt's _The Lambs_. He had
another link of a kind with Lamb in being M.P. for "sweet Calne in
Wiltshire." Jekyll's chambers were at 6 King's Bench Walk. On the same
staircase lived for a while George Colman the Younger.
Page 97, line 9 from foot. _Thomas Coventry_. Thomas Coventry became a
Bencher in 1766. He was the nephew of William, fifth Earl of Coventry,
and resided at North Cray Place, near Bexley, in Kent, and in
Serjeant's Inn, where he died in 1797, in his eighty-fifth year. He
is buried in the Temple Church. Coventry was a sub-governor of the
South-Sea House, and it was he who presented Lamb's friend, James
White, to Christ's Hospital. He was M.P. for Bridport from 1754 to
1780. As an illustration of Coventry's larger benefactions it may
be remarked that he presented L10,000 worth of South Sea stock to
Christ's Hospital in 1782.
Page 98, line 9. _Samuel Salt_. Samuel Salt was the son of the Rev.
John Salt, of Audley, in Staffordshire; and he married a daughter of
Lord Coventry, thus being connected with Thomas Coventry by marriage.
He was M.P. for Liskeard for some years, and a governor of the
South-Sea House. Samuel Salt, who became a Bencher in 1782, rented
at No. 2 Crown Office Row two sets of chambers, in one of which the
Lamb family dwelt. John Lamb, Lamb's father, who is described as a
scrivener in Charles's Christ's Hospital application form, was Salt's
right-hand man, not only in business, but privately, while Mrs. Lamb
acted as housekeeper and possibly as cook. Samuel Salt played the part
of tutelary genius to John Lamb's two sons. It was he who arranged
for Charles to be nominated for Christ's Hospital (by Timothy Yeats);
probably he was instrumental also in getting him into the East India
House; and in all likelihood it was he who paved the way for the
younger John Lamb's position in the South-Sea House. It was also
Samuel Salt who gave to Charles and Mary the freedom of his library
(see the reference in the essay on "Mackery End"): a privilege which,
to ourselves, is the most important of all. Salt died in February,
1792, and is buried in the vault of the Temple Church. He left to John
Lamb L500 in South Sea stock and a small annual sum, and to Elizabeth
Lamb L200 in money; but with his death the prosperity of the family
ceased.
Page 98, line 21. _Lovel_. See below.
Page 98, line 9 from foot. _Miss Blandy_. Mary Blandy was the daughter
of Francis Blandy, a lawyer at Henley-on-Thames. The statement that
she was to inherit L10,000 induced an officer in the marines, named
Cranstoun, a son of Lord Cranstoun, to woo her, although he already
had a wife living. Her father proving hostile, Cranstoun supplied her
with arsenic to bring about his removal. Mr. Blandy died on August
14, 1751. Mary Blandy was arrested, and hanged on April 6 in the next
year, after a trial which caused immense excitement. The defence was
that Miss Blandy was ignorant of the nature of the powder, and thought
it a means of persuading her father to her point of view. In this
belief the father, who knew he was being tampered with, also shared.
Cranstoun avoided the law, but died in the same year. Lamb had made
use of Salt's _faux pas_, many years earlier, in "Mr. H." (see Vol.
IV.).
Page 99, line 13. _His eye lacked lustre_. At these words, in the
_London Magazine_, came this passage:--
"Lady Mary Wortley Montague was an exception to her sex: she says,
in one of her letters, 'I wonder what the women see in S. I do not
think him by any means handsome. To me he appears an extraordinary
dull fellow, and to want common sense. Yet the fools are all
sighing for him.'"
I have not found the passage.
Page 99, line 14. _Susan P----_. This is Susannah Peirson, sister of
the Peter Peirson to whom we shall come directly. Samuel Salt left her
a choice of books in his library, together with a money legacy and a
silver inkstand, hoping that reading and reflection would make her
life "more comfortable." B----d Row would be Bedford Row.
Page 99, line 12 from foot, _F., the counsel_. I cannot be sure who
this was. The Law Directory of that day does not help.
Page 99, foot. _Elwes_. John Elwes, the miser (1714-1789), whose
_Life_ was published in 1790 after running through _The World_--the
work of Topham, that paper's editor, who is mentioned in Lamb's essay
on "Newspapers."
Page 100, line 15. _Lovel_. Lovel was the name by which Lamb refers to
his father, John Lamb. We know nothing of him in his prime beyond what
is told in this essay, but after the great tragedy, there are in the
_Letters_ glimpses of him as a broken, querulous old man. He died in
1799. Of John Lamb's early days all our information is contained in
this essay, in his own _Poetical Pieces_, where he describes his life
as a footman, and in the essay on "Poor Relations," where his boyish
memories of Lincoln are mentioned. Of his verses it was perhaps too
much (though prettily filial) to say they were "next to Swift and
Prior;" but they have much good humour and spirit. John Lamb's poems
were printed in a thin quarto under the title _Poetical Pieces on
Several Occasions_. The dedication was to "The Forty-Nine Members of
the Friendly Society for the Benefit of their Widows, of whom I have
the honour of making the Number Fifty," and in the dedicatory epistle
it is stated that the Society was in some degree the cause of Number
Fifty's commencing author, on account of its approving and printing
certain lines which were spoken by him at an annual meeting it the
Devil Tavern. The first two poetical pieces are apologues on marriage
and the happiness that it should bring, the characters being drawn
from bird life. Then follow verses written for the meetings of the
Society, and miscellaneous compositions. Of these the description
of a lady's footman's daily life, from within, has a good deal of
sprightliness, and displays quite a little mastery of the mock-heroic
couplet. The last poem is a long rhymed version of the story of
Joseph. With this exception, for which Lamb's character-sketch does
not quite prepare us, it is very natural to think of the author as
Lovel. One of the pieces, a familiar letter to a doctor, begins
thus:--
My good friend,
For favours to my son and wife,
I shall love you whilst I've life,
Your clysters, potions, help'd to save,
Our infant lambkin from the grave.
The infant lambkin was probably John Lamb, but of course it might have
been Charles. The expression, however, proves that punning ran in the
family. Lamb's library contained his father's copy of _Hudibras_.
Lamb's phrase, descriptive of his father's decline, is taken with a
variation from his own poems--from the "Lines written on the Day of my
Aunt's Funeral" (_Blank Verse_, 1798):--
One parent yet is left,--a wretched thing,
A sad survivor of his buried wife
A palsy-smitten, childish, old, old man,
A semblance most forlorn of what he was--
A merry cheerful man.
Page 100, line 17. "_Flapper_." This is probably an allusion to the
flappers in _Gulliver's Travels_--the servants who, in Laputa, carried
bladders with which every now and then they flapped the mouths and
ears of their employers, to recall them to themselves and disperse
their meditations.
Page 100, line 9 from foot. _Better was not concerned_. At these
words, in the _London Magazine_, came:--
"He pleaded the cause of a delinquent in the treasury of the Temple so
effectually with S. the then treasurer--that the man was allowed
to keep his place. L. had the offer to succeed him. It had been a
lucrative promotion. But L. chose to forego the advantage, because the
man had a wife and family."
Page 101, line 10. _Bayes_. Mr. Bayes is the author and stage manager
in Buckingham's "Rehearsal." This phrase is not in the play and must
have been John Lamb's own, in reference to Garrick.
Page 101, line 23. _Peter Pierson_. Peter Peirson (as his name was
rightly spelled) was the son of Peter Peirson of the parish of St.
Andrew's, Holborn, who lived probably in Bedford Row. He became a
Bencher in 1800, died in 1808, and is buried in the Temple Church.
When Charles Lamb entered the East India House in April, 1792, Peter
Peirson and his brother, John Lamb, were his sureties.
Page 101, line 11 from foot. _Our great philanthropist_. Probably John
Howard, whom, as we have seen in the essay on "Christ's Hospital,"
Lamb did not love. He was of singular sallowness.
Page 101, line 9 from foot. _Daines Barrington_. Daines Barrington
(1727-1800), the correspondent of Gilbert White, many of whose letters
in _The Natural History of Selborne_ are addressed to him. Indeed it
was Barrington who inspired that work:--a circumstance which must
atone for his exterminatory raid on the Temple sparrows. His Chambers
were at 5 King's Bench Walk. Barrington became a Bencher in 1777 and
died in 1800. He is buried in the Temple Church. His Episcopal brother
was Shute Barrington (1734-1826), Bishop successively of Llandaff,
Salisbury and Durham.
Page 102, line 1. _Old Barton_. Thomas Barton, who became a Bencher in
1775 and died in 1791. His chambers were in King's Bench Walk. He is
buried in the vault of the Temple Church.
Page 102, line 6. _Read_. John Reade, who became a Bencher in 1792 and
died in 1804. His rooms were in Mitre Court Buildings.
Page 102, line 6. _Twopenny_. Richard, Twopenny was not a Bencher, but
merely a resident in the Temple. He was strikingly thin. Twopenny was
stockbroker to the Bank of England, and died in 1809.
Page 102, line 8. _Wharry_. John Wharry, who became a Bencher in 1801,
died in 1812, and was buried in the Temple Church.
Page 102, line 22. _Jackson_. This was Richard Jackson, some time M.P.
for New Romney, to whom Johnson, Boswell tells us, refused the epithet
"Omniscient" as blasphemous, changing it to "all knowing." He was made
a Bencher in 1770 and died in 1787.
Page 102, foot. _Mingay_. James Mingay, who was made a Bencher in
1785, died in 1812. He was M.P. for Thetford and senior King's
Counsel. He was also Recorder of Aldborough, Crabbe's town. He lived
at 4 King's Bench Walk.
Page 103, line 1. _Baron Maseres_. This was Francis Maseres
(1731-1824), mathematician, reformer and Cursiter Baron of the
Exchequer. He lived at 5 King's Bench Walk, and at Reigate, and wore a
three-cornered hat and ruffles to the end. In April, 1801, Lamb wrote
to Manning:--"I live at No. 16 Mitre-court Buildings, a pistol-shot
off Baron Maseres'. You must introduce me to the Baron. I think we
should suit one another mainly. He Jives on the ground floor, for
convenience of the gout; I prefer the attic story, for the air. He
keeps three footmen and two maids; I have neither maid nor laundress,
not caring to be troubled with them! His forte, I understand, is the
higher mathematics; my turn, I confess, is more to poetry and the
belles lettres. The very antithesis of our characters would make up a
harmony. You must bring the Baron and me together."
Baron Maseres, who was made a Bencher in 1774, died in 1824.
Page 104, line 13. _Hookers and Seldens_. Richard Hooker (1554?-1600),
the "judicious," was Master of the Temple. John Selden (1584-1654),
the jurist, who lived in Paper Buildings and practised law in the
Temple, was buried in the Temple Church with much pomp.
* * * * *
Page 104. GRACE BEFORE MEAT.
_London Magazine_, November, 1821.
This was the essay, Lamb suggested, which Southey may have had in mind
when in an article in the _Quarterly Review_ he condemned _Elia_ as
wanting "a sounder religious feeling." In his "Letter to Southey"
(Vol. I.), which contained Lamb's protest against Southey's
strictures, he wrote:--"I am at a loss what particular essay you had
in view (if my poor ramblings amount to that appellation) when you
were in such a hurry to thrust in your objection, like bad news,
foremost.--Perhaps the Paper on 'Saying Graces' was the obnoxious
feature. I have endeavoured there to rescue a voluntary duty--good in
place, but never, as I remember, literally commanded--from the charge
of an undecent formality. Rightly taken, sir, that paper was not
against graces, but want of grace; not against the ceremony, but the
carelessness and slovenliness so often observed in the performance of
it."
Page 108, line 12 from foot. _C----_. Coleridge; but Lamb may really
have said it.
Page 108, foot. _The author of the Rambler_. Veal pie with prunes in
it was perhaps Dr. Johnson's favourite dish.
Page 109, line 10. _Dagon_. The fish god worshipped by the
Philistines. See Judges xvi. 23 and I Samuel v. for the full
significance of Lamb's reference.
Page 110, line 16. _C.V.L._ Charles Valentine le Grice. Later in life,
in 1798, Le Grice himself became a clergyman.
Page 110, line 19. _Our old form at school_. The Christ's Hospital
graces in Lamb's day were worded thus:--
GRACE BEFORE MEAT
Give us thankful hearts, O Lord God, for the Table which thou hast
spread for us. Bless thy good Creatures to our use, and us to thy
service, for Jesus Christ his sake. _Amen_.
GRACE AFTER MEAT
Blessed Lord, we yield thee hearty praise and thanksgiving for our
Founders and Benefactors, by whose Charitable Benevolence thou
hast refreshed our Bodies at this time. So season and refresh our
Souls with thy Heavenly Spirit, that we may live to thy Honour and
Glory. Protect thy Church, the King, and all the Royal Family. And
preserve us in peace and truth through Christ our Saviour. _Amen_.
* * * * *
Page 110. MY FIRST PLAY.
_London Magazine_, December, 1821.
Lamb had already sketched out this essay in the "Table Talk" in Leigh
Hunt's _Examiner_, December 9, 1813, under the title "Playhouse
Memoranda" (see Vol. I.). Leigh Hunt reprinted it in _The Indicator_,
December 13, 1820.
Page 111, line 1. _Garrick's Drury_. Garrick's Drury Lane was
condemned in 1791, and superseded in 1794 by the new theatre, the
burning of which in 1809 led to the _Rejected Addresses_. It has
recently come to light that Lamb was among the competitors who sent in
to the management the real addresses. The present Drury Lane Theatre
dates from 1812.
Page 111, line 11. _My godfather F._ Lamb's godfather was Francis
Fielde. _The British Directory_ for 1793 gives him as Francis
Field, oilman, 62 High Holborn. Whether or no he played the part in
Sheridan's matrimonial comedy that is attributed to him, I do not know
(Moore makes the friend a Mr. Ewart); but it does not sound like an
invented story. Richard Brinsley Sheridan carried Miss Linley, the
oratorio singer, from Bath and the persecutions of Major Mathews,
in March, 1772, and placed her in France. They were married near
Calais, and married again in England in April, 1773. Sheridan became
manager of Drury Lane, in succession to Garrick, in 1776, the first
performance under his control being on September 21. Lamb is supposed
to have had some personal acquaintance with Sheridan. Mary Lamb speaks
of him as helping the Sheridans, father and son, with a pantomime;
but of the work we know nothing definite. I do not consider the play
printed in part in the late Charles Kent's edition of Lamb, on the
authority of P.G. Patmore, either to be by Lamb or to correspond to
Mary Lamb's description.
Page 118, line 8. _His testamentary beneficence_. Lamb was not joking.
Writing to _The Athenaeum_, January 5, 1901, Mr. Thomas Greg says:--
Three-quarters of a century after it passed out of Lamb's
possession I am happy to tell the world--or that small portion of
it to whom any fact about his life is precious--exactly where and
what this landed property is. By indentures of lease and release
dated March 23 and 24, 1779, George Merchant and Thomas Wyman, two
yeomen of Braughing in the county of Hertford, conveyed to Francis
Fielde, of the parish of St. Andrew's, Holborn, in the county
of Middlesex, oilman, for the consideration of L20., all that
messuage or tenement, with the orchard, gardens, yards, barns,
edifices, and buildings, and all and singular the appurtenances
therewithal used or occupied, situate, lying, and being at West
Mill Green in the parish of Buntingford West Mill in the said
county of Hertford, etc. On March 5, 1804, Francis Fielde, of New
Cavendish Street, Esq., made his will, and, with the exception of
two, annuities to female relatives, left all his residuary estate,
real and personal, to his wife Sarah Fielde.
This will was proved on November 5, 1809. By indentures of lease
and release dated August 20 and 21, 1812, Sarah Fielde conveyed
the said property to Charles Lamb, of Inner Temple Lane,
gentleman. By an indenture of feoffment dated February 15, 1815,
made between the said Charles Lamb of the first part, the said
Sarah Fielde of the second part, and Thomas Greg the younger,
of Broad Street Buildings, London, Esq., the said property was
conveyed to the said Thomas Greg the younger for L50.
The said Thomas Greg the younger died in 1839, and left the said
property to his nephew, Robert Philips Greg, now of Coles Park, West
Mill, in the same county; and the said Robert Philips Greg in 1884
conveyed it to his nephew, Thomas Tylston Greg, of 15 Clifford's
Inn, London, in whose possession it now is in substantially the same
condition as it was in 1815.
The evidence that the Charles Lamb who conveyed the property in 1815
is Elia himself is overwhelming.
1. The essay itself gives the locality correctly: it is about two and
a half miles from Puckeridge.
2. The plot of land contains as near as possible three-quarters of an
acre, with an old thatched cottage and small barn standing upon it.
The barn, specially mentioned in all the deeds, is a most unusual
adjunct of so small a cottage. The property, the deeds of which go
back to 1708, appears to have been isolated and held by small men, and
consists of a long narrow tongue of land jutting into the property now
of the Savile family (Earls of Mexborough), but formerly of the Earls
of Hardwicke.
3. The witness to Charles Lamb's signature on the deed of 1815 is
William Hazlitt, of 19, York Street, Westminster.
4. Lamb was living in Inner Temple Lane in 1815, and did not leave the
Temple till 1817.
5. The essay was printed in the _London Magazine_ for December, 1821,
six years after "the estate has passed into more prudent hands."
6. And lastly, the following letter in Charles Lamb's own handwriting,
found with the deeds which are in my possession, clinches the
matter:--
"MR. SARGUS,--This is to give you notice that I have parted with
the Cottage to Mr. Grig Junr. to whom you will pay rent from
Michaelmas last. The rent that was due at Michaelmas I do not
wish you to pay me. I forgive it you as you may have been at some
expences in repairs.
"Yours
"CH. LAMB.
"Inner Temple Lane, London,
"_23 Feb., 1815._"
It is certainly not the fact that Lamb acquired the property, as he
states, by the will of his godfather, for it was conveyed to him
some three years after the latter's death by Mrs. Fielde. But strict
accuracy of fact in Lamb's '_Essays_' we neither look for nor desire.
In all probability Mrs. Fielde conveyed him the property in accordance
with an expressed wish of her husband in his lifetime. Reading also
between the lines of the essay, it is interesting to notice that
Francis Fielde, the Holborn oilman of 1779, in 1809 has become Francis
Fielde, Esq., of New Cavendish Street. In the letter quoted above
Lamb speaks of his purchaser as "Mr. Grig Junr.," more, I am inclined
to think, from his desire to have his little joke than from mere
inaccuracy, for he must have known the correct name of his purchaser.
But Mr. Greg, Jun., was only just twenty-one when he bought the
property, and the expression "as merry as a grig" running in Lamb's
mind might have proved irresistible to him. Lastly, the property is
now called, and has been so far back as I can trace, "Button Snap." No
such name is found in any of the title-deeds, and it was impossible
before to understand whence it arose. Now it is not: Lamb must have so
christened his little property in jest, and the name has stuck.
THOMAS GREG.
Page 113, line 1. _The maternal lap_. With the exception of a brief
mention on page 33--"the gentle posture of maternal tenderness"--this
is Lamb's only reference to his mother in all the essays--probably
from the wish not to wound his sister, who would naturally read all he
wrote; although we are told by Talfourd that she spoke of her mother
with composure. But it is possible to be more sensitive for others
than they are for themselves.
Page 113, line 3. _The play was Artaxerxes_. The opera, by Thomas
Augustine Arne (1710-1778), produced in 1762, founded on Metastasio's
"Artaserse." The date of the performance was in all probability
December 1, 1780, although Lamb suggests that it was later; for that
was the only occasion in 1780-81-82 on which "Artaxerxes" was followed
by "Harlequin's Invasion," a pantomime dating from 1759, the work of
Garrick. It shows Harlequin invading the territory of Shakespeare;
Harlequin is defeated and Shakespeare restored.
Page 113, line 20. _The Lady of the Manor_. Here Lamb's memory, I
fancy, betrayed him. This play (a comic opera by William Kenrick) was
not performed at Drury Lane or Covent Garden in the period mentioned.
Lamb's pen probably meant to write "The Lord of the Manor," General
Burgoyne's opera, with music by William Jackson, of Exeter, which was
produced in 1780. It was frequently followed in the bill by "Robinson
Crusoe," but never by "Lun's Ghost," whereas Wycherley's "Way of the
World" was followed by "Lun's Ghost" at Drury Lane on January 9, 1782.
We may therefore assume that Lamb's second visit to the theatre was to
see "The Lord of the Manor," followed by "Robinson Crusoe," some time
in 1781, and his third to see "The Way of the World," followed by
"Lun's Ghost" on January 9, 1782. "Lun's Ghost" was produced on
January 3, 1782. Lun was the name under which John Rich (1682?-1761),
the pantomimist and theatrical manager, had played in pantomime.
Page 113, last line. _Round Church ... of the Templars_. This allusion
to the Temple Church and its Gothic heads was used before by Lamb in
his story "First Going to Church" in _Mrs. Leicester's School_ (see
Vol. III.). In that volume Mary Lamb had told the story of what we
may take to be her first play (see "Visit to the Cousins"), the piece
being Congreve's "Mourning Bride."
Page 114, line 1. _The season 1781-2_. Lamb was six on February 10,
1781. He says, in his "Play-house Memoranda," of the same occasion,
"Oh when shall I forget first seeing a play, at the age of five or
six?"
Page 114, line 3. _At school_. Lamb was at Christ's Hospital from 1782
to 1789.
Page 114, end. _Mrs. Siddons in "Isabella."_ Mrs. Siddons first played
this part at Drury Lane on October 10, 1782. The play was "Isabella,"
a version by Garrick of Southerne's "Fatal Marriage." Mrs. Siddons
also appeared frequently as Isabella in "Measure for Measure;" but
Lamb clearly says "in" Isabella, meaning the play. Lamb's sonnet,
in which he collaborated with Coleridge, on Mrs. Siddons, which was
printed in the _Morning Chronicle_ in December, 1794 (see Vol. IV.),
was written when he was nineteen. It runs (text of 1797):--
As when a child on some long winter's night
Affrighted clinging to its Grandam's knees
With eager wond'ring and perturb'd delight
Listens strange tales of fearful dark decrees
Mutter'd to wretch by necromantic spell;
Or of those hags, who at the witching time
Of murky midnight ride the air sublime,
And mingle foul embrace with fiends of Hell:
Cold Horror drinks its blood! Anon the tear
More gentle starts, to hear the Beldame tell
Of pretty babes, that lov'd each other dear,
Murder'd by cruel Uncle's mandate fell:
Ev'n such the shiv'ring joys thy tones impart,
Ev'n so thou, SIDDONS! meltest my sad heart!
* * * * *
Page 115. DREAM-CHILDREN.
_London Magazine_, January, 1822.
John Lamb died on October 26, 1821, leaving all his property to his
brother. Charles was greatly upset by his loss. Writing to Wordsworth
in March, 1822, he said: "We are pretty well save colds and
rheumatics, and a certain deadness to every thing, which I think I may
date from poor John's Loss.... Deaths over-set one, and put one out
long after the recent grief." (His friend Captain Burney died in the
same month.) Lamb probably began "Dream-Children,"--in some ways,
I think, his most perfect prose work--almost immediately upon his
brother's death. The essay "My Relations" may be taken in connection
with this as completing the picture of John Lamb. His lameness was
caused by the fall of a stone in 1796, but I doubt if the leg were
really amputated.
The description in this essay of Blakesware, the seat of the Plumers,
is supplemented by the essay entitled "Blakesmoor in H----shire."
Except that Lamb substitutes Norfolk for the nearer county, the
description is accurate; it is even true that there is a legend in the
Plumer family concerning the mysterious death of two children and the
loss of the baronetcy thereby--Sir Walter Plumer, who died in the
seventeenth century, being the last to hold the title. In his poem
"The Grandame" (see Vol. IV.), Lamb refers to Mrs. Field's garrulous
tongue and her joy in recounting the oft-told tale; and it may be to
his early associations with the old story that his great affection
for Morton's play, "The Children in the Wood," which he so often
commended--particularly with Miss Kelly in the caste--was due. The
actual legend of the children in the wood belongs, however, to
Norfolk.
William Plumer's newer and more fashionable mansion was at Gilston,
which is not in the adjoining county, but also in Hertfordshire, near
Harlow, only a few miles distant from Blakesware. Mrs. Field died
of cancer in the breast in August, 1792, and was buried in Widford
churchyard, hard by Blakesware.
According to Lamb's Key the name Alice W----n was "feigned." If by
Alice W----n Lamb, as has been suggested, means Ann Simmons, of
Blenheims, near Blakesware, he was romancing when he said that he had
courted her for seven long years, although the same statement is made
in the essay on "New Year's Eve." We know that in 1796 he abandoned
all ideas of marriage. Writing to Coleridge in November of that year,
in reference to his love sonnets, he says: "It is a passion of which I
retain nothing.... Thank God, the folly has left me for ever. Not even
a review of my love verses renews one wayward wish in me." This was
1796. Therefore, as he was born in 1775, he must have begun the wooing
of Alice W----n when he was fourteen in order to complete the seven
long years of courtship. My own feeling, as I have stated in the notes
to the love sonnets in Vol. IV., is that Lamb was never a very serious
wooer, and that Alice W----n was more an abstraction around which now
and then to group tender imaginings of what might have been than any
tangible figure.
A proof that Ann Simmons and Alice W----n are one has been found
in the circumstance that Miss Simmons did marry a Mr. Bartrum, or
Bartram, mentioned by Lamb in this essay as being the father of
Alice's real children. Bartrum was a pawnbroker in Princes Street,
Coventry Street. Mr. W.C. Hazlitt says that Hazlitt had seen Lamb
wandering up and down before the shop trying to get a glimpse of his
old friend.
* * * * *
Page 118. DISTANT CORRESPONDENTS.
_London Magazine_, March, 1822.
The germ of this essay will be found in a letter to Barron Field, to
whom the essay is addressed, of August 31, 1817. Barron Field was a
son of Henry Field, apothecary to Christ's Hospital. His brother,
Francis John Field, through whom Lamb probably came to know Barron,
was a clerk in the India House.
Barron Field was associated with Lamb on Leigh Hunt's _Reflector_ in
1810-1812. He also was dramatic critic for _The Times_ for a while. In
1816 he was appointed judge of the Supreme Court of New South Wales,
where he remained until 1824. For other information see the note, in
Vol. I., to his _First-Fruits of Australian Poetry_, reviewed by Lamb.
In the same number of the _London Magazine_ which included the present
essay was Field's account of his outward voyage to New South Wales.
Page 119, line 24. _Our mutual friend P._ Not identifiable: probably
no one in particular. The Bench would be the King's Bench Prison. A
little later one of Lamb's friends, William Hone, was confined there
for three years.
Page 121, line 8. _The late Lord C._ This was Thomas Pitt, second
Baron Camelford (1775-1804), who after a quarrelsome life, first in
the navy and afterwards as a man about town, was killed in a duel at
Kensington, just where Melbury Road now is. The spot chosen by him
for his grave was on the borders of the Lake of Lampierre, near three
trees; but there is a doubt if his body ever rested there, for it lay
for years in the crypt of St. Anne's, Soho. Its ultimate fate was the
subject of a story by Charles Reade.
Page 123, line 11. _Bleach_. Illegitimacy, according to some old
authors, wears out in the third generation, enabling a natural son's
descendant to resume the ancient coat-of-arms. Lamb refers to this
sanction.
Page 123, line 20. _Hare-court_. The Lambs lived at 4 Inner Temple
Lane (now rebuilt as Johnson's Buildings) from 1809 to 1817. Writing
to Coleridge in June, 1809, Lamb says:--"The rooms are delicious, and
the best look backwards into Hare Court, where there is a pump always
going. Hare Court trees come in at the window, so that it's like
living in a garden."
Barron Field was entered on the books of the Inner Temple in 1809 and
was called to the Bar in 1814.
Page 123, last paragraph. _Sally W----r_. Lamb's Key gives "Sally
Winter;" but as to who she was we have no knowledge.
Page 123, end. _J.W._ James White. See next essay.
* * * * *
Page 124. THE PRAISE OF CHIMNEY-SWEEPERS.
_London Magazine_, May, 1822, where it has a sub-title, "A May-Day
Effusion."
This was not Lamb's only literary association with chimney-sweepers.
In Vol. I. of this edition will be found the description of a sweep
in the country which there is good reason to believe is Lamb's work.
Again, in 1824, James Montgomery, the poet, edited a book--_The
Chimney-Sweepers' Friend and Climbing Boys' Album_--with the
benevolent purpose of interesting people in the hardships of the
climbing boys' life and producing legislation to alleviate it. The
first half of the book is practical: reports of committees, and so
forth; the second is sentimental; verses by Bernard Barton, William
Lisle Bowles, and many others; short stories of kidnapped children
forced to the horrid business; and kindred themes. Among the
"favourite poets of the day" to whom Montgomery applied were Scott,
Wordsworth, Rogers, Moore, Joanna Baillie and Lamb. Lamb replied
by copying out (with the alteration of Toddy for Dacre) "The
Chimney-Sweeper" from Blake's _Songs of Innocence_, described by
Montgomery as "a very rare and curious little work." In that poem it
will be remembered the little sweep cries "weep, weep, weep." Lamb
compares the cry more prettily to the "peep, peep" of the sparrow.
Page 125, line 6. _Shop ..._ Mr. Thomas Read's Saloop Coffee House was
at No. 102 Fleet Street. The following lines were painted on a board
in Read's establishment:--
Come, all degrees now passing by,
My charming liquor taste and try;
To Lockyer come, and drink your fill;
Mount Pleasant has no kind of ill.
The fumes of wine, punch, drams and beer,
It will expell; your spirits cheer;
From drowsiness your spirits free.
Sweet as a rose your breath will be,
Come taste and try, and speak your mind;
Such rare ingredients here are joined,
Mount Pleasant pleases all mankind.
Page 127, line 12 from foot. _The young Montagu_. Edward Wortley
Montagu (1713-1776), the traveller, ran away from Westminster School
more than once, becoming, among other things, a chimney-sweeper.
Page 127, line 9 from foot. _Arundel Castle_. The Sussex seat of the
Dukes of Norfolk. The "late duke" was Charles Howard, eleventh duke,
who died in 1815, and who spent enormous sums of money on curiosities.
I can find no record of the story of the sweep. Perhaps Lamb invented
it, or applied it to Arundel.
Page 128, line 14 from foot. _Jem White_. James White (1775-1820),
who was at Christ's Hospital with Lamb, and who wrote _Falstaff's
Letters_, 1796, in his company (see Vol. I.). "There never was his
like," Lamb told another old schoolfellow, Valentine Le Grice, in
1833; "we shall never see such days as those in which he flourished."
See the essay "On Some of the Old Actors," for an anecdote of White.
Page 128, line 8 from foot. _The fair of St. Bartholomew_. Held
on September 3 at Smithfield, until 1855. George Daniel, in his
recollections of Lamb, records a visit they paid together to the Fair.
Lamb took Wordsworth through its noisy mazes in 1802.
Page 129, line 14. _Bigod_. John Fenwick (see note to "The Two Races
of Men").
Leigh Hunt, in _The Examiner_ for May 5, 1822, quoted some of the best
sentences of this essay. On May 12 a correspondent (L.E.) wrote a very
agreeable letter supporting Lamb's plea for generosity to sweeps and
remarking thus upon Lamb himself:--
I read the modicum on "Chimney-Sweepers," which your last paper
contained, with pleasure. It appears to be the production of that
sort of mind which you justly denominate "gifted;" but which is
greatly undervalued by the majority of men, because they have no
sympathies in common with it. Many who might partially appreciate
such a spirit, do nevertheless object to it, from the snap-dragon
nature of its coruscations, which shine themselves, but shew every
thing around them to disadvantage. Your deep philosophers also,
and all the laborious professors of the art of sinking, may
elevate their nasal projections, and demand "cui bono"? For my
part I prefer a little enjoyment to a great deal of philosophy. It
is these gifted minds that enliven our habitations, and contribute
so largely to those _every-day_ delights, which constitute, after
all, the chief part of mortal happiness. Such minds are ever
active--their light, like the vestal lamp, is ever burning--and in
my opinion the man who refines the common intercourse of life, and
wreaths the altars of our household gods with flowers, is more
deserving of respect and gratitude than all the sages who waste
their lives in elaborate speculations, which tend to nothing, and
which _we_ cannot comprehend--nor they neither.
On June 2, however, "J.C.H." intervened to correct what he considered
the "dangerous spirit" of Lamb's essay, which said so little of the
hardships of the sweeps, but rather suggested that they were a happy
class. J.C.H. then put the case of the unhappy sweep with some
eloquence, urging upon all householders the claims of the mechanical
sweeping machine.
* * * * *
Page 130. A COMPLAINT OF THE DECAY OF BEGGARS IN THE METROPOLIS.
_London Magazine_, June, 1822.
The origin of this essay was the activity at that time of the Society
for the Suppression of Mendicity, founded in 1818, of which a Mr. W.H.
Bodkin was the Hon. Secretary. The Society's motto was "Benefacta male
collocata, malefacta existima;" and it attempted much the same work
now performed by the Charity Organisation Society. Perhaps the delight
expressed in its annual reports in the exposure of impostors was a
shade too hearty--at any rate one can see therein cause sufficient for
Lamb's counter-blast. Lamb was not the only critic of Mr. Bodkin's
zeal. Hood, in the _Odes and Addresses_, published in 1825, included a
remonstrance to Mr. Bodkin.
The Society's activity led to a special commission of the House
of Commons in 1821 to inquire into the laws relating to vagrants,
concerning which Lamb speaks, the clergyman alluded to being Dr.
Henry Butts Owen, of Highgate. The result of the commission was an
additional stringency, brought about by Mr. George Chetwynd's bill.
It was this essay, says Hood, which led to his acquaintance with
Charles Lamb. After its appearance in the _London Magazine_, of which
Hood was then sub-editor, he wrote Lamb a letter on coarse paper
purporting to come from a grateful beggar; Lamb did not admit the
discovery of the perpetrator of the joke, but soon afterwards Lamb
called on Hood when he was ill, and a friendship followed to which we
owe Hood's charming recollections of Lamb--among the best that were
written of him by any one.
Page 131, line 14. _The Blind Beggar_. The reference is to the ballad
of "The Beggar's Daughter of Bednall Green." The version in the _Percy
Reliques_ relates the adventures of Henry, Earl of Leicester, the son
of Simon de Montfort, who was blinded at the battle of Evesham and
left for dead, and thereafter begged his way with his pretty Bessee.
In the _London Magazine_ Lamb had written "Earl of Flanders," which
he altered to "Earl of Cornwall" in _Elia_. The ballad says Earl of
Leicester.
Page 131, line 28. _Dear Margaret Newcastle_. One of Lamb's recurring
themes of praise (see "The Two Races of Men," "Mackery End in
Hertfordshire," and "Detached Thoughts on Books and Reading").
"Romancical," according to the _New English Dictionary_, is Lamb's own
word. This is the only reference given for it.
Page 133, line 7. _Spital sermons_. On Monday of Easter week it was
the custom for the Christ's Hospital boys to walk in procession to the
Royal Exchange, and on Tuesday to the Mansion House; on each occasion
returning with the Lord Mayor to hear a special sermon--a spital
sermon, as it was called--and an anthem. The sermon is now preached
only on Easter Tuesday.
Page 133, line 24. _Overseers of St. L----_. Lamb's Key states that
both the overseers and the mild rector were inventions. In the _London
Magazine_ the rector's parish is "P----."
Page 133, line 27. _Vincent Bourne_. See Lamb's essay on Vincent
Bourne, Vol. I. This poem was translated by Lamb himself, and was
first published in _The Indicator_ for May 3, 1820. See Vol. IV. for
Lamb's other translations from Bourne.
Page 135, line 2. _A well-known figure_. This beggar I take to be
Samuel Horsey. He is stated to have been known as the King of the
Beggars, and a very prominent figure in London. His mutilation is
ascribed to the falling of a piece of timber in Bow Lane, Cheapside,
some nineteen years before; but it may have been, as Lamb says, in the
Gordon Riots of 1780.
There is the figure of Horsey on his little carriage, with several
other of the more notable beggars of the day plying their calling,
in an etching of old houses at the corner of Chancery Lane and Fleet
Street, made by J.T. Smith in 1789 for his _Ancient Topography of
London_, 1815. I give it in my large edition.
Page 137, end of essay. _Feigned or not._ In the _London Magazine_ the
essay did not end here. It continued thus:--
"'Pray God your honour relieve me,' said a poor beadswoman to my
friend L---- one day; 'I have seen better days.' 'So have I, my
good woman,' retorted he, looking up at the welkin which was just
then threatening a storm--and the jest (he will have it) was as
good to the beggar as a tester.
"It was at all events kinder than consigning her to the stocks, or
the parish beadle--
"But L. has a way of viewing things in rather a paradoxical light
on some occasions.
"ELIA.
"P.S.--My friend Hume (not MP.) has a curious manuscript in his
possession, the original draught of the celebrated 'Beggar's
Petition' (who cannot say by heart the 'Beggar's Petition?') as it
was written by some school usher (as I remember) with corrections
interlined from the pen of Oliver Goldsmith. As a specimen of the
doctor's improvement, I recollect one most judicious alteration--
"_A pamper'd menial drove me from the door._
"It stood originally--
"_A livery servant drove me, &c._
"Here is an instance of poetical or artificial language properly
substituted for the phrase of common conversation; against
Wordsworth.
"I think I must get H. to send it to the LONDON, as a corollary to
the foregoing."
The foregoing passage needs some commentary. Lamb's friend L---- was
Lamb himself. He tells the story to Manning in the letter of January
2,1810.--Lamb's friend Hume was Joseph Hume of the victualling office,
Somerset House, to whom letters from Lamb will be found in Mr. W.C.
Hazlitt's _Lamb and Hazlitt_, 1900. Hume translated _The Inferno_ of
Dante into blank verse, 1812.--The "Beggar's Petition," a stock piece
for infant recitation a hundred years ago, was a poem beginning
thus:--
Pity the sorrows of a poor old man
Whose trembling limbs have borne him to your door,
Whose days are dwindled to the shortest span;
Oh give relief, and Heaven will bless your store.
In the reference to Wordsworth Lamb pokes fun at the statement, in his
friend's preface to the second edition of _Lyrical Ballads_, that
the purpose of that book was to relate or describe incidents and
situations from common life as far as possible in a selection of
language really used by men.
Lamb's _P.S._ concerning the "Beggar's Petition" was followed in the
_London Magazine_ by this _N.B._:--
"N.B. I am glad to see JANUS veering about to the old quarter. I
feared he had been rust-bound.
"C. being asked why he did not like Gold's 'London' as well as
ours--it was in poor S.'s time--replied--
"_--Because there is no WEATHERCOCK
And that's the reason why._"
The explanation of this note is that "Janus Weathercock"--one of the
pseudonyms of Thomas Griffiths Wainewright--after a long absence from
its pages, had sent to the previous month's _London Magazine_, May,
1822, an amusing letter of criticism of that periodical, commenting on
some of its regular contributors. Therein he said: "Clap Elia on the
back for such a series of good behaviour."--Who C. is cannot be said;
possibly Lamb, as a joke, intends Coleridge to be indicated; but poor
S. would be John Scott, the first editor of the _London Magazine_,
who was killed in a duel. C.'s reply consisted of the last lines
of Wordsworth's "Anecdote for Fathers; or, Falsehood Corrected."
Accurately they run:--
At Kelve there was no weather-cock
And that's the reason why.
The hero of this poem was a son of Lamb's friend Basil Montagu.
Gold's _London Magazine_ was a contemporary of the better known London
magazine of the same name. In Vol. III. appeared an article entitled
"The Literary Ovation," describing an imaginary dinner-party given by
Messrs. Baldwin, Cradock & Joy in February, 1821, at which Lamb was
supposed to be present and to sing a song by Webster, one of his old
dramatists. Mr. Bertram Dobell conjectures that Wainewright may have
written this squib.
* * * * *
Page 137. A DISSERTATION UPON ROAST PIG.
_London Magazine_, September, 1822.
There has been some discussion as to the origin of the central idea of
this essay. A resemblance is found in a passage in _The Turkish Spy_,
where, after describing the annual burnt-offering of a bull by the
Athenians, _The Spy_ continues:--
In process of time a certain priest, in the midst of his bloody
sacrifice, taking up a piece of the broiled flesh which had fallen
from the altar on the ground, and burning his fingers therewith,
suddenly clapt them to his mouth to mitigate the pain. But, when
he had once tasted the sweetness of the fat, not only longed for
more of it, but gave a piece to his assistant; and he to others;
who, all pleased with the new-found dainties, fell to eating of
flesh greedily. And hence this species of gluttony was taught to
other mortals.
"Este," a contributor to _Notes and Queries_, June 21, 1884, wrote:--
A quarto volume of forty-six pages, once in "Charles Lamb's
library" (according to a pencilled note in the volume) is before
me, entitled: _Gli Elogi del Porco, Capitoli Berneschi di Tigrinto
Bistonio P.A., E. Accademico Ducale de' Dissonanti di Modena.
In Modena per gli Eredi di Bartolmeo Soliani Stampatori Ducali
MDCCLXI. Con Licenza de' Superiori_, [wherein] some former owner
of the volume has copied out Lamb's prose with many exact verbal
resemblances from the poem.
It has also been suggested that Porphyry's tract on _Abstinence from
Animal Food_, translated by William Taylor, bears a likeness to the
passage. Taylor's translation, however, was not published till 1823,
some time after Lamb's essay.
These parallels merely go to show that the idea was a commonplace; at
the same time it is not Lamb, but Manning, who told him the story,
that must declare its origin. Not only in the essay, but in a letter
to Barton in March, 1823, does Lamb express his indebtedness to his
traveller friend. Allsop, indeed, in his _Letters of Coleridge_,
claims to give the Chinese story which Manning lent to Lamb and which
produced the "Dissertation." It runs thus:--
A child, in the early ages, was left alone by its mother in a
house in which was a pig. A fire took place; the child escaped,
the pig was burned. The child scratched and pottered among the
ashes for its pig, which at last it found. All the provisions
being burnt, the child was very hungry, and not yet having any
artificial aids, such as golden ewers and damask napkins, began to
lick or suck its fingers to free them from the ashes. A piece of
fat adhered to one of his thumbs, which, being very savoury alike
in taste and odour, he rightly judged to belong to the pig. Liking
it much, he took it to his mother, just then appearing, who also
tasted it, and both agreed that it was better than fruit or
vegetables.
They rebuilt the house, and the woman, after the fashion of good
wives, who, says the chronicle, are now very scarce, put a pig
into it, and was about to set it on fire, when an old man, one
whom observation and reflection had made a philosopher, suggested
that a pile of wood would do as well. (This must have been the
father of economists.) The next pig was killed before it was
roasted, and thus
"From low beginnings,
We date our winnings."
Manning, by the way, contributed articles on Chinese jests to the _New
Monthly Magazine_ in 1826.
A preliminary sketch of the second portion of this essay will be found
in the letter to Coleridge dated March 9, 1822. See also the letters
to Mr. and Mrs. Bruton, January 6, 1823, to Mrs. Collier, November 2,
1824, and to H. Dodwell, October 7, 1827, all in acknowledgment of
pigs sent to Lamb probably from an impulse found in this essay.
Later, Lamb abandoned the extreme position here taken. In the little
essay entitled "Thoughts on Presents of Game," 1833 (see Vol. I.), he
says: "Time was, when Elia ... preferred to all a roasted pig. But he
disclaims all such green-sickness appetites in future."
Page 141, verse. "Ere sin could blight ..." From Coleridge's "Epitaph
on an Infant."
Page 142, line 7 from foot. _My good old aunt_. Probably Aunt Hetty.
See the essay on "Christ's Hospital," for another story of her. The
phrase, "Over London Bridge," unless an invention, suggests that
before this aunt went to live with the Lambs--probably not until they
left the Temple in 1792--she was living on the Surrey side. But it was
possibly an Elian mystification. Lamb had another aunt, but of her we
know nothing.
Page 143, line 11 from foot. _St. Omer's_. The French Jesuit College.
Lamb, it is unnecessary to say, was never there.
* * * * *
Page 144. A BACHELOR'S COMPLAINT OF THE BEHAVIOUR OF MARRIED PEOPLE.
This is, by many years, the earliest of these essays. It was printed
first in _The Reflector_, No. IV., in 1811 or 1812. When Lamb brought
his _Works_ together, in 1818, he omitted it. In September, 1822, it
appeared in the _London Magazine_ as one of the reprints of Lamb's
earlier writings, of which the "Confessions of a Drunkard" (see Vol.
I.)was the first. In that number also appeared the "Dissertation upon
Roast Pig," thereby offering the reader an opportunity of comparing
Lamb's style in 1811 with his riper and richer style of 1822. The
germ of the essay must have been long in Lamb's mind, for we find him
writing to Hazlitt in 1805 concerning Mrs. Rickman: "A good-natured
woman though, which is as much as you can expect from a friend's wife,
whom you got acquainted with as a bachelor."
Page 147, line 6. "_Love me, love my dog_." See "Popular Fallacies,"
page 302, for an expansion of this paragraph.
* * * * *
Page 150. ON SOME OF THE OLD ACTORS.
In February, 1822, Lamb began a series of three articles in the
_London Magazine_ on "The Old Actors." The second was printed in April
and the third in October of the same year. Afterwards, in reprinting
them in _Elia_, he rearranged them into the essays, "On Some of the
Old Actors," "On the Artificial Comedy of the Last Century," and "On
the Acting of Munden," omitting a considerable portion altogether. The
essay in its original tripart form will be found in the Appendix to
this volume.
In one of his theatrical notices in _The Examiner_ (see Vol. I.) Lamb
remarks, "Defunct merit comes out upon us strangely," and certain
critics believe that he praised some of the old actors beyond their
deserts. But no one can regret any such excesses.
Page 150, beginning. _Twelfth Night_. When recalling early playgoing
days in "Old China," Lamb refers again to this play--Viola in Illyria.
Page 150, foot. _Whitfield, Packer, Benson, Burton, Phillimore_ and
_Barrymore_. Whitfield, who made his London debut as Trueman in
"George Barnwell" about 1776, was a useful man at Covent Garden and
Drury Lane.--John Hayman Packer (1730-1806), known in Lamb's time for
his old men. He acted at Drury Lane until 1805.--Benson, who married a
sister of Mrs. Stephen Kemble, wrote one or two plays, and was a good
substitute in emergencies. He committed suicide during brain fever
in 1796.--Burton was a creditable utility actor at Covent Garden and
Drury Lane.--Phillimore filled small parts at Drury Lane.--Barrymore
was of higher quality, a favourite character actor both at Drury Lane
and the Haymarket.
Page 151, line 6. _Mrs. Jordan_. Mrs. Jordan, born in 1762, ceased to
act in England in 1814 and died in 1816. Nell was her famous part, in
Coffey's "The Devil to Pay." Miss Hoyden is in Vanbrugh's "Relapse."
Lamb is referring to Viola in Act I., Scene 5, and Act II., Scene 4,
of "Twelfth Night."
Page 151, line 8 from foot. _Mrs. Powel_. Mrs. Powel, previously known
as Mrs. Farmer, and afterwards Mrs. Renaud, was at Drury Lane from
1788 to 1811. She ended her London career in 1816 and died in 1829.
Page 152, line 8. _Of all the actors_. The _London Magazine_ article
began at this point. Robert Bensley (1738?-1817?) was at Drury
Lane from 1775 to 1796, when he retired (alternating it with the
Haymarket). G.H. Boaden and George Colman both bear out Lamb's eulogy
of Bensley as Malvolio; but otherwise he is not the subject of much
praise.
Page 152, line 15. _Venetian incendiary_. Pierre in Otway's "Venice
Preserved." Lamb appended the passage in a footnote in the _London
Magazine_.
Page 153, line 12. _Baddeley ... Parsons ... John Kemble_. Robert
Baddeley (1733-1794), the husband of Mrs. Baddeley, and the original
Moses in the "School for Scandal." William Parsons (1736-1795), the
original Crabtree in the "School for Scandal," and a favourite actor
of Lamb's. John Philip Kemble (1757-1823), who managed Drury Lane from
1788 to 1801.
Page 153, line 11 from foot. _Of birth and feeling_. In the _London
Magazine_ a footnote came here (see page 316).
Page 153, line 6 from foot. _Length of service_. In the _London
Magazine_ a footnote came here (see page 316).
Page 154, line 24. _House of misrule_. A long passage came here in the
_London Magazine_ (see page 317).
Page 154, line 8 from foot. _Hero of La Mancha_. Compare a similar
analysis of Don Quixote's character on page 264.
Page 155, line 23. _Dodd_. James William Dodd (1740?-1796).
Page 155, line 24. _Lovegrove_. William Lovegrove (1778-1816), famous
in old comedy parts and as Peter Fidget in "The Boarding House."
Page 155, foot. _The gardens of Gray's Inn._ These gardens are said to
have been laid out under the supervision of Bacon, who retained his
chambers in the Inn until his death. As Dodd died in 1796 and Lamb
wrote in 1822, it would be fully twenty-six years and perhaps more
since Lamb met him.
Page 156, lines 26-29. _Foppington, etc._ Foppington in Vanbrugh's
"Relapse," Tattle in Congreve's "Love for Love," Backbite in
Sheridan's "School for Scandal," Acres in "The Rivals" by the same
author, and Fribble in Garrick's "Miss in her Teens."
Page 157, line 13. _If few can remember._ The praise of Suett that
follows is interpolated here from the third part of Lamb's original
essay (see page 332). Richard Suett, who had been a Westminster
chorister (not St. Paul's), left the stage in June, 1805, and died in
July.
Page 157, footnote, _Jem White_. See note above.
Page 158, line 22. _His friend Mathews._ Charles Mathews (1776-1835),
whom Lamb knew.
Page 159, line 1. _Jack Bannister._ John Bannister retired from the
stage in 1815. He died in 1836.
Page 159, line 7. _Children in the Wood._ Morton's play, of which Lamb
was so fond. It is mentioned again in "Barbara S----" and "Old China."
Page 159, line 19. _The elder Palmer._ The first part of the essay is
here resumed again. The elder Palmer was John Palmer, who died on the
stage, in 1798, when playing in "The Stranger." Lamb's remarks tend
to confuse him with Gentleman Palmer, who died before Lamb was born.
Robert Palmer, John's brother, died about 1805.
Page 159, line 22. _Moody_. John Moody (1727?-1812), famous as Teague
in "The Committee."
Page 159, lines 31 to 36. _The Duke's Servant, etc._ The Duke's
servant in Garrick's "High Life below Stairs," Captain Absolute in
Sheridan's "Rivals," Dick Amlet in Vanbrugh's "Confederacy."
Page 160, line 1. _Young Wilding ... Joseph Surface._ In Foote's
"Liar" and Sheridan's "School for Scandal."
* * * * *
Page 161. ON THE ARTIFICIAL COMEDY OF THE LAST CENTURY.
See note to the essay "On Some of the Old Actors."
See also "A Vision of Horns" (Vol. I.) for, as it seems to me, a
whimsical extension to the point of absurdity of the theory expressed
in this essay--a theory which Lord Macaulay, in his review of Leigh
Hunt's edition of the Dramatic Works of Wycherley, Congreve, etc., in
1840, opposed with characteristic vigour.
Hartley Coleridge, in a letter to Edward Moxon concerning Leigh Hunt's
edition of Wycherley and Congreve, happily remarked: "Nothing more or
better can be said in defence of these writers than what Lamb has said
in his delightful essay ... which is, after all, rather an apology for
the audiences who applauded and himself who delighted in their plays,
than for the plays themselves.... But Lamb always took things by the
better handle."
Page 163, line 16. _The Fainalls, etc_. Fainall in Congreve's "Way
of the World," Mirabel in Farquhar's "Inconstant," Dorimant in
Etheredge's "Man of Mode," and Lady Touchstone in Congreve's "Double
Dealer."
Page 163, line 12 from foot. _Angelica_. In "Love for Love."
Page 164, line 26, etc. _Sir Simon, etc_. All these characters are in
Wycherley's "Love in a Wood."
Page 166, line 21. _King_. Thomas King (1730-1805), at one time
manager of Drury Lane, the original Sir Peter Teazle, on May 8, 1777,
the first night of the "School for Scandal," and the most famous actor
in the part until he retired in 1802.
Page 167, line 14. _Miss Pope_. Jane Pope (1742-1818), the original
Mrs. Candour, left the stage in 1808.
Page 167, line 15 from foot. _Manager's comedy_. Sheridan was manager
of Drury Lane when the "School for Scandal" was produced.
Page 167, same line. _Miss Farren ... Mrs. Abingdon_. Elizabeth
Farren, afterwards Countess of Derby, played Lady Teazle for the last
time in 1797. Mrs. Abingdon had retired from Drury Lane in 1782.
Page 167, line 10 from foot. _Smith_. "Gentleman" Smith took his
farewell of the stage, as Charles Surface, in 1788.
Page 168, end of essay. _Fashionable tragedy_. See page 328, line 21,
for the continuation of this essay in the _London Magazine_.
* * * * *
Page 168. ON THE ACTING OF MUNDEN.
See note to the essay "On Some of the Old Actors" above. Lamb lifted
this essay into the _London Magazine_ from _The Examiner_, where it
had appeared on November 7 and 8, 1819, with slight changes.
Page 168, title. _Munden_. Joseph Shepherd Munden (1758-1832) acted at
Covent Garden practically continuously from 1790 to 1811. He moved
to Drury Lane in 1813, and remained there till the end. His farewell
performance was on May 31, 1824. We know Lamb to have met Munden from
Raymond's _Memoirs of Elliston_.
Page 168, line 2 of essay. _Cockletop_. In O'Keeffe's farce "Modern
Antiques." This farce is no longer played, although a skilful hand
might, I think, make it attractive to our audiences. Barry Cornwall in
his memoir of Lamb has a passage concerning Munden as Cockletop, which
helps to support Lamb's praise. Support is not necessary, but useful;
it is one of the misfortunes of the actor's calling that he can live
only in the praise of his critics.
In the Drama of "Modern Antiques," especially, space was allowed
him for his movements. The words were nothing. The prosperity of
the piece depended exclusively on the genius of the actor.
Munden enacted the part of an old man credulous beyond ordinary
credulity; and when he came upon the stage there was in him an
almost sublime look of wonder, passing over the scene and people
around him, and settling apparently somewhere beyond the moon.
What he believed in, improbable as it was to mere terrestrial
visions, you at once conceived to be quite possible,--to be true.
The sceptical idiots of the play pretend to give him a phial
nearly full of water. He is assured that this contains Cleopatra's
tear. Well; who can disprove it? Munden evidently recognised it.
"What a large tear!" he exclaimed. Then they place in his hands
a druidical harp, which to vulgar eyes might resemble a modern
gridiron. He touches the chords gently: "pipes to the spirit
ditties of no tone;" and you imagine AEolian strains. At last,
William Tell's cap is produced. The people who affect to cheat
him, apparently cut the rim from a modern hat, and place the
scull-cap in his hands; and then begins the almost finest piece of
acting that I ever witnessed. Munden accepts the accredited cap
of Tell, with confusion and reverence. He places it slowly and
solemnly on his head, growing taller in the act of crowning
himself. Soon he swells into the heroic size; a great archer; and
enters upon his dreadful task. He weighs the arrow carefully; he
tries the tension of the bow, the elasticity of the string; and
finally, after a most deliberate aim, he permits the arrow to fly,
and looks forward at the same time with intense anxiety. You hear
the twang, you see the hero's knitted forehead, his eagerness; you
tremble;--at last you mark his calmer brow, his relaxing smile,
and are satisfied that the son is saved!--It is difficult to paint
in words this extraordinary performance, which I have several
times seen; but you feel that it is transcendent. You think of
Sagittarius, in the broad circle of the Zodiac; you recollect that
archery is as old as Genesis; you are reminded that Ishmael, the
son of Hagar, wandered about the Judaean deserts and became an
archer.
Page 169, line 16. _Edwin_. This would probably be John Edwin the
Elder (1749-1790). But John Edwin the Younger (1768-1805) might have
been meant. He was well known in Nipperkin, one of Munden's parts.
Page 169, line 21. _Farley...Knight...Liston_. Charles Farley
(1771-1859), mainly known as the deviser of Covent Garden pantomimes;
Edward Knight (1774-1826), an eccentric little comedian; John Listen
(1776?-1846), whose mock biography Lamb wrote (see Vol. I.).
Page 169, line 7 from foot. _Sir Christopher Curry...Old Dornton_. Sir
Christopher in "Inkle and Yarico," by the younger Colman; Old Dornton
in Holcroft's "Road to Ruin."
Page 170, line 6. _The Cobbler of Preston_. A play, founded on "The
Taming of the Shrew," by Charles Johnson, written in 1716.
THE LAST ESSAYS OF ELIA
Page 171. PREFACE.
_London Magazine_, January, 1823, where it was entitled "A Character
of the late Elia. By a Friend." Signed Phil-Elia. Lamb did not reprint
it for ten years, and then with certain omissions.
In the _London Magazine_ the "Character" began thus:--
"A CHARACTER OF THE LATE ELIA
"BY A FRIEND
"This gentleman, who for some months past had been in a declining
way, hath at length paid his final tribute to nature. He just
lived long enough (it was what he wished) to see his papers
collected into a volume. The pages of the LONDON MAGAZINE will
henceforth know him no more.
"Exactly at twelve last night his queer spirit departed, and
the bells of Saint Bride's rang him out with the old year. The
mournful vibrations were caught in the dining-room of his friends
T. and H.; and the company, assembled there to welcome in another
First of January, checked their carousals in mid-mirth and were
silent. Janus wept. The gentle P----r, in a whisper, signified his
intention of devoting an Elegy; and Allan C----, nobly forgetful
of his countrymen's wrongs, vowed a Memoir to his _manes_, full
and friendly as a Tale of Lyddal-cross."
_Elia_ had just been published when this paper appeared, and it was
probably Lamb's serious intention to stop the series. He was, however,
prevailed to continue. T. and H. were Taylor & Hessey, the owners of
the _London Magazine_. Janus was Janus Weathercock, Thomas Griffiths
Wainewright; P----r was Bryan Waller Procter, or Barry Cornwall, who
afterwards wrote Lamb's life, and Allan C---- was Allan Cunningham,
who called himself "Nalla" in the _London Magazine_. "The Twelve Tales
of Lyddal Cross" ran serially in the magazine in 1822.
Page 171, line 9 from foot. _A former Essay_. In the _London Magazine_
"his third essay," referring to "Christ's Hospital Five and Thirty
Years Ago."
Page 172, line 7. _My late friend_. The opening sentences of this
paragraph seem to have been deliberately modelled, as indeed is the
whole essay, upon Sterne's character of Yorick in _Tristram Shandy_,
Vol. I., Chapter XI.
Page 172, line 12 from foot. _It was hit or miss with him_. Canon
Ainger has pointed out that Lamb's description of himself in
company is corroborated by Hazlitt in his essay "On Coffee-House
Politicians":--
I will, however, admit that the said Elia is the worst company in
the world in bad company, if it be granted me that in good company
he is nearly the best that can be. He is one of those of whom
it may be said, _Tell me your company, and I'll tell you your
manners_. He is the creature of sympathy, and makes good whatever
opinion you seem to entertain of him. He cannot outgo the
apprehensions of the circle; and invariably acts up or down to
the point of refinement or vulgarity at which they pitch him. He
appears to take a pleasure in exaggerating the prejudices of
strangers against him; a pride in confirming the prepossessions
of friends. In whatever scale of intellect he is placed, he is as
lively or as stupid as the rest can be for their lives. If you
think him odd and ridiculous, he becomes more and more so every
minute, _a la folie_, till he is a wonder gazed at by all--set him
against a good wit and a ready apprehension, and he brightens more
and more ...
P.G. Patmore's testimony is also corroborative:--
To those who did not know him, or, knowing, did not or could
not appreciate him, Lamb often passed for something between an
imbecile, a brute, and a buffoon; and the first impression he made
on ordinary people was always unfavourable--sometimes to a violent
and repulsive degree.
Page 174, line 3. _Some of his writings_. In the _London Magazine_ the
essay did not end here. It continued:--
"He left property behind him. Of course, the little that is left
(chiefly in India bonds) devolves upon his cousin Bridget. A few
critical dissertations were found in his escritoire, which have
been handed over to the Editor of this Magazine, in which it is
to be hoped they will shortly appear, retaining his accustomed
signature.
"He has himself not obscurely hinted that his employment lay in a
public office. The gentlemen in the Export department of the East
India House will forgive me, if I acknowledge the readiness with
which they assisted me in the retrieval of his few manuscripts.
They pointed out in a most obliging manner the desk at which he
had been planted for forty years; showed me ponderous tomes of
figures, in his own remarkably neat hand, which, more properly
than his few printed tracts, might be called his 'Works.' They
seemed affectionate to his memory, and universally commended his
expertness in book-keeping. It seems he was the inventor of some
ledger, which should combine the precision and certainty of the
Italian double entry (I think they called it) with the brevity
and facility of some newer German system--but I am not able to
appreciate the worth of the discovery. I have often heard him
express a warm regard for his associates in office, and how
fortunate he considered himself in having his lot thrown
in amongst them. There is more sense, more discourse, more
shrewdness, and even talent, among these clerks (he would say)
than in twice the number of authors by profession that I have
conversed with. He would brighten up sometimes upon the 'old
days of the India House,' when he consorted with Woodroffe, and
Wissett, and Peter Corbet (a descendant and worthy representative,
bating the point of sanctity, of old facetious Bishop Corbet), and
Hoole who translated Tasso, and Bartlemy Brown whose father (God
assoil him therefore) modernised Walton--and sly warm-hearted old
Jack Cole (King Cole they called him in those days), and Campe,
and Fombelle--and a world of choice spirits, more than I can
remember to name, who associated in those days with Jack Burrell
(the _bon vivant_ of the South Sea House), and little Eyton (said
to be a _facsimile_ of Pope--he was a miniature of a gentleman)
that was cashier under him, and Dan Voight of the Custom House
that left the famous library.
"Well, Elia is gone--for aught I know, to be reunited with
them--and these poor traces of his pen are all we have to show for
it. How little survives of the wordiest authors! Of all they said
or did in their lifetime, a few glittering words only! His Essays
found some favourers, as they appeared separately; they shuffled
their way in the crowd well enough singly; how they will _read_,
now they are brought together, is a question for the publishers,
who have thus ventured to draw out into one piece his 'weaved-up
follies.'
"PHIL-ELIA."
This passage calls for some remark. Cousin Bridget was, of course,
Mary Lamb.--Lamb repeated the joke about his _Works_ in his
"Autobiography" (see Vol. I.) and in "The Superannuated Man."--Some
record of certain of the old clerks mentioned by Lamb still remains;
but I can find nothing of the others. Whether or not Peter Corbet
really derived from the Bishop we do not know, but the facetious
Bishop Corbet was Richard Corbet (1582-1635), Bishop of Oxford and
Norwich, whose conviviality was famous and who wrote the "Fairies'
Farewell." John Hoole (1727-1803), who translated Tasso and wrote the
life of Scott of Amwell and a number of other works, was principal
auditor at the end of his time at the India House. He retired about
1785, when Lamb was ten years old. Writing to Coleridge on January 5,
1797, Lamb speaks of Hoole as "the great boast and ornament of the
India House," and says that he found Tasso, in Hoole's translation,
"more vapid than smallest small beer sun-vinegared." The moderniser
of Walton would be Moses Browne (1704-1787), whose edition of _The
Complete Angler_, 1750, was undertaken at the suggestion of Dr.
Johnson.
* * * * *
Page 174. BLAKESMOOR IN H----SHIRE
_London Magazine_, September, 1824.
With this essay Lamb made his reappearance in the magazine, after
eight months' absence.
By Blakesmoor Lamb meant Blakesware, the manor-house near Widford, in
Hertfordshire, where his grandmother, Mary Field, had been housekeeper
for many years. Compare the essay "Dream-Children."
Blakesware, which was built by Sir Francis Leventhorpe about 1640,
became the property of the Plumers in 1683, being then purchased by
John Plumer, of New Windsor, who died in 1718. It descended to William
Plumer, M.P. for Yarmouth, in the Isle of Wight, and afterwards for
Hertfordshire, who died in 1767, and was presumably Mrs. Field's first
employer. His widow and the younger children remained at Blakesware
until Mrs. Plumer's death in 1778, but the eldest son, William Plumer,
moved at once to Gilston, a few miles east of Blakesware, a mansion
which for a long time was confused with Blakesware by commentators on
Lamb. This William Plumer, who was M.P. for Lewes, for Hertfordshire,
and finally for Higham Ferrers, and a governor of Christ's Hospital,
kept up Blakesware after his mother's death in 1778 (when Lamb was
three) exactly as before, but it remained empty save for Mrs. Field
and the servants under her. Mrs. Field became thus practically
mistress of it, as Lamb says in "Dream-Children." Hence the increased
happiness of her grandchildren when they visited her. Mrs. Field died
in 1792, when Lamb was seventeen. William Plumer died in 1822, aged
eighty-six, having apparently arranged with his widow, who continued
at Gilston, that Blakesware should be pulled down--a work of
demolition which at once was begun. This lady, _nee_ Jane Hamilton,
afterwards married a Mr. Lewin, and then, in 1828, Robert Ward
(1765-1846), author of _Tremaine_ and other novels, who took the name
of Plumer-Ward, and may be read of, together with curious details of
Gilston House, in P.G. Patmore's _My Friends and Acquaintances_.
Nothing now remains but a few mounds, beneath which are bricks and
rubble. The present house is a quarter of a mile behind the old
one, high on the hill. In Lamb's day this hillside was known as the
Wilderness, and where now is turf were formal walks with clipped yew
hedges and here and there a statue. The stream of which he speaks is
the Ashe, running close by the walls of the old house. Standing there
now, among the trees which mark its site, it is easy to reconstruct
the past as described in the essay.
The Twelve Caesars, the tapestry and other more notable possessions of
Blakesware, although moved to Gilston on the demolition of Blakesware,
are there no longer, and their present destination is a mystery.
Gilston was pulled down in 1853, following upon a sale by auction,
when all its treasures were dispersed. Some, I have discovered,
were bought by the enterprising tenant of the old Rye House Inn
at Broxbourne, but absolute identification of anything now seems
impossible.
Blakesware is again described in _Mrs. Leicester's School_, in Mary
Lamb's story of "The Young Mahometan." There the Twelve Caesars are
spoken of as hanging on the wall, as if they were medallions; but Mr.
E.S. Bowlby tells me that he perfectly remembers the Twelve Caesars at
Gilston, about 1850, as busts, just as Lamb says. In "Rosamund Gray"
(see Vol. I.) Lamb describes the Blakesware wilderness. See also notes
to "The Last Peach," Vol. I., to "Dream-Children" in this volume, and
to "Going or Gone," Vol. IV.
Lamb has other references to Blakesware and the irrevocability of his
happiness there as a child, in his letters. Writing to Southey on
October 31, 1799, he says:--"Dear Southey,--I have but just got
your letter, being returned from Herts, where I have passed a few
red-letter days with much pleasure. I would describe the county to
you, as you have done by Devonshire; but alas! I am a poor pen at that
same. I could tell you of an old house with a tapestry bedroom, the
'Judgment of Solomon' composing one pannel, and 'Actaeon spying Diana
naked' the other. I could tell of an old marble hall, with Hogarth's
prints, and the Roman Caesars in marble hung round. I could tell of
a _wilderness_, and of a village church, and where the bones of my
honoured grandam lie; but there are feelings which refuse to be
translated, sulky aborigines, which will not be naturalised in another
soil. Of this nature are old family faces, and scenes of infancy."
And again, to Bernard Barton, in August, 1827:--"You have well
described your old-fashioned grand paternall Hall. Is it not odd that
every one's earliest recollections are of some such place. I had my
Blakesware (Blakesmoor in the 'London'). Nothing fills a child's mind
like a large old Mansion ... better if un- or partially-occupied;
peopled with the spirits of deceased members of the County and
Justices of the Quorum. Would I were buried in the peopled solitude of
one, with my feelings at 7 years old!
"Those marble busts of the Emperors, they seem'd as if they were to
stand for ever, as they had stood from the living days of Rome, in
that old Marble Hall, and I to partake of their permanency; Eternity
was, while I thought not of Time. But he thought of me, and they are
toppled down, and corn covers the spot of the noble old Dwelling and
its princely gardens. I feel like a grasshopper that chirping about
the grounds escaped his scythe only by my littleness. Ev'n now he is
whetting one of his smallest razors to clean wipe me out, perhaps.
Well!"
Writing to Barton in August, 1824, concerning the present essay, Lamb
describes it as a "futile effort ... 'wrung from me with slow pain'."
Page 175, line 15 from foot. _Mrs. Battle_. There was a haunted room
at Blakesware, but the suggestion that the famous Mrs. Battle died
in it was probably due to a sudden whimsical impulse. Lamb states in
"Dream-Children" that Mrs. Field occupied this room.
Page 177, line 22. _The hills of Lincoln_. See Lamb's sonnet "On the
Family Name," Vol. IV. Lamb's father came from Lincoln.
Page 177, line 11 from foot. _Those old W----s_. Lamb thus disguised
the name of Plumer. He could not have meant Wards, for Robert Ward did
not marry William Plumer's widow till four years after this essay was
printed.
Page 178, line 2. _My Alice_. See notes to "Dream-Children."
Page 178, line 2. _Mildred Elia, I take it_. Alter these words, in the
_London Magazine_, came this passage:--
"From her, and from my passion for her--for I first learned love
from a picture--Bridget took the hint of those pretty whimsical
lines, which thou mayst see, if haply thou hast never seen them,
Reader, in the margin.[1] But my Mildred grew not old, like the
imaginery Helen."
This ballad, written in gentle ridicule of Lamb's affection for the
Blakesware portrait, and Mary Lamb's first known poem, was printed in
the _John Woodvil_ volume, 1802, and in the _Works_, 1818.
[Footnote 1:
"High-born Helen, round your dwelling,
These twenty years I've paced in vain:
Haughty beauty, thy lover's duty
Hath been to glory in his pain.
"High-born Helen, proudly telling
Stories of thy cold disdain;
I starve, I die, now you comply,
And I no longer can complain.
"These twenty years I've lived on tears,
Dwelling for ever on a frown;
On sighs I've fed, your scorn my bread;
I perish now you kind are grown.
"Can I, who loved ray beloved
But for the scorn 'was in her eye,'
Can I be moved for my beloved,
When she returns me sigh for sigh?
"In stately pride, by my bedside,
High-born Helen's portrait hung;
Deaf to my praise, my mournful lays
Are nightly to the portrait sung.
"To that I weep, nor ever sleep,
Complaining all night long to her.--
Helen, grown old, no longer cold,
Said--'you to all men I prefer.'"]
* * * * *
Page 178. POOR RELATIONS.
_London Magazine_, May, 1823.
Page 179, line 10. _A pound of sweet._ After these words, in the
_London Magazine_, came one more descriptive clause--"the bore _par
excellence_."
Page 181, line 4, _Richard Amlet, Esq._ In "The Confederacy" by Sir
John Vanbrugh--a favourite part of John Palmer's (see the essay "On
Some of the Old Actors").
Page 181, line 16. _Poor W----_. In the Key Lamb identifies W---- with
Favell, who "left Cambridge because he was asham'd of his father, who
was a house-painter there." Favell has already been mentioned in the
essay on "Christ's Hospital."
Page 183, line 22. _At Lincoln._ The Lambs, as we have seen, came from
Lincolnshire. The old feud between the Above and Below Boys seems now
to have abated, but a social gulf between the two divisions of the
city remains.
Page 184, line 11 from foot. _John Billet_. Probably not the real
name. Lamb gives the innkeeper at Widford, in "Rosamund Gray," the
name of Billet, when it was really Clemitson.
* * * * *
Page 185. STAGE ILLUSION.
_London Magazine_, August, 1825, where it was entitled "Imperfect
Dramatic Illusion."
This was, I think, Lamb's last contribution to the _London_, which had
been growing steadily heavier and less hospitable to gaiety. Some one,
however, contributed to it from time to time papers more or less in
the Elian manner. There had been one in July, 1825, on the Widow
Fairlop, a lady akin to "The Gentle Giantess." In September, 1825, was
an essay entitled "The Sorrows of ** ***" (an ass), which might,
both from style and sympathy, be almost Lamb's; but was, I think, by
another hand. And in January, 1826, there was an article on whist,
with quotations from Mrs. Battle, deliberately derived from her
creator. These and other essays are printed in Mr. Bertram Dobell's
_Sidelights on Charles Lamb_, 1903, with interesting comments.
The present essay to some extent continues the subject treated of in
"The Artificial Comedy," but it may be taken also as containing some
of the matter of the promised continuation of the essay "On the
Tragedies of Shakspeare," which was to deal with the comic characters
of that dramatist (see Vol. I.).
Page 185, line 15 from foot. _Jack Bannister_. See notes to the essay
on "The Old Actors." His greatest parts were not those of cowards; but
his Bob Acres was justly famous. Sir Anthony Absolute and Tony Lumpkin
were perhaps his chief triumphs. He left the stage in 1815.
Page 186, line 24. _Gatty_. Henry Gattie (1774-1844), famous for
old-man parts, notably Monsieur Morbleu in Moncrieffs "Monsieur
Tonson." He was also the best Dr. Caius, in "The Merry Wives of
Windsor," of his time. He left the stage in 1833, and settled down as
a tobacconist and raconteur at Oxford.
Page 186, line 30. _Mr. Emery._ John Emery (1777-1822), the best
impersonator of countrymen in his day. Zekiel Homespun in Colman's
"Heir at Law" was one of his great parts. Tyke was in Morton's "School
of Reform," produced in 1805, and no one has ever played it so well.
He also played Caliban with success.
Page 187, line 4 from foot. _A very judicious actor._ This actor
I have not identified. Benjamin Wrench (1778-1843) was a dashing
comedian, a Wyndham of his day. In "Free and Easy" he played Sir John
Freeman.
* * * * *
Page 188. To THE SHADE OF ELLISTON.
_Englishman's Magazine_, August, 1831, where it formed, with the
following essay, one article, under the title "Reminiscences of
Elliston."
Robert William Elliston (1774-1831), actor and manager, famous for his
stage lovers, both in comedy and tragedy. His Charles Surface was said
to be unequalled, and both in Hotspur and Hamlet he was great. His
last performance was in June, 1831, a very short time before his
death.
Page 189, line 7. _Thin ghosts._ In the _London Magazine_ the passage
ran:--
"Thin ghosts of Figurantes (never plump on earth) admire, while
with uplifted toe retributive you inflict vengeance incorporeal
upon the shadowy rear of obnoxious author, just arrived:--
"'what _seem'd_ his tail
The likeness of a kingly kick had on.
* * * * *
"'Yet soon he heals: for spirits, that live throughout
Vital in every part, not as frail man
In entrails, head, or heart, liver or veins,
Can in the liquid texture mortal wound
Receive no more, than can the liquid air,
All heart they live, all head, all eye.'"
Page 189, line 11 from foot. _A la Foppington_. In Vanbrugh's
"Relapse."
In the _Englishman's Magazine_ the article ended, after "Plaudito, et
Valeto," with: "Thy friend upon Earth, though thou did'st connive at
his d----n."
The article was signed Mr. H., the point being that Elliston had
played Mr. H. at Drury Lane in Lamb's unlucky farce of that name in
1806.
* * * * *
Page 190. ELLISTONIANA.
See note at the head of "To the Shade of Elliston," above.
Page 190, line 3 of essay. _My first introduction._ This paragraph was
a footnote in the _Englishman's Magazine_. Elliston, according to
the _Memoirs_ of him by George Raymond, which have Lamb's phrase,
"Joyousest of once embodied spirits," for motto, opened a circulating
library at Leamington in the name of his sons William and Henry, and
served there himself at times.
Possibly Lamb was visiting Charles Chambers at Leamington when he saw
Elliston. That he did see him there we know from Raymond's book, where
an amusing occurrence is described, illustrating Munden's frugality.
It seems that Lamb, Elliston and Munden drove together to Warwick
Castle. On returning Munden stopped the carriage just outside
Leamington, on the pretext that he had to make a call on an old
friend--a regular device, as Elliston explained, to avoid being
present at the inn when the hire of the carriage was paid.
Page 191, line 11. _Wrench_. See notes to "The Old Actors." Wrench
succeeded Elliston at Bath, and played in the same parts, and with
something of the same manner.
Page 191, line 11 from foot. _Appelles ... G.D._ Apelles, painter to
Alexander the Great, was said to let no day pass without experimenting
with his pencil. G.D. was George Dyer, whom we first met in "Oxford in
the Vacation."
Page 192, line 6. _Ranger_. In Hoadley's "Suspicious Husband," one of
Elliston's great parts.
Page 192, line 17 from foot. _Cibber_. Colley Cibber (1671-1757), the
actor, who was a very vain man, created the part of Foppington in
1697--his first great success.
Page 192, last line. _St. Dunstan's ... punctual giants._ Old St.
Dunstan Church, in Fleet Street, had huge figures which struck the
hours, and which disappeared with the church, pulled down to make room
for the present one some time before 1831. They are mentioned in Emily
Barton's story in _Mrs. Leicester's School_ (see Vol. III.). Moxon
records that Lamb shed tears when the figures were taken away.
Page 193, line 6. _Drury Lane_. Drury Lane opened, under Elliston's
management, on October 4, 1819, with "Wild Oats," in which he played
Rover. He left the theatre, a bankrupt, in 1826.
Page 193, line 19. _The ... Olympic._ Lamb is wrong in his dates.
Elliston's tenancy of the Olympic preceded his reign at Drury Lane.
It was to the Surrey that he retired after the Drury Lane period,
producing there Jerrold's "Black-Eyed Susan" in 1829.
Page 193, line 12 from foot. _Sir A---- C----_. Sir Anthony Carlisle
(see note to "A Quakers' Meeting").
Page 194, line 7. _A Vestris_. Madame Vestris (1797-1856), the great
comedienne, who was one of Elliston's stars at Drury Lane.
Page 195, line 6. _Latinity_. Elliston was buried in St. John's
Church, Waterloo Road, and a marble slab with a Latin inscription
by Nicholas Torre, his son-in-law, is on the wall. Elliston was the
nephew of Dr. Elliston, Master of Sidney Sussex College, Cambridge,
who sent him to St. Paul's School--not, however, that founded by
Colet--but to St. Paul's School, Covent Garden. He was intended for
the Church.
* * * * *
Page 195. DETACHED THOUGHTS ON BOOKS AND READING.
_London Magazine_, July, 1822, where, at the end, were the words, "To
be continued;" but Lamb did not return to the topic.
For some curious reason Lamb passed over this essay when collecting
_Elia_ for the press. It was not republished till 1833, in the _Last
Essays_.
Page 195, motto. _The Relapse_. The comedy by Sir John Vanbrugh.
Lamb liked this quotation. He uses it in his letter about William
Wordsworth, junior, to Dorothy Wordsworth, November 25, 1819; and
again in his "Reminiscence of Sir Jeffery Dunstan" (see Vol. I.).
Page 195, foot. _I can read any thing which I call a book_. Writing to
Wordsworth in August, 1815, Lamb says: "What any man can write, surely
I may read."
Page 195, last line. _Pocket Books_. In the _London Magazine_ Lamb
added in parenthesis "the literary excepted," the reference being to
the _Literary Pocket Book_ which Leigh Hunt brought out annually from
1819 to 1822.
Page 196, line 2. _Hume ... Jenyns_. Hume would be David Hume
(1711-1776), the philosopher and historian of England; Edward Gibbon
(1737-1794), historian of Rome; William Robertson, D.D. (1721-1793),
historian of America, Charles V., Scotland and India; James Beattie
(1735-1803), author of "The Minstrel" and a number of essays, who
had, however, one recommendation to Lamb, of which Lamb may have been
unaware--he loved Vincent Bourne's poems and was one of the first
to praise them; and Soame Jenyns (1704-1787), author of _The Art
of Dancing_, and the _Inquiry into Evil_ which Johnson reviewed so
mercilessly. It is stated in Moore's _Diary_, according to Procter,
that Lamb "excluded from his library Robertson, Gibbon and Hume,
and made instead a collection of the works of the heroes of _The
Dunciad_."
Page 196, line 14. _Population Essay_. That was the day of population
essays. Malthus's _Essay on Population_, 1798, had led to a number of
replies.
Page 196, line 22. _My ragged veterans_. Crabb Robinson recorded in
his diary that Lamb had the "finest collection of shabby books" he
ever saw; "such a number of first-rate works in very bad condition is,
I think, nowhere to be found." Leigh Hunt stated in his essay on "My
Books" in _The Literary Examiner_, July 5, 1823, that Lamb's library
had
an handsome contempt for appearance. It looks like what it is, a
selection made at precious intervals from the book-stalls;--now
a Chaucer at nine and twopence; now a Montaigne or a Sir Thomas
Browne at two shillings; now a Jeremy Taylor, a Spinoza; an old
English Dramatist, Prior, and Sir Philip Sidney; and the books are
"neat as imported." The very perusal of the backs is a "discipline
of humanity." There Mr. Southey takes his place again with an old
Radical friend: there Jeremy Collier is at peace with Dryden:
there the lion, Martin Luther, lies down with the Quaker lamb,
Sewel: there Guzman d'Alfarache thinks himself fit company for Sir
Charles Grandison, and has his claims admitted. Even the "high
fantastical" Duchess of Newcastle, with her laurel on her head,
is received with grave honours, and not the less for declining to
trouble herself with the constitutions of her maids.
It is in the same essay that Leigh Hunt mentions that he once saw
Lamb kiss an old folio--Chapman's Homer--the work he paraphrased for
children under the title _The Adventures of Ulysses_.
Page 197, line 15. _Life of the Duke of Newcastle_. Lamb's copy, a
folio containing also the "Philosophical Letters," is in America.
Page 197, line 20. _Sydney, Bishop Taylor, Milton_... I cannot say
where are Lamb's copies of Sidney and Fuller; but the British Museum
has his Milton, rich in MS. notes, a two-volume edition, 1751. The
Taylor, which Lamb acquired in 1798, is the 1678 folio _Sermons_. I
cannot say where it now is.
Page 197, line 26. _Shakspeare_. Lamb's Shakespeare was not sold at
the sale of his library; only a copy of the _Poems_, 12mo, 1714.
His annotated copy of the _Poems_, 1640, is in America. There is a
reference to one of Rowe's plates in the essay "My First Play." The
Shakespeare gallery engravings were the costly series of illustrations
to Shakespeare commissioned by John Boydell (1719-1804), Lord Mayor of
London in 1790. The pictures were exhibited in the Shakespeare Gallery
in Pall Mall, and the engravings were published in 1802.
After the word "Shakespeare," in the _London Magazine_, came the
sentence: "You cannot make a _pet_ book of an author whom everybody
reads."
In a letter to Wordsworth, February 1, 1806, Lamb says: "Shakespear is
one of the last books one should like to give up, perhaps the one just
before the Dying Service in a large Prayer book." In the same letter
he says of binding: "The Law Robe I have ever thought as comely and
gentlemanly a garb as a Book would wish to wear."
Page 197, line 7 from foot. _Beaumont and Fletcher._ See note to "The
Two Races of Men" for an account of Lamb's copy, now in the British
Museum.
Page 197, line 5 from foot. _No sympathy with them._ After these
words, in the _London Magazine_, came, "nor with Mr. Gifford's Ben
Jonson." This edition by Lamb's old enemy, William Gifford, editor of
the _Quarterly_, was published in 1816. Lamb's copy of Ben Jonson was
dated 1692, folio. It is now in America, I believe.
Page 197, foot. _The reprint of the Anatomy of Melancholy_. This
reprint was, I think, published in 1800, in two volumes, marked ninth
edition. Lamb's copy was dated 1621, quarto. I do not know where it
now is.
Page 198, line 4. _Malone_. This was Edmund Malone (1741-1812), the
critic and editor of Shakespeare, who in 1793 persuaded the Vicar of
Stratford-on-Avon to whitewash the bust of the poet in the
chancel. A _Gentleman's Magazine_ epigrammatist, sharing Lamb's view,
wrote:--
Stranger, to whom this monument is shown,
Invoke the poet's curse upon Malone;
Whose meddling zeal his barbarous taste betrays,
And daubs his tombstone, as he mars his plays.
Lamb has been less than fair to Malone. To defend his action in the
matter of the bust of Shakespeare is impossible, except by saying that
he acted in good faith and according to the fashion of his time. But
he did great service to the fame of Shakespeare and thus to English
literature, and was fearless and shrewd in his denunciation of the
impostor Ireland.
Page 198, line 26. _The Fairy Queen_. Lamb's copy was a folio, 1617,
12, 17, 13. Against Canto XI., Stanza 32, he has written: "Dear Venom,
this is the stave I wot of. I will maintain it against any in the
book."
Page 199, line 14. _Nando's_. A coffee-house in Fleet Street, at the
east corner of Inner Temple Lane, and thus at one time close to Lamb's
rooms.
Page 199, line 16. "_The Chronicle is in hand, Sir._" In the _London
Magazine_ the following paragraph was here inserted:--
"As in these little Diurnals I generally skip the Foreign News,
the Debates--and the Politics--I find the Morning Herald by far
the most entertaining of them. It is an agreeable miscellany,
rather than a newspaper."
The _Morning Herald_, under Alexander Chalmers, had given more
attention to social gossip than to affairs of State; but under Thomas
Wright it suddenly, about the time of Lamb's essay, became politically
serious and left aristocratic matters to the _Morning Post_.
Page 199, line 20. _Town and Country Magazine_. This magazine
flourished between 1769 and 1792.
Page 199, line 26. _Poor Tobin_. Possibly John Tobin (1770-1804), the
playwright, though I think not. More probably the Tobin mentioned in
Lamb's letter to Wordsworth about "Mr. H." in June, 1806 (two years
after John Tobin's death), to whom Lamb read the manager's letter
concerning the farce. This would be James, John Tobin's brother.
Page 200, line 13. _The five points_. After these words came, in the
_London Magazine_, the following paragraph:--
"I was once amused--there is a pleasure in _affecting_
affectation--at the indignation of a crowd that was justling in
with me at the pit-door of Covent Garden theatre, to have a sight
of Master Betty--then at once in his dawn and his meridian--in
Hamlet. I had been invited quite unexpectedly to join a party,
whom I met near the door of the playhouse, and I happened to have
in my hand a large octavo of Johnson and Steevens's Shakspeare,
which, the time not admitting of my carrying it home, of course
went with me to the theatre. Just in the very heat and pressure
of the doors opening--the _rush_, as they term it--I deliberately
held the volume over my head, open at the scene in which the young
Roscius had been most cried up, and quietly read by the lamplight.
The clamour became universal. 'The affectation of the fellow,'
cried one. 'Look at that gentleman _reading_, papa,' squeaked a
young lady, who in her admiration of the novelty almost forgot her
fears. I read on. 'He ought to have his book knocked out of his
hand,' exclaimed a pursy cit, whose arms were too fast pinioned to
his side to suffer him to execute his kind intention. Still I read
on--and, till the time came to pay my money, kept as unmoved,
as Saint Antony at his Holy Offices, with the satyrs, apes, and
hobgoblins, mopping, and making mouths at him, in the picture,
while the good man sits undisturbed at the sight, as if he were
sole tenant of the desart.--The individual rabble (I recognised
more than one of their ugly faces) had damned a slight piece of
mine but a few nights before, and I was determined the culprits
should not a second time put me out of countenance."
Master Betty was William Henry West Betty (1791-1874), known as the
"Young Roscius," whose Hamlet and Douglas sent playgoers wild in
1804-5-6. Pitt, indeed, once adjourned the House in order that his
Hamlet might be witnessed. His most cried-up scenes in "Hamlet" were
the "To be or not to be" soliloquy, and the fencing scene before the
king and his mother. The piece of Lamb's own which had been hissed
was, of course, "Mr. H.," produced on December 10, 1806; but very
likely he added this reference as a symmetrical afterthought, for he
would probably have visited Master Betty much earlier in his career,
that phenomenon's first appearance at Covent Garden being two years
before the advent of the ill-fated Hogsflesh.
Page 200, line 22. _Martin B----_. Martin Charles Burney, son of
Admiral Burney, and a lifelong friend of the Lambs--to whom Lamb
dedicated the prose part of his _Works_ in 1818 (see Vol. IV.).
Page 200, line 28. _A quaint poetess_. Mary Lamb. The poem is in
_Poetry for Children_, 1809 (see Vol. III. of this edition). In line
17 the word "then" has been inserted by Lamb. The punctuation also
differs from that of the _Poetry for Children_.
* * * * *
Page 201. THE OLD _MARGATE HOY_.
_London Magazine_, July, 1823. This, like others of Lamb's essays, was
translated into French and published in the _Revue Britannique_ in
1833. It was prefaced by the remark: "L'auteur de cette delicieuse
esquisse est Charles Lamb, connu sous le nom d'Eliah."
Page 201, beginning. _I have said so before._ See "Oxford in the
Vacation."
Page 201, line 5 of essay. _My beloved Thames._ Lamb describes a
riparian holiday at and about Richmond in a letter to Robert Lloyd in
1804.
Page 201, line 8 of essay. _Worthing_... There is no record of the
Lambs' sojourn at Worthing or Eastbourne. They were at Brighton in
1817, and Mary Lamb at any rate enjoyed walking on the Downs there; in
a letter to Miss Wordsworth of November 21, 1817, she described them
as little mountains, _almost as good as_ Westmoreland scenery. They
were at Hastings--at 13 Standgate Street--in 1823 (see Lamb's letters
to Bernard Barton, July 10, 1823, to Hood, August 10, 1824, and to
Dibdin, June, 1826). The only evidence that we have of Lamb knowing
Worthing is his "Mr. H.". That play turns upon the name Hogsflesh,
afterwards changed to Bacon. The two chief innkeepers at Worthing at
the end of the eighteenth century and the beginning of its prosperity
were named Hogsflesh and Bacon, and there was a rhyme concerning them
which was well known (see notes to "Mr. H." in Vol. IV.).
Page 201, line 11 of essay. _Many years ago_. A little later Lamb says
he was then fifteen. This would make the year 1790. It was probably on
this visit to Margate that Lamb conceived the idea of his sonnet, "O,
I could laugh," which Coleridge admired so much (see Vol. IV.).
Page 201, line 17 of essay. _Thou old Margate Hoy_. This old
sailing-boat gave way to a steam-boat, the _Thames_, some time after
1815. The _Thames_, launched in 1815, was the first true steam-boat
the river had seen. The old hoy, or lighter, was probably sloop
rigged.
Page 202, foot. _Our enemies_. Lamb refers here to the attacks of
_Blackwood's Magazine_ on the Cockneys, among whom he himself had been
included. In the _London Magazine_ he had written "unfledged" for
"unseasoned."
Page 206, line 14. _Gebir_. _Gebir_, by Walter Savage Landor
(1775-1864), who was a fortnight older than Lamb, and who afterwards
came to know him personally, was published in 1798.
Page 206, line 16. _This detestable Cinque Port_. A letter from Mary
Lamb to Randal Norris, concerning this, or another, visit to Hastings,
says: "We eat turbot, and we drink smuggled Hollands, and we walk
up hill and down hill all day long." Lamb, in a letter to Barton,
admitted a benefit: "I abused Hastings, but learned its value."
Page 208, line 5. _Lothbury_. Probably in recollection of Wordsworth's
"Reverie of Poor Susan," which Lamb greatly liked.
* * * * *
Page 208. THE CONVALESCENT.
_London Magazine_, July, 1825.
We learn from the _Letters_ that Lamb had a severe nervous breakdown
in the early summer of 1825 after liberation from the India House.
Indeed, his health was never sound for long together after he became a
free man.
* * * * *
Page 212. SANITY OF TRUE GENIUS.
_New Monthly Magazine_, May, 1826, where it appeared as one of the
Popular Fallacies under the title, "That great Wit is allied to
Madness;" beginning: "So far from this being true, the greatest wits
will ever be found to be the sanest writers..." and so forth. Compare
the essay "On the Tragedies of Shakespeare," Vol. I. Lamb's thesis is
borrowed from Dryden's couplet (in _Absalom and Achitophel_, Part I.,
lines 163, 164):--
Great wits are sure to madness near allied,
And thin partitions do their bounds divide.
Page 213, line 14. _Kent ... Flavius_. Lamb was always greatly
impressed by the character of Kent (see his essay on "Hogarth," Vol.
I.; his "Table Talk," Vol. I.; and his versions, in the _Tales from
Shakespear_, of "King Lear" and "Timon," Vol. III.).
* * * * *
Page 215. CAPTAIN JACKSON.
_London Magazine_, November, 1824.
No one has yet been able to identify Captain Jackson. The suggestion
has been made that Randal Norris sat for the picture; but the
circumstance that Lamb, in the first edition of the _Last Essays_,
included "A Death-Bed," with a differing portrait of Randal Norris
therein, is, I think, good evidence against this theory. Perhaps the
captain was one of the imaginary characters which Lamb sent out every
now and then, as he told Bernard Barton (in the letter of March 20,
1826), "to exercise the ingenuity of his friends;" although his
reality seems overpowering.
Apart from his own interest, the captain is noteworthy in
constituting, with Ralph Bigod (see page 27), a sketch (possibly
unknown to Dickens) for Wilkins Micawber.
Page 217, line 22. _Glover ... Leonidas_. Richard Glover (1712-1785),
the poet, author of _Leonidas_, 1737. I cannot find that he ever lived
at Westbourne Green.
Page 218, foot. _The old ballad_. The old ballad "Waly, Waly." This
was among the poems copied by Lamb into Miss Isola's Extract Book.
Page 219, line 8. _Tibbs, and Bobadil_. Beau Tibbs in Goldsmith's
"Citizen of the World," and Bobadil in Ben Jonson's "Every Man in His
Humour."
* * * * *
Page 219. THE SUPERANNUATED MAN.
_London Magazine_, May, 1825.
Except that Lamb has disguised his real employment, this essay is
practically a record of fact. After thirty-three years of service at
the East India House he went home "for ever" on Tuesday, March 29,
1825, with a pension of L441, or two-thirds of his regular salary,
less a small annual deduction as a provision for his sister. At
a Court of Directors held on that day this minute was drawn up:
"Resolved that the resignation of Mr. Charles Lamb, of the Accountant
General's office, on account of certified ill health, be accepted, and
it appearing that he has served the Company faithfully for 33 years,
and is now in receipt of an income of L730 per annum, he be allowed
a pension of L450 ... to commence from this day." Lamb's letters to
Wordsworth, April 6, 1825, to Barton, the same date, and to Miss
Hutchinson, a little later, all tell the story. This is how Lamb put
it to Barton:--
"DEAR B.B.--My spirits are so tumultuary with the novelty of my
recent emancipation, that I have scarce steadiness of hand, much
more mind, to compose a letter.
"I am free, B.B.--free as air.
"The little bird that wings the sky
Knows no such Liberty!
"I was set free on Tuesday in last week at 4 o'clock.
"I came home for ever!...
"I went and sat among 'em all at my old 33 years desk yester
morning; and deuce take me if I had not yearnings at leaving all
my old pen-and-ink fellows, merry sociable lads, at leaving them
in the Lurch, fag, fag, fag.
"I would not serve another 7 years for seven hundred thousand
pound."
To Miss Hutchinson Lamb said; "I would not go back to my prison for
seven years longer for L10000 a year."
In the _London Magazine_ the essay was divided into two parts, with
the two quotations now at the head apportioned each to one part.
Part II. began at "A fortnight has passed," on page 224. The essay
was signed "J.D.," whose address was given as "Beaufort-terrace,
Regent-street; late of Ironmonger-court, Fenchurch-street."
Page 220, line 3. _Recreation_. At "recreation," in the _London
Magazine_, came the footnote:--
"Our ancestors, the noble old Puritans of Cromwell's day,
could distinguish between a day of religious rest and a day of
recreation; and while they exacted a rigorous abstinence from all
amusements (even to the walking out of nursery maids with their
little charges in the fields) upon the Sabbath; in the lieu of the
superstitious observance of the Saints days, which they abrogated,
they humanely gave to the apprentices, and poorer sort of people,
every alternate Thursday for a day of entire sport and recreation.
A strain of piety and policy to be commended above the profane
mockery of the Stuarts and their Book of Sports."
Lamb had said the same thing to Barton in a letter in the spring,
1824, referring there to "Southey's book" as his authority--this being
_The Book of the Church_, 1824.
Page 220, line 25. _Native ... Hertfordshire_. This was a slight
exaggeration. Lamb was London born and bred. But Hertfordshire was his
mother and grandmother's county, and all his love of the open air was
centred there (see the essay on "Mackery End").
Page 221, line 1. _My health_. Lamb had really been seriously unwell
for some time, as the _Letters_ tell us.
Page 221, line 6. _I was fifty_. Lamb was fifty on February 10, 1825.
Page 231, line 7. _I had grown to my desk_. In his first letter to
Barton (September 11, 1822) Lamb wrote: "I am like you a prisoner to
the desk. I have been chained to that galley thirty years, a long
shot. I have almost grown to the wood." Again, to Wordsworth: "I sit
like Philomel all day (but not singing) with my breast against this
thorn of a Desk."
Page 222, line 7. _Boldero, Merryweather ..._ Feigned names of course.
It was Boldero that Lamb once pretended was Leigh Hunt's true name.
And in his fictitious biography of Liston (Vol. I.) Liston's mother
was said to have been a Miss Merryweather. In Lamb's early city days
there was a banking firm in Cornhill, called Boldero, Adey, Lushington
& Boldero.
Page 222, line 12 from foot. _I could walk it away_. Writing to
Wordsworth in March, 1822, concerning the possibility of being
pensioned off, Lamb had said:--"I had thought in a green old age (O
green thought!) to have retired to Ponder's End--emblematic name--how
beautiful! in the Ware road, there to have made up my accounts with
heaven and the Company, toddling about between it and Cheshunt, anon
stretching on some fine Izaac Walton morning, to Hoddsdon or Amwell,
careless as a Beggar, but walking walking ever till I fairly walkd
myself off my legs, dying walking."
And again, writing to Southey after the emancipation, he says (August,
1825): "Mary walks her twelve miles a day some days, and I twenty on
others. 'Tis all holiday with me now, you know."
Page 224, line 9. _Ch----_. John Chambers, son of the Rev. Thomas
Chambers, Vicar of Radway-Edgehill, Warwickshire, and an old Christ's
Hospitaller, to whom Lamb wrote the famous letter on India House
society, printed in the _Letters_, Canon Ainger's edition, under
December, 1818. John Chambers lived until 1872, and had many stories
of Lamb.
Page 224, line 9. _Do----_. Probably Henry Dodwell, to whom Lamb wrote
the letters of July, 1816, from Calne, and that of October 7, 1827,
thanking him for a gift of a sucking pig. But there seems (see the
letter to Chambers above referred to) to have been also a clerk named
Dowley. It was Dodwell who annoyed Lamb by reading _The Times_ till
twelve o'clock every morning.
Page 224, line 10. _Pl----_. According to the late H.G. Bohn's notes
on Chambers' letter, this was W.D. Plumley.
Page 224, line 18. My "_works_." See note to the preface to the _Last
Essays of Elia_. The old India House ledgers of Lamb's day are no
longer in existence, but a copy of Booth's _Tables of Interest_ is
preserved, with some mock notices from the press on the fly-leaves in
Lamb's hand. Lamb's portrait by Meyer was bought for the India Office
in 1902.
Page 224, line 12 from foot. _My own master_. As a matter of fact Lamb
found the time rather heavy on his hands now and then; and he took to
searching for beauties in the Garrick plays in the British Museum as a
refuge. The Elgin marbles were moved there in 1816.
Page 225, line 16 from foot. _And what is it all for_? At these words,
in the _London Magazine_, came the passage:--
"I recite those verses of Cowley, which so mightily agree with my
constitution.
"Business! the frivolous pretence
Of human lusts to shake off innocence:
Business! the grave impertinence:
Business! the thing which I of all things hate:
Business! the contradiction of my fate.
"Or I repeat my own lines, written in my Clerk state:--
"Who first invented work--and bound the free
And holyday-rejoicing spirit down
To the ever-haunting importunity
Of business, in the green fields, and the town--
To plough, loom, anvil, spade--and oh! most sad,
To this dry drudgery of the desk's dead wood?
Who but the Being unblest, alien from good,
Sabbathless Satan! he who his unglad
Task ever plies 'mid rotatory burnings,
That round and round incalculably reel--
For wrath divine hath made him like a wheel--
In that red realm from whence are no returnings;
Where toiling, and turmoiling, ever and aye
He, and his thoughts, keep pensive worky-day!
"O this divine Leisure!--Reader, if thou art furnished with the
Old Series of the London, turn incontinently to the third volume
(page 367), and you will see my present condition there touched in
a 'Wish' by a daintier pen than I can pretend to. I subscribe to
that Sonnet _toto corde_."
The sonnet referred to, beginning--
They talk of time and of time's galling yoke,
will be found quoted above, in the notes to "New Year's Eve." It was,
of course, by Lamb himself. To the other sonnet he gave the title
"Work" (see Vol. IV.). Cowley's lines are from "The Complaint."
Page 225, line 14 from foot. _NOTHING-TO-DO_. Lamb wrote to Barton in
1827: "Positively, the best thing a man can have to do, is nothing,
and next to that perhaps--good works."
* * * * *
Page 226. THE GENTEEL STYLE IN WRITING.
_New Monthly Magazine_, March, 1826, where it was one of the Popular
Fallacies, under the title, "That my Lord Shaftesbury and Sir William
Temple are models of the Genteel Style in Writing.--We should prefer
saying--of the Lordly and the Gentlemanly. Nothing," &c.
Page 226, beginning. _My Lord Shaftesbury_, Anthony Ashley Cooper,
third Earl of Shaftesbury (1671-1713), the grandson of the great
statesman, and the author of the _Characteristicks of Men, Manners,
Opinions and Times_, 1711, and other less known works. In the essay
"Detached Thoughts on Books and Reading" Lamb says, "Shaftesbury is
not too genteel for me."
Page 226, beginning. _Sir William Temple._ Sir William Temple
(1628-1699), diplomatist and man of letters, the patron of Swift,
and the husband of the letter-writing Dorothy Osborne. His first
diplomatic mission was in 1665, to Christopher Bernard von Glialen,
the prince-bishop of Munster, who grew the northern cherries (see page
228). Afterwards he was accredited to Brussels and the Hague, and
subsequently became English Ambassador at the Hague. He was recalled
in 1670, and spent the time between then and 1674, when he returned,
in adding to his garden at Sheen, near Richmond, and in literary
pursuits. He re-entered active political life in 1674, but retired
again in 1680, and moved to an estate near Farnham; which he named
Moor Park, laid out in the Dutch style, and made famous for its wall
fruit. Hither Swift came, as amanuensis, in 1689, and he was there,
with intervals of absence, in 1699, when Temple died, "and with him,"
Swift wrote in his _Diary_, "all that was good and amiable among men."
He was buried in Westminster Abbey, but his heart, by his special
wish, was placed in a silver casket under the sun-dial at Moor Park,
near his favourite window seat.
Temple's essays, under the title of _Miscellanea_, were published in
1680 and 1692; his works, in several volumes, between 1700 and 1709.
The best-known essay is that on "Ancient and Modern Learning," but
Lamb refers also to those "On Health and Long Life," "Of the Cure of
the Gout," "Of Gardening." The quotation on page 228 does not exactly
end Temple's garden essay, as Lamb says. Lamb has slightly altered
Temple's punctuation.
* * * * *
Page 230. BARBARA S----.
_London Magazine_, April, 1825.
This little story exhibits, perhaps better than anything that Lamb
wrote, his curious gift of blending fact and fancy, of building upon
a foundation of reality a structure of whimsicality and invention.
In the late Charles Kent's edition of Lamb's works is printed a
letter from Miss Kelly, the actress, and a friend of the Lambs,
in which the true story is told; for it was she, as indeed Lamb
admitted to Wordsworth in a letter in 1825, who told him the
incident--"beautifully," he says elsewhere.
Miss Kelly wrote, in 1875:--
I perfectly remember relating an incident of my childhood to
Charles Lamb and his dear sister, and I have not the least doubt
that the intense interest he seemed to take in the recital,
induced him to adopt it as the principal feature in his beautiful
story of "Barbara S----." Much, however, as I venerate the
wonderful powers of Charles Lamb as a writer--grateful as I ever
must feel to have enjoyed for so many years the friendship of
himself and his dear sister, and proudly honoured as I am by the
two exquisite sonnets he has given to the world as tributary to my
humble talent, I have never been able thoroughly to appreciate the
extraordinary skill with which he has, in the construction of his
story, desired and contrived so to mystify and characterize
the events, as to keep me out of sight, and render it utterly
impossible for any one to guess at me as the original heroine....
In the year 1799, Miss Jackson, one of my mother's daughters, by
her first husband, was placed under the special care of dear old
Tate Wilkinson, proprietor of the York Theatre, there to practice,
as in due progression, what she had learned of Dramatic Art, while
a Chorus Singer at the Theatre Royal, Drury Lane, coming back, as
she did after a few years, as the wife of the late celebrated,
inimitable Charles Mathews, to the Haymarket Theatre. In 1799,
through the influence of my uncle, Michael Kelly, the celebrated
singer and composer of that day, I was allowed to become a
miniature chorister in her place....
One Saturday, during the limited season of nine months in the
year, Mr. Peake (dear, good old gentleman!) looking, as I remember
he always did--anxiously perplexed--doubtless as to how he could
best dole out the too frequently insufficient amount provided for
the ill-paid company, silently looked me in the face, while he
carefully folded a very _dirty, ragged_ bank note--put it into my
hand, patted my cheek, and with a slight pressure on my shoulder,
hinting there was no time for our usual gossip--as good as said,
"go, my dear," and I hurried down the long gallery, lined down
each side with performers of all degrees, more than one of whom
whispered as I passed--"Is it full pay, dear?" I nodded "Yes," and
proceeded to my seat on the window of the landing-place.
It was a great comfort in those days, to have a bank-note to
look at; but not always easy to open one. Mine had been cut and
repaired with a line of gum paper, about twenty times as thick as
the note itself, threatening the total destruction of the thin
part.
Now observe in what small matters Fanny and Barbara were in a
marked degree different characters. Barbara, at 11 years of age,
was some time before she felt the different size of a guinea to a
half guinea, _held tight in her hand_. I, at nine years old, was
not so untaught, or innocent. I was a woman of the world. I took
_nothing_ for granted. I had a deep respect for Mr. Peake, but the
join might have disfigured the note--destroyed its currency; and
it was my business to see all safe. So, I carefully opened it. A
two pound-note instead of one! The blood rushed into my face, the
tears into my eyes, and for a moment, something like an ecstasy
of joy passed through my mind. "Oh! what a blessing to my dear
mother!"--"To whom?"--in an instant said my violently beating
heart,--"My mother?" Why she would spurn me for the wish. How
shall I ever own to her my guilty thought? I trembled violently--I
staggered back on my way to the Treasury, but no one would let me
pass, until I said, "But Mr. Peake has given me too much." "Too
much, has he?" said one, and was followed by a coarse, cold,
derisive, general laugh. Oh! how it went to my heart; but on I
went.
"If you please, Mr. Peake, you have given me a two--"
"A what?"
"A two, Sir!"
"A two!--God bless my soul!--tut-tut-tut-tut--dear, dear,
dear!--God bless my soul! There, dear," and without another word,
he, in exchange, laid a one pound note on the desk; a new one,
quite clean,--a bright, honest looking note,--mine, the one I had
a right to,--my own,--within the limit of my poor deservings.
Thus, my dear sir, I give (as you say you wish to have the _facts_
as accurately stated as possible) the simple, absolute truth.
As a matter of fact Miss Kelly did afterwards play in Morton's
"Children in the Wood," to Lamb's great satisfaction. The incident of
the roast fowl is in that play.
In Vol. I. will be found more than one eulogy of Miss Kelly's acting.
Page 231, last line. _Real hot tears_. In Crabb Robinson's diary Miss
Kelly relates that when, as Constance, in "King John," Mrs. Siddons
(not Mrs. Porter) wept over her, her collar was wet with Mrs. Siddons'
tears. Miss Kelly, of course, was playing Arthur.
Page 232, line 7. _Impediment ... pulpit_. This is more true than
the casual reader may suppose. Had Lamb not had an impediment in his
speech, he would have become, at Christ's Hospital, a Grecian, and
have gone to one of the universities; and the ordinary fate of a
Grecian was to take orders.
Page 232, line 13. _Mr. Liston_. Mrs. Cowden Clarke says that Liston
the comedian and his wife were among the visitors to the Lambs' rooms
at Great Russell Street.
Page 232, line 14. _Mrs. Charles Kemble_, _nee_ Maria Theresa De Camp,
mother of Fanny Kemble.
Page 232, line 16. _Macready_. The only record of any conference
between Macready and Lamb is Macready's remark in his _Diary_ that he
met Lamb at Talfourd's, and Lamb said that he wished to draw his last
breath through a pipe, and exhale it in a pun. But this was long after
the present essay was written.
Page 232, line 17. _Picture Gallery ... Mr. Matthews_. See note below.
Page 232, line 26. _Not Diamond's_. Dimond was the proprietor of the
old Bath Theatre.
Page 235, first line. _Mrs. Crawford_. Anne Crawford (1734-1801),
_nee_ Street, who was born at Bath, married successively a Mr. Dancer,
Spranger Barry the actor, and a Mr. Crawford. Her great part was Lady
Randolph in Home's "Douglas."
* * * * *
Page 235. THE TOMBS IN THE ABBEY.
_London Magazine_, October, 1823, where, with slight differences,
it formed the concluding portion of the "Letter of Elia to Robert
Southey, Esquire," which will be found in Vol. I. The notes in that
volume should be consulted; but a little may be said here. This, the
less personal portion of the "Letter to Southey," seems to have been
all that Lamb cared to retain. He admitted afterwards, when his
anger against Southey had cooled, that his "guardian angel" had been
"absent" at the time he wrote it.
The Dean of Westminster at the time was Ireland, the friend of
Gifford--dean from 1815 to 1842. Lamb's protest against the
two-shilling fee was supported a year or so later than its first
appearance by Reynolds, in _Odes and Addresses_, 1825, in a sarcastic
appeal to the Dean and Chapter of Westminster to reduce that sum. The
passage in Lamb's essay being reprinted in 1833, suggests that the
reform still tarried. The evidence, however, of J.T. Smith, in his
_Book for a Rainy Day_, is that it was possible in 1822 to enter
Poets' Corner for sixpence. Dean Stanley, in his _Historical Memorials
of Westminster Abbey_, writes: "Free admission was given to the larger
part of the Abbey under Dean Ireland. Authorised guides were first
appointed in 1826, and the nave and transepts opened, and the fees
lowered in 1841...."
Lamb's reference to Southey and to Andre's monument is
characteristically mischievous. He is reminding Southey of his early
sympathy with rebels--his "Wat Tyler" and pantisocratic days. Major
John Andre, Sir Henry Clinton's adjutant-general, was caught returning
from an interview with an American traitor--a perfectly honourable
proceeding in warfare--and was hanged by Washington as a spy in 1780.
No blame attached either to judge or victim. Andre's remains were
reburied in the Abbey in 1821. Lamb speaks of injury to Andre's figure
in the monument, but the usual thing was for the figure of Washington
to be attacked. Its head has had to be renewed more than once. Minor
thefts have also been committed. According to Mrs. Gordon's _Life of
Dean Buckland_, one piece of vandalism at any rate was the work of an
American, who returned to the dean two heads which he had appropriated
as relics.
In _The Examiner_ for April 8, 1821, is quoted from _The Traveller_
the following epigram, which may not improbably be Lamb's, and which
shows at any rate that his protest against entrance fees for churches
was in the air.
ON A VISIT TO ST. PAUL'S
What can be hop'd from Priests who, 'gainst the Poor,
For lack of two-pence, shut the church's door;
Who, true successors of the ancient leaven,
Erect a turnpike on the road to Heaven?
"Knock, and it shall be open'd," saith our LORD;
"Knock, and pay two-pence," say the Chapter Board:
The Showman of the booth the fee receives,
And God's house is again a "den of thieves."
* * * * *
Page 237. AMICUS REDIVIVUS.
_London Magazine_, December, 1823.
A preliminary sketch of the first portion of this essay will be
found in the letter from Lamb to Sarah Hazlitt, written probably in
November, 1823. In Barry Cornwall's _Memoir_ of Lamb, Chapter VI.,
there is also an account of the accident to Dyer--Procter (Barry
Cornwall) having chanced to visit the Lambs just after the event. For
an account of George Dyer see notes to the essay on "Oxford in the
Vacation". In 1823 he was sixty-eight; later he became quite blind.
We have another glimpse of G.D. on that fatal day, in the
reminiscences of Mr. Ogilvie, an India House clerk with Lamb,
as communicated to the Rev. Joseph H. Twichell (see _Scribner's
Magazine_, March, 1876):--
At the time George Dyer was fished out of New River in front of
Lamb's house at Islington, after he was resuscitated, Mary brought
him a suit of Charles's clothes to put on while his own were
drying. Inasmuch as he was a giant of a man, and Lamb undersized;
inasmuch, moreover, as Lamb's wardrobe afforded only knee breeches
for the nether limbs (Dyer's were colossal), the spectacle he
presented when the clothes were on--or as much on as they could
be--was vastly ludicrous.
Allsop, in a letter to Mr. Percy Fitzgerald, remarked, of Dyer's
immersion, that Lamb had said to him: "If he had been drowned it would
have made me famous. Think of having a Crowner's quest, and all the
questions and dark suspicions of murder. People would haunt the spot
and say, 'Here died the poet of Grongar Hill.'" The poet of "Grongar
Hill" was, of course, John Dyer--another of Lamb's instances of the
ambiguities arising from proper names.
Page 238, line 19. _The rescue_. At these words, in the _London
Magazine_, Lamb put this footnote:--
"The topography of my cottage, and its relation to the river,
will explain this; as I have been at some cost to have the whole
engraved (in time, I hope, for our next number), as well for
the satisfaction of the reader, as to commemorate so signal a
deliverance."
The cottage at Colebrooke Row, it should be said, stands to this day
(1911); but the New River has been covered in. There is, however, no
difficulty in reproducing the situation. One descends from the front
door by a curved flight of steps, a little path from which, parallel
with the New River, takes one out into Colebrooke Row (or rather
Duncan Terrace, as this part of the Row is now called). Under the
front door-steps is another door from which Dyer may possibly have
emerged; if so it would be the simplest thing for him to walk straight
ahead, and find himself in the river.
Page 240, line 22. _That Abyssinian traveller_. James Bruce
(1730-1794), the explorer of the sources of the Nile, was famous many
years before his _Travels_ appeared, in 1790, the year after which
Lamb left school. The New River, made in 1609-1613, has its source
in the Chadwell and Amwell springs. It was peculiarly Lamb's river:
Amwell is close to Blakesware and Widford; Lamb explored it as a boy;
at Islington he lived opposite it, and rescued George Dyer from its
depths; and he retained its company both at Enfield and Edmonton.
In the essay on "Newspapers" is a passage very similar to this.
Page 240, line 32. _Eternal novity_. Writing to Hood in 1824 Lamb
speaks of the New River as "rather elderly by this time." Dyer, it
should be remembered, was of Emmanuel College, and the historian of
Cambridge University.
Page 241, last paragraph. George Dyer contributed "all that was
original" to Valpy's edition of the classics--141 volumes. He also
wrote the _History of The University and Colleges of Cambridge,
including notices relating to the Founders and Eminent Men_. Among
the eminent men of Cambridge are Jeremiah Markland (1693-1776), of
Christ's Hospital and St. Peter's, the classical commentator; and
Thomas Gray, the poet, the sweet lyrist of Peterhouse, who died
in 1771, when Dyer was sixteen. Tyrwhitt would probably be Thomas
Tyrwhitt (1730-1786), of Queen's College, Oxford, the editor of
Chaucer; but Robert Tyrwhitt (1735-1817), his brother, the Unitarian,
might be expected to take interest in Dyer also, for G.D. was, in
Lamb's phrase, a "One-Goddite" too. The mild Askew was Anthony Askew
(1722-1772), doctor and classical scholar, who, being physician to
Christ's Hospital when Dyer was there, lent the boy books, and was
very kind to him.
* * * * *
Page 242. SOME SONNETS OF SIR PHILIP SYDNEY.
_London Magazine_, September, 1823, where it was entitled "Nugae
Criticae. By the Author of Elia. No. 1. Defence of the Sonnets of Sir
Philip Sidney." Signed "L." The second and last of the "Nugae Criticae"
series was the note on "The Tempest" (see Vol. I.).
It may be interesting here to relate that Henry Francis Gary, the
translator of Dante, and Lamb's friend, had, says his son in his
memoir, lent Lamb Edward Phillips's _Theatrum Poetarum Anglicanorum_,
which was returned after Lamb's death by Edward Moxon, with the leaf
folded down at the account of Sir Philip Sidney. Mr. Gary thereupon
wrote his "Lines to the memory of Charles Lamb," which begin:--
So should it be, my gentle friend;
Thy leaf last closed at Sidney's end.
Thou, too, like Sidney, wouldst have given
The water, thirsting and near heaven.
Lamb has some interesting references to Sidney in the note to Beaumont
and Fletcher's "Maid's Tragedy" in the _Dramatic Specimens_.
Page 243, line 5. _Tibullus, or the ... Author of the Schoolmistress_.
In the _London Magazine_ Lamb wrote "Catullus." Tibullus was one of
the tenderest of Latin poets. William Shenstone (1714-1763) wrote "The
Schoolmistress," a favourite poem with Lamb. The "prettiest of poems"
he called it in a letter to John Clare.
Page 243, line 9. _Ad Leonoram_. The following translation of Milton's
sonnet was made by Leigh Hunt:--
TO LEONORA SINGING AT ROME
To every one (so have ye faith) is given
A winged guardian from the ranks of heaven.
A greater, Leonora, visits thee:
Thy voice proclaims the present deity.
Either the present deity we hear,
Or he of the third heaven hath left his sphere,
And through the bosom's pure and warbling wells,
Breathes tenderly his smoothed oracles;
Breathes tenderly, and so with easy rounds
Teaches our mortal hearts to bear immortal sounds.
If God is all, and in all nature dwells,
In thee alone he speaks, mute ruler in all else.
The Latin in Masson's edition of Milton differs here and there from
Lamb's version.
Page 243. _Sonnet I_. Lamb cites the sonnets from _Astrophel and
Stella_, in his own order. That which he calls I. is XXXI.; II.,
XXXIX.; III., XXIII.; IV., XXVII.; V., XLI.; VI., LIII.; VII., LXIV.;
VIII., LXXIII.; IX., LXXIV.; X., LXXV.; XI., CIII.; XII., LXXXIV.
I have left the sonnets as Lamb copied them, but there are certain
differences noted in my large edition.
Page 247, middle. _Which I have ... heard objected_. A criticism of
Hazlitt's, in his sixth lecture on Elizabethan literature, delivered
in 1820 at the Surrey Institution, is here criticised. Hazlitt's
remarks on Sidney were uniformly slighting. "His sonnets inlaid in the
Arcadia are jejune, far-fetch'd and frigid.... [The _Arcadia_] is to
me one of the greatest monuments of the abuse of intellectual power
upon record.... [Sidney is] a complete intellectual coxcomb, or nearly
so;" and so forth. The lectures were published in 1821. Elsewhere,
however, Hazlitt found in Sidney much to praise.
Page 248, line 3. _Thin diet of dainty words_. To this sentence, in
the _London Magazine_, Lamb put the following footnote:--
"A profusion of verbal dainties, with a disproportionate lack of
matter and circumstance, is I think one reason of the coldness
with which the public has received the poetry of a nobleman now
living; which, upon the score of exquisite diction alone, is
entitled to something better than neglect. I will venture to copy
one of his Sonnets in this place, which for quiet sweetness, and
unaffected morality, has scarcely its parallel in our language.
"TO A BIRD THAT HAUNTED THE WATERS OF LACKEN IN THE WINTER
"_By Lord Thurlow_
"O melancholy Bird, a winter's day,
Thou standest by the margin of the pool,
And, taught by God, dost thy whole being school
To Patience, which all evil can allay.
God has appointed thee the Fish thy prey;
And given thyself a lesson to the Fool
Unthrifty, to submit to moral rule,
And his unthinking course by thee to weigh.
There need not schools, nor the Professor's chair,
Though these be good, true wisdom to impart.
He who has not enough, for these, to spare
Of time, or gold, may yet amend his heart,
And teach his soul, by brooks, and rivers fair:
Nature is always wise in every part."
This sonnet, by Edward Hovell-Thurlow, second Baron Thurlow
(1781-1829), an intense devotee of Sir Philip Sidney's muse, was a
special favourite with Lamb. He copied it into his Commonplace Book,
and De Quincey has described, in his "London Reminiscences," how Lamb
used to read it aloud.
Page 248, line 27. _Epitaph made on him_. After these words, in the
_London Magazine_, came "by Lord Brooke." Fulke Greville, Lord Brooke,
wrote Sidney's _Life_, published in 1652. After Sidney's death
appeared many elegies upon him, eight of which were printed at the end
of Spenser's _Colin Clout's Come Home Again_, in 1595. That which Lamb
quotes is by Matthew Roydon, Stanzas 15 to 18 and 26 and 27. The poem
beginning "Silence augmenteth grief" is attributed to Brooke, chiefly
on Lamb's authority, in Ward's _English Poets_. This is one stanza:--
He was (woe worth that word!) to each well-thinking mind
A spotless friend, a matchless man, whose virtue ever shined,
Declaring in his thoughts, his life and that he writ,
Highest conceits, longest foresights, and deepest works of wit.
Sidney was only thirty-two at his death.
* * * * *
Page 249. NEWSPAPERS THIRTY-FIVE YEARS AGO.
_Englishman's Magazine_, October, 1831, being the second paper under
the heading "Peter's Net," of which "Recollections of a Late Royal
Academician" was the first (see note, Vol. I.).
The title ran thus:--
PETER'S NET
BY THE AUTHOR OF "ELIA"
_No. II.--On the Total Defect of the faculty of Imagination
observable in the works of modern British Artists._
For explanation of this title see note to the essay that follows. When
reprinting the essay in the _Last Essays of Elia_, 1833, Lamb altered
the title to the one it now bears: the period referred to thus seeming
to be about 1798, but really 1801-1803.
Page 249, first line of essay. _Dan Stuart_. See below.
Page 249, line 2 of essay. _The Exhibition at Somerset House._ Between
the years 1780 and 1838 the Royal Academy held its exhibitions at
Somerset House. It then moved, first to Trafalgar Square, in a portion
of the National Gallery, and then to Burlington House, its present
quarters, in 1869. The _Morning Post_ office is still almost opposite
Somerset House, at the corner of Wellington Street.
Page 250, line 5. _A word or two of D.S._ Daniel Stuart (1766-1846),
one of the Perthshire Stuarts, whose father was out in the '45, and
his grandfather in the '15, began, with his brother, to print the
_Morning Post_ in 1788. In 1795 they bought it for L600, Daniel
assumed the editorship, and in two years' time the circulation had
risen from 350 to 1,000. Mackintosh (afterwards Sir James), Stuart's
brother-in-law, was on the staff; and in 1797 Coleridge began to
contribute. Coleridge's "Devil's Walk" was the most popular thing
printed in Stuart's time; his political articles also helped
enormously to give the paper prestige. Stuart sold the _Morning Post_
in 1803 for L25,000, and then turned his attention to the development
of _The Courier_, an evening paper, in which he also had occasional
assistance from Coleridge and more regular help from Mackintosh.
Lamb's memory served him badly in the essay. So far as I can discover,
his connection with the _Morning Post_, instead of ending when Stuart
sold the paper, can hardly be said to have existed until after that
event. The paper changed hands in September, 1803 (two years after the
failure of The _Albion_), and Lamb's hand almost immediately begins to
be apparent. He had, we know, made earlier efforts to get a footing
there, but had been only moderately successful. The first specimens
prepared for Stuart, in 1800, were not accepted. In the late summer of
1801 he was writing for the _Morning Chronicle_--a few comic letters,
as I imagine--under James Perry; but that lasted only a short time. At
the end of 1801 Lamb tried the _Post_ again. In January and February,
1802, Stuart printed some epigrams by him on public characters, two
criticisms of G.F. Cooke, in Richard III. and Lear, and the essay "The
Londoner" (see Vol. I.). Probably there were also some paragraphs. In
a letter to Rickman in January, 1802, Lamb says that he is leaving
the _Post_, partly on account of his difficulty in writing dramatic
criticisms on the same night as the performance.
We know nothing of Lamb's journalistic adventures between February,
1802, and October, 1803, when the fashion of pink stockings came in,
and when he was certainly back on the _Post_ (Stuart having sold it to
establish _The Courier_), and had become more of a journalist than he
had ever been. I quote a number of the paragraphs which I take to be
his on this rich topic; but the specimen given in the essay is not
discoverable:--
"_Oct_. 8.--The fugitive and mercurial matter, of which a _Lady's
blush_ is made, after coursing from its natural position, the
_cheek_, to the _tip_ of the _elbow_, and thence diverging for a
time to the _knee_, has finally settled in the _legs_, where, in
the form of a pair of _red hose_, it combines with the posture and
situation of _the times_, to put on a most _warlike_ and _martial
appearance_."
"_Nov_. 2.--Bartram, who, as a _traveller_, was possessed of a
very _lively fancy_, describes vast plains in the interior of
America, where his _horse's fetlocks_ for miles were dyed a
perfect _blood colour_, in the juice of the _wild strawberries_.
A less ardent fancy than BARTRAM'S may apply this beautiful
phenomenon of summer, to solve the present _strawberry appearance_
of the _female leg_ this autumn in England."
"_Nov_. 3.--The _roseate tint_, so agreeably diffused through the
silk stockings of our females, induces the belief that the _dye is
cast_ for their lovers."
"_Nov_. 8.--A popular superstition in the North of Germany is said
to be the true original of the well-known sign of Mother REDCAP.
Who knows but that _late posterity_, when, what is regarded by
us now as _fashion_, shall have long been classed among the
superstitious observances of an age gone by, may dignify their
signs with the antiquated personification of a Mother RED LEGS?"
"_Nov_. 9.--Curiosity is on tip-toe for the arrival of ELPHY
BEY'S fair _Circassian_ Ladies. The attraction of their
_naturally-placed, fine, proverbial bloom_, is only wanting to
reduce the wandering colour in the 'elbows' and 'ancles' of our
_belles_, back to its native _metropolis_ and _palace_, the
'cheek.'"
"_Nov_. 22.--_Pink stockings_ beneath _dark pelices_ are emblems
of _Sincerity_ and _Discretion_; signifying a _warm heart_ beneath
a _cool exterior_."
"_Nov_. 29.--The decline of red stockings is as fatal to the wits,
as the going out of a fashion to an overstocked jeweller: some
of these gentry have literally for some months past _fed_ on
_roses_."
"_Dec_. 21.--The fashion of red stockings, so much cried down,
dispraised, and followed, is on the eve of departing, to be
consigned to the family tomb of 'all the fashions,' where sleep
in peace the _ruffs_ and _hoops_, and _fardingales_ of past
centuries; and
"All its beauty, all its pomp, decays
Like _Courts removing_, or like _ending plays_."
On February 7, 1804, was printed Lamb's "Epitaph on a young Lady who
Lived Neglected and Died Obscure" (see Vol. IV.), and now and then we
find a paragraph likely to be his; but, as we know from a letter from
Mary Lamb to Sarah Stoddart, he had left the _Post_ in the early
spring, 1804. I think this was the end of his journalism, until he
began to write a little for _The Examiner_ in 1812.
In 1838 Stuart was drawn into a correspondence with Henry Coleridge
in the _Gentleman's Magazine_ (May, June, July and August) concerning
some statements about Coleridge's connection with the _Morning Post_
and _The Courier_ which were made in Gillman's _Life_, Stuart, in the
course of straightening out his relations with Coleridge, referred
thus to Lamb:--
But as for good Charles Lamb, I never could make anything out of
his writings. Coleridge often and repeatedly pressed me to settle
him on a salary, and often and repeatedly did I try; but it would
not do. Of politics he knew nothing; they were out of his line of
reading and thought; and his drollery was vapid, when given in
short paragraphs fit for a newspaper; yet he has produced some
agreeable books, possessing a tone of humour and kind feeling,
in a quaint style, which it is amusing to read, and cheering to
remember.
For further remarks concerning Lamb's journalism see below when we
come to _The Albion_ and his connection with it.
Page 250, line 6. _Perry, of the Morning Chronicle._ James Perry
(1756-1821) the editor of the _Morning Chronicle_--the leading Whig
paper, for many years--from about 1789. Perry was a noted talker and
the friend of many brilliant men, among them Porson. Southey's letters
inform us that Lamb was contributing to the _Chronicle_ in the summer
of 1801, and I fancy I see his hand now and then; but his identifiable
contributions to the paper came much later than the period under
notice. Coleridge contributed to it a series of sonnets to eminent
persons in 1794, in one of which, addressed to Mrs. Siddons, he
collaborated with Lamb (see Vol. IV.).
Page 250, line 14. _The Abyssinian Pilgrim_. For notes to this passage
about the New River see the essay "Amicus Redivivus."
Page 250, foot. _In those days ..._ This paragraph began, in the
_Englishman's Magazine_, with the following sentence:--
"We ourself--PETER--in whose inevitable NET already Managers and
R.A.s lie caught and floundering--and more peradventure shall
flounder--were, in the humble times to which we have been
recurring, small Fishermen indeed, essaying upon minnows; angling
for quirks, not _men_."
The phrase "Managers and R.A.s" refers to the papers on Elliston and
George Dawe which had preceded this essay, although the Elliston essay
had not been ranged under the heading "Peter's Net." The George Dawe
paper is in Vol. I. of this edition.
Page 252, line 25. _Basilian water-sponges._ The Basilian order of
monks were pledged to austerity; but probably Lamb intended merely a
joke upon his friend Basil Montagu's teetotalism (see note in Vol.
I. to "Confessions of a Drunkard," a paper quoted in Montagu's _Some
Enquiries into the Effects of Fermented Liquors_). In John Forster's
copy of the _Last Essays of Elia_, in the South Kensington Museum,
a legacy from Elia, there is written "Basil Montagu!" against
this passage. Moreover the context runs, "we were right toping
Capulets"--as opposed to the (Basil) Montagus.
Page 253, line 23. _Bob Allen._ See the essay on "Christ's Hospital"
and note.
Page 253, line 24. _The "Oracle."_ This daily paper was started in the
1780's by Peter Stuart, Daniel Stuart's brother, as a rival to _The
World_ (see below).
Page 253, line 31. _Mr. Deputy Humphreys._ I am disappointed to have
been able to find nothing more about this Common Council butt.
Page 254, lines 11 and 12. _The "True Briton_," _the "Star_," _the
"Traveller_." _The True Briton_, a government organ in the 1790's,
which afterwards assimilated Cobbett's Porcupine. _The Star_ was
founded by Peter Stuart, Daniel Stuart's brother, in 1788. It was
the first London evening paper to appear regularly. _The Traveller_,
founded about 1803, still flourishes under the better-known title of
_The Globe_.
Page 254, lines 24-26. _Este ... Topham ... Boaden_. Edward Topham
(1751-1820), author of the _Life of John Elwes_, the miser, founded
_The World_, a daily paper, in 1787. Parson Este, the Rev. Charles
Este, was one of his helpers. James Boaden (1762-1839), dramatist,
biographer and journalist, and editor of _The Oracle_ for some years,
wrote the _Life of Mrs. Siddons_, 1827.
Page 254, foot. _The Albion_. Lamb's memory of his connection with
_The Albion_ was at fault. His statement is that he joined it on the
sale of the _Morning Post_ by Stuart, which occurred in 1803; but as a
matter of fact his association with it was in 1801. This we know from
his letters to Manning in August of that year, quoting the epigram on
Mackintosh (see below) and announcing the paper's death. Mackintosh,
says Lamb, was on the eve of departing to India to reap the fruits of
his apostasy--referring to his acceptance of the post of Recordership
of Bombay offered to him by Addington. But this was a slip of memory.
Mackintosh's name had been mentioned in connection with at least
two posts before this--a judgeship in Trinidad and the office of
Advocate-General in Bengal, and Lamb's epigram may have had reference
to one or the other. In the absence of a file of _The Albion_, which I
have been unable to find, it is impossible to give exact dates or to
reproduce any of Lamb's other contributions.
Page 255, line 6. _John Fenwick_. See the essay "The Two Races of
Men," and note. Writing to Manning on September 24, 1802, Lamb
describes Fenwick as a ruined man hiding from his creditors. In
January, 1806, he tells Stoddart that Fenwick is "coming to town on
Monday (if no kind angel intervene) to surrender himself to prison."
And we meet him again as late as 1817, in a letter to Barron Field, on
August 31, where his editorship of The Statesman is mentioned. In
Mary Lamb's letters to Sarah Stoddart there are indications that Mrs.
Fenwick and family were mindful of the Lambs' charitable impulses.
After "Fenwick," in the _Englishman's Magazine_, Lamb wrote: "Of him,
under favour of the public, something may be told hereafter." It is
sad that the sudden discontinuance of the magazine with this number
for ever deprived us of further news of this man.
Page 255, line 11. _Lovell_. Daniel Lovell, subsequently owner and
editor of _The Statesman_, which was founded by John Hunt, Leigh
Hunt's brother, in 1806. He had a stormy career, much chequered by
imprisonment and other punishment for freedom of speech. He died in
1818.
Page 255, line 20. _Daily demands of the Stamp Office._ The newspaper
stamp in those days was threepence-halfpenny, raised in 1815 to
fourpence. In 1836 it was reduced to a penny, and in 1855 abolished.
Page 255, line 28. _Accounted very good men now._ A hit, I imagine,
particularly at Southey (see note to "The Tombs in the Abbey"). Also
at Wordsworth and Mackintosh himself.
Page 256, line 3. _Sir J----s M----h_. Sir James Mackintosh
(1765-1832), the philosopher, whose apostasy consisted in his public
recantation of the opinions in favour of the French Revolution
expressed in his _Vindiciae Gallicae_, published in 1791. In 1803 he
accepted the offer of the Recordership of Bombay. Lamb's epigram,
which, as has been stated above, cannot have had reference to this
particular appointment, runs thus in the version quoted in the letter
to Manning of August, 1801:--
Though thou'rt like Judas, an apostate black,
In the resemblance one thing thou dost lack:
When he had gotten his ill-purchased pelf,
He went away, and wisely hang'd himself:
This thou may'st do at last; yet much I doubt,
If thou hash any bowels to gush out.
Page 256, line 6. _Lord ... Stanhope_. This was Charles, third earl
(1753-1816), whose sympathies were with the French Revolution. His
motion in the House of Lords against interfering with France's
internal affairs was supported by himself alone, which led to a medal
being struck in his honour with the motto, "The Minority of One,
1795;" and he was thenceforward named "Minority," or "Citizen,"
Stanhope. George Dyer, who had acted as tutor to his children, was one
of Stanhope's residuary legatees.
Page 256, line 10. _It was about this time ..._ With this sentence
Lamb brought back his essay to its original title, and paved the way
for the second part--now printed under that heading.
At the end of this paper, in the _Englishman's Magazine_, were the
words, "To be continued." For the further history of the essay see the
notes that follow.
* * * * *
Page 256. BARRENNESS OF THE IMAGINATIVE FACULTY IN THE PRODUCTIONS OF
MODERN ART.
_Athenaeum_, January 12, 19, 26, and February 2, 1833, where it was
thus entitled: "On the Total Defects of the Quality of Imagination,
observable in the Works of Modern British Artists." By the Author of
the Essays signed "Elia."
The following editorial note was prefixed to the first
instalment:--"This Series of Papers was intended for a new periodical,
which has been suddenly discontinued. The distinguished writer having
kindly offered them to the ATHENAEUM, we think it advisable to perfect
the Series by this reprint; and, from the limited sale of the work in
which it originally appeared, it is not likely to have been read by
one in a thousand of our subscribers."
The explanation of this passage has been made simple by the researches
of the late Mr. <DW18>s Campbell. Lamb intended the essay originally for
the _Englishman's Magazine_, November number, to follow the excursus
on newspapers. But that magazine came to an end with the October
number. In the letter from Lamb to Moxon dated October 24, 1831, Lamb
says, referring to Moxon's announcement that the periodical would
cease:--"Will it please, or plague, you, to say that when your Parcel
came I damned it, for my pen was warming in my hand at a ludicrous
description of a Landscape of an R.A., which I calculated upon sending
you to morrow, the last day you gave me."
That was the present essay. Subsequently--at the end of 1832--Moxon
started a weekly paper entitled _The Reflector_, edited by John
Forster, in which the printing of Lamb's essay was begun. It lasted
only a short time, and on its cessation Lamb sent the ill-fated
manuscript to _The Athenaeum_, where it at last saw publication
completed. Of _The Reflector_ all trace seems to have vanished, and
with it possibly other writings of Lamb's.
In _The Athenaeum_ of December 22, 1832, the current _Reflector_ (No.
2) is advertised as containing "An Essay on Painters and Painting by
Elia."
Page 256, line 1 of essay. _Hogarth_. Compare Lamb's criticism of
Hogarth, Vol. I.
Page 256, foot. _Titian's "Ariadne."_ This picture is now No. 35
in the National Gallery. Writing to Wordsworth in May, 1833, it is
amusing to note, Lamb says: "Inter nos the Ariadne is not a darling
with me, several incongruous things are in it, but in the composition
it served me as illustrative." The legend of Ariadne tells that after
being abandoned by Theseus, whom she loved with intense passion, she
was wooed by Bacchus.
Page 258, line 2. _Somerset House._ See note above to the essay on
"Newspapers."
Page 258, line 14. _Neoteric ... Mr. ----_. Probably J.M.W. Turner and
his "Garden of the Hesperides," now in the National Gallery. It is
true it was painted in 1806, but Lamb does not describe it as a
picture of the year and Turner was certainly the most notable
neoteric, or innovator, of that time.
Page 259, line 1. _Of a modern artist._ In _The Athenaeum_ this
had been printed "of M----," meaning John Martin (1789-1854). His
"Belshazzar's Feast," which Lamb analyses below, was painted in 1821,
and made him famous. It was awarded a L200 premium, and was copied on
glass and exhibited with great success as an illuminated transparency
in the Strand. Lord Lytton said of Martin that "he was more original,
more self-dependent, than Raphael or Michael Angelo." Lamb had
previously expressed his opinion of Martin, in a letter to Bernard
Barton, dated June 11, 1827, in a passage which contains the germ
of this essay:--"Martin's Belshazzar (the picture) I have seen.
Its architectural effect is stupendous; but the human figures,
the squalling, contorted little antics that are playing at being
frightened, like children at a sham ghost who half know it to be a
mask, are detestable. Then the _letters_ are nothing more than a
transparency lighted up, such as a Lord might order to be lit up on a
sudden at a Christmas Gambol, to scare the ladies. The _type_ is
as plain as Baskervil--they should have been dim, full of mystery,
letters to the mind rather than the eye."
Page 259, line 13. _The late King_. George IV., who built, when Prince
of Wales, the Brighton Pavilion. As I cannot find this incident in any
memoirs of the Regency, I assume Lamb to have invented it, after his
wont, when in need of a good parallel. "Mrs. Fitz-what's-her-name"
stands of course for Mrs. Fitzherbert.
Page 259, line 33. _The ingenious Mr. Farley_. Charles Farley
(1771-1859), who controlled the pantomimes at Covent Garden from 1806
to 1834, and invented a number of mechanical devices for them. He also
acted, and had been the instructor of the great Grimaldi. Lamb alludes
to him in the essay on "The Acting of Munden."
Page 262, line 10. "_Sun, stand thou still ..._" See Joshua x. 12.
Martin's picture of "Joshua commanding the Sun to stand still" was
painted in 1816. Writing to Barton, in the letter quoted from above,
Lamb says: "Just such a confus'd piece is his Joshua, fritter'd into
1000 fragments, little armies here, little armies there--you should
see only the _Sun_ and _Joshua_ ... for Joshua, I was ten minutes
finding him out."
Page 262, line 29. _The great picture at Angerstein's_. This picture
is "The Resurrection of Lazarus," by Fra Sebastiano del Piombo, with
the assistance, it is conjectured, of Michael Angelo. The picture is
now No. 1 in the National Gallery, the nucleus of which collection was
once the property of John Julius Angerstein (1735-1823). Angerstein's
art treasures were to be seen until his death in his house in Pall
Mall, where the Reform Club now stands.
Page 263, line 35. _The Frenchmen, of whom Coleridge's friend_. See
the _Biographia Literaria_, 1847 ed., Vol. II., pp. 126-127.
Page 265, line 5. "_Truly, fairest Lady ..._" The passage quoted by
Lamb is from Skeltoa's translation of _Don Quixote_, Part II., Chapter
LVIII. The first sentence runs: "Truly, fairest Lady, Actaeon was not
more astonished or in suspense when on the sodaine he saw Diana," and
so forth.
Page 266, line 9. "_Guzman de Alfarache_." The Picaresque romance by
Mateo Aleman--_Vida y Lechos del picaro Guzman de Alfarache_, Part I.,
1599; Part II., 1605. It was translated into English by James Mabbe in
1622 as _The Rogue; or, The Life of Guzman de Alfarache_. Lamb had a
copy, which is now in my possession, with Mary Lamb's name in it.
* * * * *
Page 266. REJOICINGS UPON THE NEW YEAR'S COMING OF AGE.
_London Magazine_, January, 1823.
This paper, being printed in the same number as that which announced
Elia's death, was signed "Elia's Ghost."
Lamb returned to this vein of fancy two years or so later when (in
1825) he contributed to his friend William Hone's _Every-Day Book_
the petition of the Twenty-Ninth of February, a day of which Hone had
taken no account, and of the Twelfth of August, which from being kept
as the birthday of King George IV. during the time that he was Prince
of Wales, was, on his accession to the throne, disregarded in favour
of April 23, St. George's Day. For these letters see Vol. I. of this
edition.
Page 271, line 15. "_On the bat's back ..._" From Ariel's song in
"The Tempest." Lamb confesses, in at least two of his letters, to a
precisely similar plight.
* * * * *
Page 271. THE WEDDING.
_London Magazine_, June, 1825.
The wedding was that of Sarah Burney, daughter of Lamb's old friends,
Rear-Admiral James Burney and his wife Sarah Burney, to her cousin,
John Payne, of Pall Mall, at St. Margaret's, Westminster, in April,
1821. The clergyman was the Rev. C.P. Burney, who was not, however,
vicar of St. Mildred's in the Poultry, but of St. Paul's, Deptford, in
Kent. Admiral Burney lived only six months longer, dying in November.
Canon Ainger pointed out that when Lamb was revising this essay for
its appearance in the _Last Essays of Elia_, he was, like the admiral,
about to lose by marriage Emma Isola, who was to him and his sister
what Miss Burney had been to her parents. She married Edward Moxon in
July, 1833.
Page 274, line 8. _An unseasonable disposition to levity_. Writing to
P.G. Patmore in 1827 Lamb says: "I have been to a funeral, where I
made a pun, to the consternation of the rest of the mourners." Again,
writing to Southey: "I am going to stand godfather; I don't like the
business; I cannot muster up decorum for these occasions; I shall
certainly disgrace the font; I was at Hazlitt's marriage and was like
to have been turned out several times during the ceremony. Anything
awful makes me laugh. I misbehaved once at a funeral."
Page 274, line 24. _Miss T----s_. In the _London Magazine_ "Miss
Turner's."
Page 274, line 27. _Black ... the costume of an author_. See note
below.
Page 274, line 29. _Lighter colour_. Here the _London Magazine_ had:
"a pea-green coat, for instance, like the bridegroom."
Page 274, line 34. _A lucky apologue_. I do not find this fable; but
Lamb's father, in his volume of poems, described in a note on page
381, has something in the same manner in his ballad "The Sparrow's
Wedding":--
The chatt'ring Magpye undertook
Their wedding breakfast for to cook,
He being properly bedight
In a cook's cloathing, black and white.
Page 275, foot. _The Admiral's favourite game_. Admiral Burney wrote a
treatise on whist (see notes to "Mrs. Battle's Opinions on Whist").
* * * * *
Page 276. THE CHILD ANGEL.
_London Magazine_, June, 1823.
Thomas Moore's _Loves of the Angels_ was published in 1823. Lamb used
it twice for his own literary purposes: on the present occasion, with
tenderness, and again, eight years later, with some ridicule, for
his comic ballad, "Satan in Search of a Wife," 1831, was ironically
dedicated to the admirers of Moore's poem (see Vol. IV.).
* * * * *
Page 279. A DEATH-BED.
Hone's _Table Book_, Vol. I., cols. 425-426, 1827. Signed "L.," and
dated London, February 10, 1827. The essay is very slightly altered
from a letter written by Lamb to Crabb Robinson, January 20, 1827,
describing the death of Randal Morris. It was printed in the first
edition only of the _Last Essays of Elia_; its place being taken
afterwards by the "Confessions of a Drunkard," an odd exchange. The
essay was omitted, in deference, it is believed, to the objection of
Mrs. Norris to her reduced circumstances being made public. As the
present edition adheres to the text of the first edition, "The
Death-Bed" is included in its original place as decided by the author.
The "Confessions of a Drunkard" will be found in Vol. I.
Randal Norris was for many years sub-treasurer of the Inner Temple
(see postscript to the essay on the "Old Benchers"). Writing to
Wordsworth in 1830 Lamb spoke of him as "sixty years ours and our
father's friend." An attempt has been made to identify him with the
Mr. Norris of Christ's Hospital who was so kind to the Lambs after the
tragedy of September, 1796. I cannot find any trace of Randal Norris
having been connected with anything but the law and the Inner Temple;
but possibly the Mr. Norris of the school was a relative.
Mrs. Randal Norris was connected with Widford, the village adjoining
Blakesware, where she had known Mary Field, Lamb's grandmother. It was
thither that she and her son retired after Randal Norris's death, to
join her daughters, Miss Betsy and Miss Jane, who had a school for
girls known as Goddard House School. Lamb kept up his friendship with
them to the end, and they corresponded with Mary Lamb after his death.
Mrs. Norris died in 1843, aged seventy-eight, and was buried at
Widford. The grave of Richard Norris, the son, is also there. He died
in 1836. One of the daughters, Elizabeth, married Charles Tween, of
Widford, and lived until 1894. The other daughter, Jane, married
Arthur Tween, his brother, and lived until 1891.
Mary Lamb was a bridesmaid at the Norris's wedding and after the
ceremony accompanied the bride and bridegroom to Richmond for the day.
So one of their daughters told Canon Ainger.
Crabb Robinson seems to have exerted himself for the family, as Lamb
wished. Mr. W.C. Hazlitt says that an annuity of L80 was settled upon
Mrs. Norris.
Page 279, last line. _To the last he called me Jemmy_. In the letter
to Crabb Robinson--"To the last he called me Charley. I have none to
call me Charley now."
Page 280, line 2. _That bound me to B----_. In the letter to Crabb
Robinson--"that bound me to the Temple."
Page 280, line 14. _Your Corporation Library_. In the letter--"The
Temple Library."
Page 280, line 19. _He had one Song_. Garrick's "Hearts of Oak."
* * * * *
Page 281. OLD CHINA.
_London Magazine_, March, 1823.
This essay forms a pendant, or complement, to "Mackery End in
Hertfordshire," completing the portrait of Mary Lamb begun there.
It was, with "The Wedding," Wordsworth's favourite among the _Last
Essays_.
Page 282, line 23. _The brown suit_. P.G. Patmore, in his
recollections of Lamb in the _Court Journal_, 1835, afterwards
reprinted, with some alterations, in his _My Friends and
Acquaintances_, stated that Lamb laid aside his snuff- suit
in favour of black, after twenty years of the India House; and he
suggests that Wordsworth's stanzas in "A Poet's Epitaph" was the
cause:--
But who is he, with modest looks,
And clad in homely russet brown?
He murmurs near the running brooks
A music sweeter than their own.
He is retired as noontide dew,
Or fountain in a noon-day grove;
And you must love him, ere to you
He will seem worthy of your love.
Whatever Patmore's theory may be worth, it is certain that Lamb
adhered to black after the change.
Page 282, line 25. _Beaumont and Fletcher_. See note to "Books and
Reading."
Page 282, line 27. _Barker's_. Barker's old book-shop was at No. 20
Great Russell Street, over which the Lambs went to live in 1817. It
had then, however, become Mr. Owen's, a brazier's (Wheatley's _London
Past and Present_ gives Barker's as 19, but a contemporary directory
says 20). Great Russell Street is now Russell Street.
Page 282, line 30. _From Islington_. This would be when Lamb and his
sister lived at 36 Chapel Street, Pentonville, a stone's throw from
the Islington boundary, in 1799-1800, after the death of their father.
Page 283, line 11. _The "Lady Blanch._" See Mary Lamb's poem on this
picture, Vol. IV. and note.
Page 283, line 15. _Colnaghi's_. Colnaghi, the printseller, then in
Cockspur Street, now Pall Mall East. After this word came in the
_London Magazine_ "(as W---- calls it)." The reference, Mr. Rogers
Rees tells me, is to Wainewright's article "C. van Vinkbooms, his
Dogmas for Dilletanti," in the same magazine for December, 1821, where
he wrote: "I advise Colnaghi and Molteno to import a few impressions
immediately of those beautiful plates from Da Vinci. The ... and Miss
Lamb's favourite, 'Lady Blanche and the Abbess,' commonly called
'Vanitas et Modestia' (Campanella, los. ed.), for I foresee that this
Dogma will occasion a considerable call for them--let them, therefore,
be ready."
Page 283, line 5 from foot. _To see a play_. "The Battle of Hexham"
and "The Surrender of Calais" were by George Colman the Younger; "The
Children in the Wood," a favourite play of Lamb's, especially with
Miss Kelly in it, was by Thomas Morton. Mrs. Bland was Maria Theresa
Bland, _nee_ Romanzini, 1769-1838, who married Mrs. Jordan's brother.
Jack Bannister we have met, in "The Old Actors."
Page 286, line 12. _The Great yew R----_. This would be Nathan Meyer
Rothschild (1777-1836), the founder of the English branch of the
family and the greatest financier of modern times.
* * * * *
Page 286. POPULAR FALLACIES.
This series of little essays was printed in the _New Monthly Magazine_
in 1826, beginning in January. The order of publication there was not
the same as that in the _Last Essays of Elia_; one of the papers,
"That a Deformed Person is a Lord," was not reprinted by Lamb at all
(it will be found in Vol. I. of this edition); and two others were
converted into separate essays (see "The Sanity of True Genius" and
"The Genteel Style in Writing").
After Lamb's death a new series of Popular Fallacies was contributed
to the _New Monthly Magazine_ by L.B. (Laman Blanchard) in 1835,
preceded by an invocation to the spirit of Charles Lamb.
Page 286. I.--THAT A BULLY is ALWAYS A COWARD.
_New Monthly Magazine_, January, 1826.
Page 287, line 1. _Hickman_. This would be Tom Hickman, the pugilist.
In Hazlitt's fine account of "The Fight," Hickman or the Gas-Man,
"vapoured and swaggered too much, as if he wanted to grin and bully
his adversary out of the fight." And again, "'This is the _grave
digger_' (would Tom Hickman exclaim in the moments of intoxication
from gin and success, showing his tremendous right hand); 'this will
send many of them to their long homes; I haven't done with them yet.'"
But he went under to Neale, of Bristol, on the great day that Hazlitt
describes.
Page 287, line 2. _Him of Clarissa_. Mr. Hickman, in Richardson's
novel _Clarissa_, the lover of Miss Bayes.
Page 287. II.--THAT ILL-GOTTEN GAIN NEVER PROSPERS.
_New Monthly Magazine_, January, 1826.
Page 287. III.--THAT A MAN MUST NOT LAUGH AT HIS OWN JEST.
_New Monthly Magazine_, January, 1826.
Page 288, line 12. _In Mandeville_. In Bernard Mandeville's Fable of
the Bees, a favourite book of Lamb's. See Vol. I., note to "The Good
Clerk."
Page 288. IV.--THAT SUCH A ONE SHOWS HIS BREEDING, ETC.
_New Monthly Magazine_, January, 1826.
Page 288. V.--THAT THE POOR COPY THE VICES OF THE RICH.
_New Monthly Magazine_, January, 1826.
Page 290. VI.--THAT ENOUGH is AS GOOD AS A FEAST.
_New Monthly Magazine_, January, 1826.
Page 291. VII.--OF TWO DISPUTANTS, THE WARMEST IS GENERALLY IN THE
WRONG.
_New Monthly Magazine_, January, 1826.
Page 291, line 4 from foot. _Little Titubus_. I do not know who this
was, if any more than an abstraction; but it should be remembered that
Lamb himself stammered.
Page 292. VIII.--THAT VERBAL ALLUSIONS ARE NOT WIT, ETC.
_New Monthly Magazine_, January, 1826.
Page 292. IX.--THAT THE WORST PUNS ARE THE BEST.
_New Monthly Magazine_, January, 1826.
Compare the reflections on puns in the essay on "Distant
Correspondents." Compare also the review of Hood's _Odes and
Addresses_ (Vol. I.). Cary's account of a punning contest after Lamb's
own heart makes the company vie with each in puns on the names
of herbs. After anise, mint and other words had been ingeniously
perverted Lamb's own turn, the last, was reached, and it seemed
impossible that anything was left for him. He hesitated. "Now then,
let us have it," cried the others, all expectant. "Patience," he
replied; "it's c-c-cumin."
Page 293, line 18. _One of Swift's Miscellanies_. This joke, often
attributed to Lamb himself, will be found in _Ars Punica, sine flos
Linguarum, The Art of Punning; or, The Flower of Languages_, by Dr.
Sheridan and Swift, which will be found in Vol. XIII. of Scott's
edition of Swift. Among the directions to the punster is this:--
Rule 3. The Brazen Rule. He must have better assurance, like Brigadier
C----, who said, "That, as he was passing through a street, he made to
a country fellow who had a hare swinging on a stick over his shoulder,
and, giving it a shake, asked him whether it was his own _hair_ or a
periwig!" Whereas it is a notorious Oxford jest.
Page 294, line 8. _Virgil ... broken Cremona_. Swift (as Lamb
explained in the original essay in the _New Monthly Magazine_), seeing
a lady's mantua overturning a violin (possibly a Cremona), quoted
Virgil's line: "Mantua vae miserae nimium vicina Cremonae!" (_Eclogues_,
IX., 28), "Mantua, alas! too near unhappy Cremona."
Page 294. X.--THAT HANDSOME IS THAT HANDSOME DOES.
_New Monthly Magazine_, March, 1826.
Whether a Mrs. Conrady existed, or was invented or adapted by Lamb to
prove his point, I have not been able to discover. But the evidence of
Lamb's "reverence for the sex," to use Procter's phrase, is against
her existence. _The Athenaeum_ reviewer on February 16, 1833, says,
however, quoting the fallacy: "Here is a portrait of Mrs. Conrady. We
agree with the writer that 'no one that has looked on her can pretend
to forget the lady.'" The point ought to be cleared up.
Page 296. XI.--THAT WE MUST NOT LOOK A GIFT-HORSE IN THE MOUTH.
_New Monthly Magazine_, April, 1826.
Page 297, line 13. _Our friend Mitis_. I do not identify Mitis among
Lamb's many friends.
Page 297, line 11 from foot. _Presentation copies_. The late Mr.
Thomas Westwood, the son of the Westwoods with whom the Lambs lived
at Edmonton, writing to Notes and Queries some thirty-five years ago,
gave an amusing account of Lamb pitching presentation copies out of
the window into the garden--a Barry Cornwall, a Bernard Barton, a
Leigh Hunt, and so forth. Page 298, line 6. _Odd presents of game_.
Compare the little essay on "Presents of Game," Vol. I.
Page 298. XII.--THAT HOME IS HOME THOUGH IT IS NEVER SO HOMELY.
_New Monthly Magazine_, March, 1826. In that place the first sentence
began with the word "Two;" the second ended with "of our assertions;"
and (fourteenth line of essay) it was said of the very poor man
that he "can ask" no visitors. Lamb, in a letter, wished Wordsworth
particularly to like this fallacy and that on rising with the lark.
Page 300, line 9. _It has been prettily said_. By Lamb himself, or
more probably by his sister, in _Poetry for Children_, 1809. See "The
First Tooth," Vol. III., which ends upon the line
A child is fed with milk and praise.
Page 301, line 3. _There is yet another home_. Writing to Mrs.
Wordsworth on February 18, 1818, Lamb gives a painful account, very
similar in part to this essay, of the homeless home to which he was
reduced by visitors. But by the time he wrote the essay, when all his
day was his own, the trouble was not acute. He tells Bernard Barton
on March 20, 1826, "My tirade against visitors was not meant
_particularly_ at you or A.K. I scarce know what I meant, for I do not
just now feel the grievance. I wanted to make an _article_." Compare
the first of the "Lepus" papers in Vol. I.
Page 301, line 20. _It is the refreshing sleep of the day_. After this
sentence, in the magazine, came this passage:--
"O the comfort of sitting down heartily to an old folio, and
thinking surely that the next hour or two will be your own--and
the misery of being defeated by the useless call of somebody, who
is come to tell you, that he is just come from hearing Mr. Irving!
What is that to you? Let him go home, and digest what the good man
said to him. You are at your chapel, in your oratory."
Mr. Irving was the Rev. Edward Irving (1792-1834), whom Lamb knew
slightly and came greatly to admire.
Page 302. XIII.--THAT YOU MUST LOVE ME, AND LOVE MY DOG.
_New Monthly Magazine_, February, 1826.
Compare "A Bachelor's Complaint." I cannot identify the particular
friend whom Lamb has hidden under asterisks; although his cousin would
seem to have some likeness to one of the Bethams mentioned in the
essay "Many Friends" (Vol. I.), and in the letter to Landor of
October, 1832 (usually dated April), after his visit to the Lambs.
Page 304, line 15. _Honorius dismiss his vapid wife_. Writing to
Bernard Barton on March 20, 1826, Lamb says:--"In another thing I
talkd of somebody's _insipid wife_, without a correspondent object in
my head: and a good lady, a friend's wife, whom I really _love_ (don't
startle, I mean in a licit way) has looked shyly on me ever since. The
blunders of personal application are numerous. I send out a character
every now and then, on purpose to exercise the ingenuity of my
friends."
Page 304, line 11 from foot. _Merry, of Delia Cruscan memory_. Robert
Merry (1755-1798), an affected versifier who settled in Florence as a
young man, and contributed to the _Florence Miscellany_. He became
a member of the Delia Cruscan Academy, and on returning to England
signed his verses, in _The World_, "Delia Crusca." A reply to his
first effusion, "Adieu and Recall to Love," was written by Mrs. Hannah
Cowley, author of _The Belle's Stratagem_, and signed "Anna Matilda;"
this correspondence continued; a fashion of sentiment was thus
started; and for a while Delia Cruscan poetry was the rage. The
principal Delia Cruscan poems were published in the _British Album_
in 1789, and the collection was popular until Gifford's _Baviad_
(followed by his _Maeviad_) appeared in 1791, and satirised its
conceits so mercilessly that the school collapsed. A meeting with Anna
Matilda in the flesh and the discovery that she was twelve years his
senior had, however, put an end to Merry's enthusiasm long before
Gifford's attack. Merry afterwards threw in his lot with the French
Revolution, and died in America. He married, as Lamb says, Elizabeth
Brunton, an excellent tragic actress, in 1791. But that was in
England. The journey to America came later.
The story of Merry's avoidance of the lady of his first choice is
probably true. Carlo Antonio Delpini was a famous pantomimist in his
day at Drury Lane, Covent Garden and the Haymarket. He also was
stage manager at the Opera for a while, and occasionally arranged
entertainments for George IV. at Brighton. He died in 1828.
Page 305. XIV.--THAT WE SHOULD RISE WITH THE LARK.
_New Monthly Magazine_, February, 1826.
Compare "The Superannuated Man," to which this little essay, which,
with that following, is one of Lamb's most characteristic and perfect
works, serves as a kind of postscript.
Page 308. XV.--THAT WE SHOULD LIE DOWN WITH THE LAMB.
_New Monthly Magazine_, February, 1826.
Page 309. XVI.--THAT A SULKY TEMPER IS A MISFORTUNE.
_New Monthly Magazine_, September, 1826.
This was the last of the series and Lamb's last contribution to the
_New Monthly Magazine_.
APPENDIX
Page 315. ON SOME OF THE OLD ACTORS, ETC.
See notes to the essays "On Some of the Old Actors," "The Artificial
Comedy" and "The Acting of Munden." Two portions of these essays, not
reprinted by Lamb, call for comment: the story of the first night of
"Antonio," and the account of Charles Mathews' collection of pictures.
Page 328, line 14 from foot. _My friend G.'s "Antonio."_ William
Godwin's tragedy, produced on December 13, 1800, at Drury Lane. Lamb
had written the epilogue (see Vol. IV.). Compare the letter to Manning
of December 16, 1800.
Page 329, line 28. _M. wiped his cheek_. Writing to Godwin after the
failure Lamb says: "The breast of Hecuba, where she did suckle Hector,
looked not to be more lovely than Marshal's forehead when it spit
forth sweat, at Critic-swords contending. I remember two honest lines
by Marvel ...
"'Where every Mower's wholesome heat
Smells like an Alexander's sweat.'"
And again, to Manning: "His [Marshal's] face was lengthened, and all
over perspiration; I never saw such a care-fraught visage; I could
have hugged him, I loved him so intensely. 'From every pore of him a
perfume fell.'"
Page 329, foot. _R----s the dramatist_. I imagine this to be Frederic
Reynolds (1764-1841), author of "The Dramatist" and many other plays.
We know Lamb to have known him later, from a mention in a letter to
J.B. Dibdin.
Page 330, foot, _Brutus ... Appius_. Brutus in "Julius Caesar," or
possibly in the play called "Brutus," by John Howard Payne, Lamb's
friend (produced December 3, 1818), in which Brutus kills his son--a
closer parallel. Appius was probably a slip of the pen for Virginius,
who in Sheridan Knowles' drama that bears his name kills his daughter
to protect her from Appius.
Page 331, line 7. _G. thenceforward_. Godwin did, however, write
another play, "Faulkener," for which Lamb wrote the prologue. It was
moderately successful.
Page 331, 1st line of essay. _I do not know, etc_. The paragraph
beginning with these words is often printed by editors of Lamb as
a separate article entitled "The Old Actors." Charles Mathews'
collection of theatrical portraits is now in the Garrick Club. In
his lifetime it occupied the gallery at Ivy Lodge, Highgate (or more
properly Kentish Town). A year or so before Mathews' death in 1835,
his pictures were exhibited at the Queen's Bazaar in Oxford Street,
Lamb's remarks being printed in the catalogue _raisonne_.
INDEX
A
Accountants, Lamb on, 3.
Actors and acting, Lamb's essays on, 150, 161, 168, 185, 188, 190, 230,
315, 322, 331.
Actors among Lamb's friends, 232.
Adams, Parson, 49.
Agar's wish, 348.
Aguecheek, Lamb on, 155.
Ainger, Canon, his notes on Lamb, 345, 353, 361, 403, 436, 438.
_Albion, The_, and Lamb, 254, 429, 432.
Alice W----n, 32, 44, 116, 117, 339, 363, 389.
ALL FOOLS' DAY, 48, 367.
Allen, Bob, 25, 253, 355, 431.
Allsop, Thomas, quoting Lamb, 357.
---- and "Roast Pig," 396.
---- quotes Lamb on G.H., 425.
Almsgiving, Lamb on, 137.
Alsatia, the debtors' sanctuary, 162.
America, Lamb relics in, 344, 357, 358, 362, 412.
AMICUS REDIVIVUS, 237, 424.
Anatomy and love, 64.
_Anatomy of Melancholy_ quoted, 46.
Andre, Major, 237, 424.
Anna Matilda, 443.
Antiquity, Lamb on, 11.
"Antonio," by Godwin, 328, 444.
_Arcadia, The_, by Sidney, 242.
Arrowsmith, Aaron, 369.
"Artaxerxes," 113, 387.
Artificial comedy, Lamb's essay on, 161, 399.
Artists, their want of imagination, 256.
Arundel Castle and the chimney-sweep legend, 127.
_As when a child on some long winter's night_, 388.
_Athenaeum, The_, Lamb's contribution to, 433.
_Athenian Oracle, The_, 303.
Australia, Lamb on, 122.
Ayrton, William, 361, 363.
B
BACHELOR'S COMPLAINT OF THE BEHAVIOUR OF MARRIED PEOPLE, 144, 397.
Badams, Mrs., 362.
Baldwin, Cradock & Joy, 340.
Bannister, Jack, 159, 185, 399, 408.
BARBARA S----, 230, 421.
Barker's book-shop, 282, 439.
BARRENNESS OF THE IMAGINATIVE FACULTY IN THE PRODUCTIONS OF MODERN ART,
256, 433.
Barrington, Daines, 101, 383.
Bartholomew Fair, 128, 391.
Barton, Bernard, Lamb's letters to, 341, 406, 417, 420, 435, 442.
-- Thomas, 102, 383.
Baskett prayer-book, 9.
Battle, Mrs., 37, 175, 406.
---- on whist, 37.
---- her identity, 361.
Beaumont and Fletcher, Lamb's copy, 357.
Beauty, Lamb on, 295.
"Beggar's Petition," 394.
Begging, Lamb's essay on, 130, 392.
Belisarius, 131.
"Belshazzars Feast," Martin's picture of, 259, 434.
Benchers, The Old, Lamb's essay on, 94.
Bensley, Robert, 152, 318, 398.
Betty, Master, 414.
Bigod, Ralph, Lamb's name for Fenwick, 27, 356.
Billet, John, 184.
Binding, Lamb on, 412.
_Blackwood's Magazine_ and Scott, 340.
Blake, William, and Lamb, 391.
BLAKESMOOR IN H----SHIRE, 174, 405.
Blakesware near Widford, 115, 174, 388, 405.
Bland, Mrs., 283, 439.
Blandy, Miss, the poisoner, 98, 380.
Bodkin, W.H., 392.
_Book of Sports, The_, 418.
Books, Lamb on, 34, 360.
-- that are not books, 195, 411.
Booth's _Tables of Interest_ and Lamb, 419.
Borrowing, Lamb on, 26.
Bourne, Vincent, 133, 393.
Bowles, William Lisle, 38, 362.
Boyer, James, 23, 353.
Braham, John, 71, 371.
Breeding, Lamb on, 288.
Bridget, Elia. _See_ Elia.
Brighton and the Lambs, 415.
-- Lamb's imaginery scene there, 259.
British Museum, a careful vandal, 357.
Browne, Moses, 404.
-- Sir Thomas, 58, 66, 80.
Bruce, James, 240, 425.
Bruton, Miss Sarah, 376.
Brutons, Lamb's relations, 88, 89.
Buckland, Dean, and the American vandal, 424.
Bullies, Lamb on, 286, 440.
_Buncle, The Life of_, 30, 357.
Burney, Edward, 65, 370.
-- James, 361.
Burney, Martin, 200, 414.
-- Mrs., and Mrs. Battle, 361.
-- Sarah, her wedding, 271, 436.
Burns, Robert, and Lamb, 70, 370.
Burton, Robert, quoted, 46, 77.
_Business! the frivolous pretence_, 419.
Button Snap, Lamb's cottage, 385, 386, 387.
_But who is he, with modest looks_, 438.
C
Cambridge, Lamb at, 345.
Camelford, Lord, 121, 390.
Candle-light, Lamb on, 308.
CAPTAIN JACKSON, 215, 416.
Card playing, essay on, in _Every-Day Book_, 362.
Carlisle, Sir Anthony, 193, 372, 410.
Cary, H.F., his verses on Lamb, 426.
-- on Lamb's puns, 441.
Cave, Edward, 344.
Chambers, John, 224, 419.
Chapman's _Homer_ kissed by Lamb, 412.
CHAPTER ON EARS, A, 43, 363.
CHARACTER OF THE LATE ELIA, A, 171, 402.
Chess and Mrs. Battle, 42.
CHILD ANGEL, THE, 276, 437.
Children and the dark, 77.
Chimney-sweepers, Lamb's essay on, 124, 390.
CHINA, OLD, 281, 438.
-- its first roast pork, 138.
CHRIST'S HOSPITAL FIVE AND THIRTY YEARS AGO, 14, 350.
---- prayer-book, 9.
---- food in Lamb's day, 14, 350.
---- holidays in Lamb's day, 15, 351.
---- the dungeon, 19.
---- flogging, 23.
---- Grecians, 26, 355.
---- its graces, 110, 384.
---- the Coleridge memorial, 354.
---- the Lamb medal, 355.
Clapdishes, 131.
"Cobbler of Preston," by Johnson, 170, 401.
Cockletop, in "Modern Antiques," 168, 400.
Colebrooke cottage, 425.
Coleridge, Hartley, on Lamb, 400.
-- S.T., at Christ's Hospital, 15, 350, 351.
-- his wit combats, 25.
-- his treatment of books, 29, 356.
-- his "Ode on the Departing Year," 31, 359.
-- on apple-dumplings, 108, 384.
-- his "Epitaph on an Infant," 141, 397.
-- on Boyer, 353.
-- and the Christ's Hospital memorial, 354.
-- his military name, 356.
-- Lamb's letters to, 356, 368, 396.
-- his marginalia, 358.
-- his notes in Beaumont and Fletcher, 357.
------ in Donne, 358.
-- on Lamb, 359.
-- Lamb's letter to, concerning Quakers, 368.
-- and Christopher North, 371.
-- his sonnets with Lamb, 388.
-- and the _Morning Post_, 429, 430.
Colet, Dean, his _Accidence_, 59.
Colnaghi's print shop, 283, 439.
Comberback, Coleridge's military name, 29, 356.
_Come, all degrees now passing by_, 391.
Comedy and its licence, 161.
COMPLAINT OF THE DECAY OF BEGGARS IN THE METROPOLIS, 130, 392.
CONFESSIONS OF A DRUNKARD, 437.
Congreve, Lamb on, 160, 162.
Conrady, Mrs., 294, 441.
CONVALESCENT, THE, 208, 416.
Corbet, Peter, 404.
Coventry, Thomas, 97, 380.
Cowards and bullies, 286.
Cowley, on business, 419.
Crawford, Anne, 423.
Cresseid, 131.
Curry, Sir Christopher, in "Inkle and Yarico," 169, 401.
D
Da Vinci, Leonardo, and Lamb's beauty, 69, 370.
Dawson, Bully, 287.
Days, Lamb's fantasy upon, 266.
DEATH-BED, A, 279, 437.
Delia Cruscan poetry, 443.
Delpini, 305, 443.
Dennis, John, 292.
De Quincey on Lamb, 377.
DETACHED THOUGHTS ON BOOKS AND READING, 195, 411.
Dickens anticipated by Lamb, 356, 417.
Disputes, Lamb on, 291.
DISSERTATION UPON ROAST PIG, 137, 395.
DISTANT CORRESPONDENTS, 118, 389.
Dobell, Mr. Bertram, his notes on Lamb, 342, 395, 408.
Doctor, the, at Islington, 238.
Dodd, James William, 155.
Dodwell, Henry, 224, 419.
Dornton in "The Road to Ruin," 169, 401.
Dorrell, William, the Lambs' enemy, 32, 360.
DREAM-CHILDREN, 115, 388.
Dreams, Lamb on, 79.
Drowning in dreams, 241.
Drury Lane Theatre, 111, 385.
Dyer, George, 11, 237, 241, 347, 348, 349, 424, 425, 433.
---- and the New River, 237, 424.
E
Early rising, Lamb on, 305.
East India House, Lamb at, 219.
------ Lamb's superannuation, 219, 417.
------ Lamb's fellow clerks, 223, 224, 403, 404.
Edwards, Thomas, 92, 379.
Eel-soup, 374.
Elgin marbles, 225, 419.
ELIA, 1823, suggested dedication, 337.
-- its poor reception, 338.
-- second series. American edition, 339.
Elia, F.A., 337.
-- Lamb on, 8.
-- his death, 171.
-- Lamb's character of, 171, 402.
-- origin of name, 337.
-- his birthplace, 365.
-- Bridget (Mary Lamb), 43, 362.
---- her taste in reading, 86.
---- her regrets for poverty, 282.
ELLISTON, TO THE SHADE OF, 188, 409.
ELLISTONIANA, 190, 410.
Elliston, R.W., Lamb's essays on, 188, 190, 409, 410.
---- at Leamington, 190.
---- his grave, 411.
---- Lamb and Munden on an excursion, 410.
Elton, Sir C.A., his poem to Lamb, 358.
Emery, John, 186, 409.
Endor, the Witch of, 75, 372.
_Englishman's Magazine_, 342.
---- Lamb's contributions to, 188, 190, 249.
Evans, William, 3, 343.
Evelyn, John, quoted, 72.
_Every-Day Book_, essay on card-playing, 362.
_Examiner, The_, and Lamb's "Chimney-Sweepers," 392.
---- Lamb's contributions to, 63, 168.
---- "On a visit to St. Paul's," 424.
Example, Lamb on, 288.
Excursions, the Lambs', 283.
F
_Faerie Queene_, Lamb's copy, 413.
FALLACIES, POPULAR. _See_ POPULAR FALLACIES.
_Family Pictures_, by Anne Manning, 378.
Farley, Charles, 169, 259, 401, 435.
"Father, A," his remonstrance with Lamb, 360.
Favell, Joseph, 25, 181, 355, 408.
Feasting, Lamb on, 290.
Fenwick, John, 27, 129, 255, 356, 432.
Field, Barron, 90, 118, 363, 377, 389.
-- Mary, 361, 405.
-- Matthew, 20, 352.
Fielde, Francis, Lamb's godfather, 111, 385.
Flecknoe, quoted, 51.
Flogging, Lamb on, 23.
Fools, Lamb's essay on, 48, 367.
Fountains, Lamb on, 96.
Fox, George, 53, 368.
French translation of Lamb, 415.
Fuller, Thomas, quoted, 71.
Funerals and Lamb, 274, 436.
G
Gallantry, Lamb on, 90, 377.
"Garden, The," by Marvell, 96.
Gattie, Henry, 186, 408.
Gebir and the Tower of Babel, 49.
_Gebir_, by Landor, 206, 415.
GENTEEL STYLE IN WRITING, THE, 226, 420.
Gentility, Lamb on, 176.
George IV., 259, 268, 435, 436.
Gladmans, Lamb's relations, 88, 89, 90.
_Gli Elogi del Porco_, 396.
Gluttony and grace, Lamb on, 105.
Godwin, William, his play "Antonio," 328, 444.
-- Lamb's friend, 376.
-- Lamb's letter to, 444.
Gold's _London Magazine_, 395.
GRACE BEFORE MEAT, 104, 384.
Graces at Christ's Hospital, 110, 384.
Gray's Inn Gardens, 155, 399.
Grecians at Christ's Hospital, 26, 355.
Greg, Mr. Thomas, and Lamb's property, 385.
Guildhall giants, 29.
_Gulliver's Travels_, 382.
H
Hare Court, Lamb's rooms in, 390.
"Harlequin's Invasion," 113, 387.
Hastings and the Lambs, 206, 416.
Hawes, Dr., 241.
Hazlitt, William, on Sidney, 247, 427.
---- on Lamb in the country, 345.
---- knocked down by John Lamb, 347.
---- his interest in John Buncle, 357.
---- as Duns Scotus, 367.
---- Lamb's letter to, 397.
---- on Lamb, 403.
---- his wedding, 436.
-- W.C., his notes on Lamb, 357, 438.
Helicon and Hippocrene confused, 37.
Hertfordshire hair, 178.
-- and Lamb, 220, 418.
-- Lamb's praise of, 375.
_He was (woe worth that word!) to each well-thinking mind_, 428.
Heywood, Thomas, quoted, 67.
Hickman, Tom, the prize fighter, 287, 440.
_High-born Helen, round your dwelling_, 407.
Hodges (or Huggins), 352.
Hogarth, his chimney-sweeper, 126.
Hogsflesh and Bacon, 415.
Hogs Norton and the pigs, 109.
Holcroft, Thomas, 376.
Hone's _Table Book_, Lamb's contribution to, 279.
Hood, Thomas, his friendship with Lamb, 393.
---- on beggars, 393.
Hooker, Richard, 104, 384.
Hoole, John, 404.
Horsey, Samuel, 135, 393.
Huggins (or Hodges), 352.
Hugh of Lincoln, 70, 371.
Hume, David, 70, 371.
-- Joseph, Lamb's friend, 394.
Humphreys, Mr. Deputy, 253.
Hunt, Leigh, and Lamb, 360.
---- chaffed by Lamb, 364.
Hunt, Leigh, replies to Lamb, 365.
---- and Lamb's "Chimney Sweepers," 392.
---- on Lamb's books, 412.
---- his translation of Milton, 426.
-- Thornton, 77, 372.
Hutchinson, Sarah, Lamb's letter to, 417.
I
_I can remember when a child the maids_, 372.
_I have not forgot how thou didst love thy Charles_, 350.
Illusion on the stage, 185.
Imagination, its lack in the artists of Lamb's day, 256.
Imitators of Lamb, 339.
IMPERFECT SYMPATHIES, 66, 370.
Ino Leucothea, 79.
Ireland, Dean, 423.
Irving, Edward, and Lamb, 442.
Isola, Emma, 436.
J
JACKSON, CAPTAIN, 215, 416.
-- "Omniscient," 102, 383.
"Janus Weathercock." _See_ Wainewright.
Jekyll, Joseph, 97, 379.
_John Woodvil_ quoted, 368, 372.
Johnson, Dr. Samuel, 250, 344, 383.
Jokes to order, Lamb on, 252.
Jonson, Ben, quoted, 89.
Jordan, Mrs., 151, 398.
Joshua, Martin's picture of, 262, 435.
Journalism and Lamb, 251.
K
Kelly, Fanny, and BARBARA S----, 421.
---- and Mrs. Siddons, 422.
Kemble, John Philip, 153, 168, 327, 398.
Kenney, James, 30, 357.
Kent, Charles, his edition of Lamb, 421.
King, Thomas, 166, 400.
L
"Lady of the Manor," 113, 387.
Lamb, Charles, on the South-Sea House, 1.
---- on accountants, 3.
---- on Elia, 8.
---- on Oxford, 10.
---- on antiquity, 11.
---- on old libraries, 11.
---- on George Dyer, 11.
---- on his school-days, 14.
---- on Coleridge's school-days, 14.
---- on Matthew Fielde, 21.
---- on James Boyer, 22.
---- on borrowers and borrowing, 26.
---- on John Fenwick, 27.
---- on Coleridge as a book borrower, 29.
---- on the Duchess of Newcastle, 30.
---- on the New Year, 31.
---- on bells, 31.
---- on his childhood, 32, 75.
---- on the joy of life, 33.
---- on death, 34.
---- on Mrs. Battle and whist, 37,
---- his want of ear, 43.
---- his piano playing, 44.
---- on oratorios, 45.
---- on Novello's evenings, 47.
---- on fools, 48.
---- on Quakers, 51, 55, 72.
---- on silence, 51.
---- on Sewel's _History_, 53.
---- on John Woolman, 54.
---- and the Quaker "wit," 55.
---- his reading, 56.
---- on schoolmasters, 59.
---- on Valentine's Day, 63.
---- on anatomy and love, 64.
---- on door knocks, 64.
---- on Edward Burney's valentine, 65.
---- on imperfect sympathies, 66.
---- on Scotchmen, 67.
---- on Jews, 70.
---- on Braham, 71.
---- on <DW64>s, 71.
---- on Quakers, 72.
---- on witches, 74.
---- on his childhood, 75.
---- on children and the dark, 77.
---- on Thornton Hunt's bringing up, 77.
---- on dreams, 79.
---- on his relations, 80.
---- on Sarah Lamb, 80.
---- on John Lamb, jr., 81, 117.
---- on his sister Mary, 86.
---- his dislike of stories, 86.
---- on the Duchess of Newcastle again, 87.
---- on Mackery End, 88.
---- his Hertfordshire relations, 88.
---- on the comely Brutons, 89.
---- on gallantry, 90.
---- on Joseph Paice, 92.
---- on the Temple, 94.
---- on sun-dials, 95.
---- on fountains, 96.
---- on the old Benchers, 97.
---- on Joseph Jekyll, 97.
---- on Samuel Salt, 98, 103.
---- on Thomas Coventry, 99.
---- on his father, 99.
---- on Daines Barrington, 101.
---- on James Mingay, 102.
---- on Baron Maseres, 103.
---- on saying grace, 104.
---- on Milton, 107.
---- his godfather Field, 111.
---- as a landed proprietor, 112.
---- his first play, 112.
---- and his imaginary children, 115.
---- his grandmother, 115.
---- on Blakesware, 116.
---- on distant correspondents, 118.
---- on Lord Camelford's whim, 121.
---- on puns, 122.
---- on Australia, 122.
---- on chimney-sweepers, 124.
---- on Saloop, 125.
---- and fine teeth, 127.
---- and James White, 128.
---- on beggars, 130.
---- his translation from Bourne, 133.
Lamb, Charles, on Samuel Horsey, 135.
---- on almsgiving, 137.
---- on the origin of roast pig, 137.
---- on roast pig, 140.
---- and his plum cake, 142.
---- on married people, 144.
---- on "Twelfth Night," 150.
---- on Mrs. Jordan, 151.
---- on Mrs. Powel, 151.
---- on Bensley's Malvolio, 152.
---- on Dodd's Aguecheek, 155.
---- on Dicky Suett, 157.
---- on Jack Bannister, 159.
---- on Jack Palmer, 159, 165.
---- on the artificial comedy, 161.
---- on Wycherley and Congreve, 162.
---- on the "School for Scandal," 164.
---- on J.P. Kemble, 168.
---- on Munden's faces, 169.
---- on Elia's death, 172.
---- on family mansions, 174.
---- on Blakesware, 175.
---- on the feeling of gentility, 176.
---- on poor relations, 178.
---- on Favell's sensitiveness, 181.
---- on John Billet, 183.
---- on stage illusion, 185.
---- on Gattie's old men, 186.
---- on Emery as Tyke, 186.
---- on Elliston, 188, 190.
---- entertains Elliston, 194.
---- on reading, 195.
---- on books that are not books, 195.
---- on binding, 196.
---- on editions of the great authors, 197.
---- on the names of poets, 198.
---- on Shakespeare, 198.
---- his adventure on Primrose Hill, 199.
---- on watering-places, 201.
---- on the voyage to Margate, 21.
---- on a good liar, 202.
---- on the ocean, 205.
---- on Hastings, 206.
---- on smuggling, 207.
---- on convalescence, 208.
---- on the sanity of genius, 212.
---- on Captain Jackson, 215.
---- on his clerk-state, 219.
---- his superannuation, 221.
---- on leisure, 222.
---- on the genteel style in writing, 226.
---- on Sir William Temple, 226.
---- on Miss Kelly's reminiscence. 230.
---- on his friends among actors, 232.
---- on Westminster Abbey fees, 235.
---- on Andrews monument, 237.
---- on George Dyer's immersion, 237.
---- on the Islington doctor, 238,
---- on the New River, 240.
---- on drowning in dreams, 241.
---- on Sidney's sonnets, 242.
---- on Milton's Latin sonnet, 243.
---- on Hazlitt s opinion of Sidney, 248.
---- on James Bruce, 250.
---- on Dan Stuart, 250.
---- on the _Morning Post_ days, 250.
---- on joking to order, 252.
---- on Bob Allen, 253.
---- on _The Albion_, 254.
---- and Sir James Mackintosh, 256.
---- on modern painters, 256.
---- on Titian's "Ariadne," 256.
---- on Raphael, 257.
---- on J.M.W. Turner, 258.
---- his imaginary scene at Brighton, 259.
---- on John Martin, 260.
---- on Don Quixote, 264.
---- his fantasy on the Days, 266.
---- on Miss Burney's wedding, 271.
---- on mothers and daughters, 273.
---- on his behaviour on solemn occasions, 274.
Lamb, Charles, on Admiral Burney, 275.
---- his fantasy on the child angel, 276.
---- on Randal Norris's death, 279.
---- on old china, 281.
---- his sister's regrets for poverty, 282.
---- and the folio Beaumont and Fletcher, 282.
---- and his sister's excursions, 283.
---- and his sister's playgoing, 283.
---- on bullies and cowards, 286.
---- on ill-gotten gains, 287.
---- on jokes and laughter, 287.
---- on breeding, 288.
---- on the poor and the rich, 288.
---- on sayings concerning money, 290.
---- on disputants, 291.
---- on puns, 292.
---- on Mrs. Conrady, 294.
---- on beauty, 295.
---- on presents, 296.
---- on home, 298.
---- on friendship, 302.
---- on Merry's wedding day, 304.
---- on early rising, 305.
---- on superannuation, 307.
---- on going to bed late, 308.
---- on candle-light, 308.
---- on sulky tempers, 309.
---- on Kemble in Godwin's "Antonio," 329.
---- on Mathews' collection of portraits, 331.
---- on the name Elia, 337.
---- his dedication to _Elia_, 337,
---- his imitators, 339.
---- his Key to _Elia_, 339.
---- and the _London Magazine_, 340.
---- on Taylor's editing, 341.
---- his _post London Magazine_ days, 342.
---- at the South-Sea House, 342.
---- in the country, 345.
---- at Oxford, 346.
---- his sonnet on Cambridge, 346.
---- on Milton's MSS., 346.
---- his jokes with George Dyer, 347.
---- on George Dyer's career, 348, 349.
---- his lines to his aunt, 350.
---- his popularity at school, 355.
---- on Grecians and Deputy-Grecians, 355.
---- on reading and borrowing, 356.
---- and Luther's _Table Talk_, 357.
---- Coleridge as a reader, 357.
---- his copy of Beaumont and Fletcher, 357.
---- his copy of Donne, 358.
---- his books in America, 358.
---- his reply to "Olen," 358.
---- his sonnet "Leisure," 359.
---- Coleridge's description of him, 359.
---- on Coleridge's "Ode," 359.
---- his sonnet on Innocence, 360.
---- rebuked by "A Father," 360.
---- and the Burneys, 361.
---- elementary rules of whist, 362.
---- his ear for music, 363.
---- weathering a Mozartian storm, 364.
---- his chaff of Hunt, 364.
---- on Elia's ancestors, 364.
---- chaffed by Hunt, 365.
---- Maginn thinks him a Jew, 365.
---- on birthplaces, 365.
---- on turning Quaker, 368.
---- kisses a copy of Burns, 371.
---- his threat concerning Burns, 371.
---- rebuked by Christopher North, 371.
---- his admiration of Braham, 371.
---- on Sir Anthony Carlisle, 372.
---- his sisters, 373.
---- on John Lamb's pamphlet, 374.
Lamb, Charles, his cousins, 376.
---- his blank verse fragment, 377.
---- on Wordsworth's "Yarrow Visited," 377.
---- De Quincey's description of him, 377.
---- his chivalry, 377.
---- Barry Cornwall's anecdote of him, 377.
---- his birthplace, 379.
---- his patron, 380.
---- his father, 381.
---- and Baron Maseres, 383.
---- and Southey's criticism of _Elia_, 384.
---- as a landowner, 385.
---- his letter to his tenant, 386.
---- and his mother, 387.
---- his sonnet to Mrs. Siddons, 388.
---- and Alice W----, 389.
---- his love period, 389.
---- and chimney-sweepers, 390.
---- at Bartholomew Fair, 391.
---- his acquaintance with Hood, 393.
---- his joke to a beggar, 394.
---- on the "Beggar's Petition," 394.
---- his joke on Wainewright, 395.
---- the origin of his "Roast Pig," 395.
---- his recantation, 397.
---- his aunts, 397.
---- on Mrs. John Rickman, 397.
---- criticised by Macaulay, 399.
---- praised by Hartley Coleridge, 400.
---- on Elia's character, 402.
---- on the East India House clerks, 404.
---- letter to Southey about Blakesware, 406.
---- letter to Barton on same subject, 406.
---- his excursion with Elliston and Munden, 410.
---- his books described by Leigh Hunt, 412.
---- his affectation of affectation, 414.
---- and watering-places, 415.
---- at Hastings, 416.
---- leaves the India House, 417.
---- letter to Barton on his liberty, 417.
---- on the Puritans, 418.
---- his love of walking, 419.
---- his sonnet on "Work," 419.
---- his remark to Macready, 423.
---- his remark to Allsop about Dyer, 425.
---- the last book he read, 426.
---- on Lord's Thurlow's poems, 427.
---- his paragraphs for the _Morning Post_, 429.
---- as he appeared to Dan Stuart, 430.
---- his epigrams on Mackintosh, 433.
---- his real opinion of Titian's "Ariadne," 434.
---- letter to Barton on John Martin, 435.
---- at Hazlitt's wedding, 436.
---- his clothes, 438.
---- his pun at Cary's, 441.
---- his treatment of presentation copies, 441.
-- Elizabeth, Lamb's mother, 387.
-- John (Lovel), 100, 381.
---- his boyhood, 183, 408.
---- quoted, 437.
---- jr., his character, 81.
---- his childhood, 117.
---- at the South-Sea House, 344.
---- and Hazlitt, 347.
---- his _Letter ... on Cruelty to Animals_, 374.
---- his death, 388.
-- Mary (Bridget Elia), Lamb's sister, 43, 86, 362, 376.
---- her account of a schoolmaster, 62.
---- a quaint poetess, 200, 414.
---- her first play, 387.
---- her poem "Helen," 407.
-- Sarah (Lamb's aunt), 15, 142, 350, 397.
---- her character, 80.
Lamb, Sarah, her sarcasm, 184.
-- family, 81, 373.
"LAST ESSAYS OF ELIA," 339.
Laughter, Lamb on, 287.
"Lazarus, The Raising of," by Piombo, 262, 435.
Le Grice, Charles Valentine, 25, 110, 354, 384.
---- Samuel, 25, 355.
Leisure, Lamb on, 420.
Letter-writing, Lamb on, 118.
Liar, a good, 202.
Libraries, Lamb on, 11.
_Life of John Buncle_, by Amory, 30, 357.
Lincoln, John Lamb's boyhood, 183, 408.
Liston, John, 169, 401, 423.
Lloyd, Charles, 360.
Lombardy and the pawnbrokers, 254.
London, Lamb's homes in, 379.
_London Magazine_, history of, 340.
---- Lamb's contributions to, 1-56, 66-185, 195-208, 215, 219, 230,
235, 237, 242, 271, 276, 281, 315, 322, 331.
---- Lamb's last contribution to, 408.
Love and anatomy, 64.
"Love for Love," by Congreve, 160.
Lovel. _See_ John Lamb.
Lovell, Daniel, 255, 432.
Lully, Raymond, 49, 196.
"Lun's Ghost," 113, 387.
Luther's _Table Talk_ and Coleridge, 357.
"Lycidas" in its original form, 346.
M
Macaulay, Lord, 399.
MACKERY END, IN HERTFORDSHIRE, 86, 375.
Mackintosh, Sir James, 433.
Macready, W.C., and Lamb, 423.
Maginn, William, 365.
Make-believe, an artist in, 215.
Malone, Edmund, 198, 413.
Malvolio, the character of, 316.
Man, Henry, 6, 344.
Manning, Miss Anne, quoted, 378.
-- Thomas, 56, 369.
---- and "Roast Pig," 137, 396.
---- Lamb's letter to, 376, 444.
---- and Baron Maseres, 383.
Margate, Lamb at, 415.
Hoy, Lamb's essay on, 201, 415.
Marriage, Lamb on, 144.
Married people, Lamb's essay on, 144, 397.
Marshal, Godwin's friend, 329, 444.
Martin, John, 259, 434.
Marvell, Andrew, quoted, 96, 176.
Maseres, Baron, 103, 383.
Mathews, Charles, his pictures, 331, 445.
Mendicity, Society for Suppression of, 130, 392.
Merry, Robert, 304, 443.
Micawber, Wilkins, anticipated, 356, 417.
Middleton, Thomas Fanshaw, 23, 24, 354.
Milton, John, on education, 60, 369.
---- Lamb on, 107.
---- adapted by Lamb, 188.
---- on the _Arcadia_, 242.
---- and the civil war, 242.
---- his Latin sonnet, "Ad Leonoram," 243, 426.
---- Lamb's copy of, 412.
Mingay, James, 102, 383.
MODERN GALLANTRY, 90, 377.
Money, sayings concerning, 290.
Montagu, Basil, 12, 252, 348, 431.
Lady Mary Wortley, 381.
Montgomery, James, and Lamb, 390.
Moore, Thomas, his _Loves of the Angels_, 276, 437.
Moore's _Diary_ quoted, 411.
_Morning Chronicle_ and Lamb, 429, 431.
-- _Herald_, 413.
-- _Post_ and Lamb, 249, 429.
Mothers and daughters, Lamb on, 273.
"Mourning Bride," Mary Lamb's first play, 387.
Moxon, Lamb's letter to, 434.
Mozart, Lamb copes with, successfully, 364.
"Mr. H." and Elliston, 409.
MRS. BATTLE'S OPINIONS ON WHIST, 37, 361.
Munden, Joseph Shepherd, 168, 400.
Music, Lamb's difficulty with, 44, 363.
MY FIRST PLAY, 110, 385.
_My good friend, for favours to my son and wife_, 382.
MY RELATIONS, 80, 373.
N
Names of poets, Lamb on, 198.
<DW64>s, Lamb on, 71.
_New Monthly Magazine_, 342.
------ Lamb's contributions to, 212, 226, 286-309.
New River, the, and G.D., 237, 424.
NEW YEAR'S EVE, 31, 358.
Newcastle, Margaret, Duchess of, 30, 87, 131, 197, 357, 393, 412.
NEWSPAPERS THIRTY-FIVE YEARS AGO, 249, 428.
Newspaper stamps, 433.
Night-fears, Lamb on, 77.
_Nobleman, The Unfortunate Young_, 81.
Norris, Randal, 279, 416, 437.
North, Christopher (John Wilson), 371.
Novello, Vincent, 47, 363.
Nyren, John, 363.
O
_Odes and Addresses_ quoted, 392.
OF TWO DISPUTANTS, THE WARMEST IS GENERALLY IN THE WRONG, 291, 440.
Ogilvie, his memories of G.D., 424.
OLD ACTORS, THE, 322, 444.
-- BENCHERS OF THE INNER TEMPLE, THE, 94, 379.
-- CHINA, 281, 438.
-- MARGATE HOY, THE, 201, 415.
OLD AND THE NEW SCHOOLMASTER, THE, 56, 369.
"Olen," Sir C.A. Elton's pseudonym, 358.
_O melancholy Bird, a winter's day_, 427.
_One parent vet is left,--a wretched thing_, 382.
ON SOME OF THE OLD ACTORS, 150, 397. _See_ also APPENDIX.
ON THE ACTING OF MUNDEN, 168, 400. _See_ also APPENDIX.
ON THE ARTIFICIAL COMEDY OF THE LAST CENTURY, 161, 399. _See_ also
APPENDIX.
Orrery lectures, 60, 370.
OXFORD IN THE VACATION, 8, 345.
Oxford, Lamb at, 8, 345.
P
Paice, Joseph, 92, 343, 378.
Palmer, John, 159, 399.
Paltock's _Peter Wilkins_, 21, 122, 353.
Paracelsus, Lamb on, 196.
_Paradise Regained_, 107.
Patmore, P.G., on Lamb, 403.
---- Lamb's letter to, 436.
---- on Lamb's dress, 438.
Peirson, Peter, 101, 382.
Susannah, 99, 381.
Penn, William, and the judges, 73.
Perry, James, 250, 431.
_Peter Wilkins_, 21, 122, 353.
"Peter's Net," 428, 431.
Pianoforte, Lamb's solo, 44.
Pig, Lamb's essay upon, 137, 395.
Piombo, his "Raising of Lazarus," 262, 435.
Piquet and Mrs. Battle, 41.
_Pity the sorrows of a poor old man_, 394.
Playgoing, the Lambs, 283.
Plumer, Richard, 7, 344.
-- Walter, 7, 40, 345, 362.
-- William, 344, 389, 405.
_Poetical Pieces on Several Occasions_ by John Lamb, 381.
Polar expeditions, 58, 369.
Poor, Lamb on the, 288, 298.
POOR RELATIONS, 178, 408.
Pope, Alexander, _The Rape of the Lock_, 38.
-- Miss, 167, 400.
POPULAR FALLACIES, 212, 226, 286, 287, 288, 290, 291, 292, 294, 296, 298,
302, 305, 308, 309, 439 _et seq_.
Pork, Lamb's essay on, 137.
Porphyry on _Abstinence from Animal Food_, 396.
Poverty and pleasure, 282.
Powell, Mrs., 151.
PRAISE OF CHIMNEY-SWEEPERS, THE, 124, 390.
Presentation copies, Lamb on, 297, 441.
Presents, Lamb on, 296.
Procter, B.W. (Barry Cornwall), his dream, 79, 373.
---- quoted, 371, 377.
---- on Munden, 400.
Puckeridge and Lamb's property, 112.
Pulham, Brook, 363.
Punning, Lamb on, 122, 292, 441.
Puritans and Sunday, 418.
Q
Quadrille and Mrs. Battle, 38.
Quakerism and Lamb, 368.
QUAKER'S MEETING, A, 51, 367.
Quarrels, Lamb on, 309.
Quick, John, 332.
Quixote, Don, 154, 265, 398, 435.
R
Ramsay, London Librarian, 49, 367.
Raphael, his "Bible," 257.
Raymond, George, his _Memoirs of Elliston_, 410.
Reade, John, 102, 383.
Reading, Lamb's essay upon, 195, 411.
Red stockings, and Lamb's jokes, 251, 429.
_Reflector, The_, Lamb's contribution to, 144.
---- Moxon's paper, 434.
REJOICINGS UPON THE NEW YEAR'S COMING OF AGE, 266, 436.
Relations, poor, Lamb s essay on, 178, 408.
Restoration comedy, Lamb on, 160, 161.
Rickman, Mrs. John, Lamb's opinion of, 397.
Robinson, Crabb, quoted, 370.
---- Lamb's letters to, 374, 437.
---- on Lamb's books, 411.
Romano, Julio, 263.
Rover, in "Wild Oats," 188.
Roydon, Matthew, his elegy upon Sidney, 248, 428.
Rutter, Mr. J.A., his notes on Lamb, 343.
S
St. Dunstan's giants, 192, 410.
Saloop, Lamb on, 125.
Salt, Samuel, 98, 352, 380.
Samuel and the Witch of Endor, 75, 372.
Sandwich, Lord, epigram on, 344.
SANITY OF TRUE GENIUS, 212, 416.
Sargus, Mr. Lamb's tenant, 386.
"School for Scandal," Lamb on, 164.
School-days, Lamb on his, 14.
Schoolmasters, Lamb's essay on, 56, 369.
Scotchmen, Lamb on, 67, 371.
Scott, John, editor of the _London_, 340.
Sea, the, Lamb on, 204.
Sedition, Lamb's exercises in, 255.
Selden, John, 104, 384.
Sensitiveness, Lamb on, 181.
Sewel, William, historian of Quakers, 369.
Shaftesbury, Lord, 226, 420.
Shakespeare, Lamb on, 197, 412.
-- his bust at Stratford-on-Avon, 198, 413.
Sharp, Granville, 50, 367.
Shenstone, William, 243, 426.
Sheridan, R.B., 26, 111, 167, 356, 385, 400.
Siddons, Mrs., in "Isabella," 114, 388.
Sidney, Sir Philip, his sonnets, 242, 426.
Sitting up late, Lamb on, 308.
Smith, the Scotchman, 69, 370.
John Thomas, 394.
Smollett, Tobias George, 70, 371.
Smuggling, Lamb on, 207.
SOME SONNETS OF SIR PHILIP SIDNEY, 242, 426.
_So should it be, my gentle friend_, 426.
South Downs, Lamb on, 415.
SOUTH-SEA HOUSE, THE, 1, 342.
Southey at Westminster School, 235.
-- Robert, his criticism of _Elia_, 359.
-- Lamb's letters to, 384, 406, 419, 423, 436.
Spencer, Lord, epigram on, 344.
Spenser, Lamb's copy of the _Faerie Queene_, 413.
Stackhouse's _History of the Bible_, 75, 372.
STAGE ILLUSION, 185, 408.
Stanhope, Lord, 433.
Stocks, Lamb in the, 363.
_Stranger, to whom this monument is shown_, 413.
Stuart, Daniel, 250, 429. 430.
Suett, Dicky, 157, 399.
Sulkiness, its pleasures, 309.
Sun-dials in the Temple, 95.
SUPERANNUATED MAN, THE, 219, 417.
Superannuation, Lamb on, 219, 307.
Surface, Joseph and Charles, 166.
Swift's _Ars Punica_, 293, 441.
T
Taylor, Bishop, on the sunrise, 309.
-- John, 337, 341, 358.
Teeth, Lamb's admiration of, 127.
Temple, The, and Lamb, 94, 113, 379, 387.
-- the winged horse, 97.
-- Sir William, 226, 420,
THAT A BULLY IS ALWAYS A COWARD, 286, 440.
-- A MAN MUST NOT LAUGH AT HIS OWN JEST, 287, 440.
-- A SULKY TEMPER IS A MISFORTUNE, 309, 443.
-- ENOUGH IS AS GOOD AS A FEAST, 290, 440.
-- HANDSOME IS AS HANDSOME DOES, 294, 441.
-- HOME IS HOME THOUGH IT IS NEVER SO HOMELY, 298, 442.
-- ILL-GOTTEN GAIN NEVER PROSPERS, 287, 440.
-- SUCH A ONE SHOWS HIS BREEDING, ETC., 288, 440.
-- THE POOR COPY THE VICES OF THE RICH, 288, 440.
-- THE WORST PUNS ARE THE BEST, 292, 440.
-- VERBAL ALLUSIONS ARE NOT WIT, ETC., 292, 440.
-- WE MUST NOT LOOK A GIFT-HORSE IN THE MOUTH. 296, 441.
-- WE SHOULD LIE DOWN WITH THE LAME, 308, 443.
-- WE SHOULD RISE WITH THE LARK, 305, 443.
-- YOU MUST LOVE ME, AND LOVE MY DOG, 302, 442.
_The chatt'ring Magpye undertook_, 437.
Thelwall, John, 376.
_They talk of time, and of time's galling yoke_, 359.
Thomson, James, 70.
_Though thou'rt like Judas, an apostate black_, 433.
Thurlow, Lord, his sonnet, 427.
Tipp, John, 5, 343.
Titian, his "Ariadne," 256, 434.
_To every one (so have ye faith) is given_, 426.
TO THE SHADE OK ELLISTON, 188, 409.
Tobin, James Webbe, 16, 352.
-- John, 199, 413.
TOMBS IN THE ABBEY, THE, 235, 423.
_Tristram Shandy_, a parallel to Lamb, 403.
Trollope, A.W., quoted, 351.
_Turkish Spy_ and Lamb's roast-pig essay, 395.
Turner, J.M.W., 258, 434.
"Twelfth Night," Lamb's remarks on, 150, 153, 284, 316.
Twelve Caesars, 405, 406.
_Two Lords whose names if I should quote_, 344.
TWO RACES OF MEN, THE, 26, 355.
Twopenny, Richard, 102, 383.
-- post in 1825, 370.
U
Ugliness, Lamb on, 295.
Unitarianism, 81, 373.
V
VALENTINE'S DAY, 63, 370.
Vallans, his "Tale of Two Swans," 375.
Virgil, his Latin pun, 294, 441.
Visitors, Lamb on, 301, 442.
W
Wainewright, T.G., 395, 439.
Ward, Robert, afterwards Plumer-Ward, 405.
Watering-places, Lamb on, 201, 415.
Weathercock, Janus. _See_ Wainewright.
WEDDING, THE, 271, 436.
-- an interrupted, 305.
Westminster Abbey, the price for admission, 235, 423.
Westwood, Thomas, on Lamb, 441.
_We were two pretty babes, the youngest she_, 360.
Wharry, John, 102, 383.
_What can be hop'd from Priests who, 'gainst the Poor_, 424.
_What seem'd his tail the likeness of a kingly kick had on_, 409.
Whist, 37, 275, 361, 362, 437.
White, James, 123, 157, 390, 391.
---- and the chimney-sweepers, 128.
---- and Dodd, 157.
"Wild Oats," 188.
_Who first invented work--and bound the free_, 419.
Wilson, John. _See_ Christopher North.
Winstanley, Susan, and Joseph Paice, 92.
WITCHES, AND OTHER NIGHT-FEARS, 74, 372.
Woolman, John, 54, 369.
Wordsworth, Mrs., Lamb's letter to, 442.
-- William, his "Yarrow Visited," 89, 377.
---- Lamb's letters to, 356, 388, 412, 417, 418, 434.
---- his theory of language, 394.
---- his "Anecdote for Fathers," 395.
---- his "Poet's Epitaph," 438.
"Work," Lamb's sonnet on, 419.
Worthing and the Lambs, 415.
Wrench, Benjamin, 191, 410.
Wycherley, Lamb on, 162.
Y
_Yet can I fancy, wandering 'mid thy towers_, 346.
***
|
{
"redpajama_set_name": "RedPajamaBook"
}
| 346
|
from django.db.backends.base.base import NO_DB_ALIAS
from django.db.backends.postgresql.base import (
DatabaseWrapper as Psycopg2DatabaseWrapper,
)
from .features import DatabaseFeatures
from .introspection import PostGISIntrospection
from .operations import PostGISOperations
from .schema import PostGISSchemaEditor
class DatabaseWrapper(Psycopg2DatabaseWrapper):
SchemaEditorClass = PostGISSchemaEditor
def __init__(self, *args, **kwargs):
super(DatabaseWrapper, self).__init__(*args, **kwargs)
if kwargs.get('alias', '') != NO_DB_ALIAS:
self.features = DatabaseFeatures(self)
self.ops = PostGISOperations(self)
self.introspection = PostGISIntrospection(self)
def prepare_database(self):
super(DatabaseWrapper, self).prepare_database()
# Check that postgis extension is installed.
with self.cursor() as cursor:
cursor.execute("CREATE EXTENSION IF NOT EXISTS postgis")
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 80
|
\section{Introduction} \label{s:intro}
\vspace{-0.2cm}
X-ray security screening plays a pivotal role in aviation security. However, manual inspection of potentially prohibited items is challenging due to the clutter and occlusion present within X-ray scanned baggage.
A modern X-ray security scanner makes use of multiple X-ray energy levels in order to facilitate effective materials discrimination \cite{singh2003explosives}. Subsequently, a dual-energy X-ray scanner imagery consists of two intensity images acquired at two discrete energy levels ({\it low} and {\it high}), facilitating the recovery of material properties (effective atomic number, effective-$z$). The information is fused with the help of a colour transfer function into a single pseudo-colour X-ray image (Figure \ref{fig:ex_fchlz}A) to facilitate the interpretation of the baggage contents \cite{turcsany13xray}.
\begin{figure}[htb!]
\centering
\includegraphics[width=\linewidth]{fc-raw-ex.pdf}
\vspace{-0.8cm}
\caption{Exemplar {\it rgb} (A), {\it high} (B), {\it low} (C), and effective-$z$ (D) X-ray imagery from {\it deei6} dataset containing target classes in bounding boxes.}
\label{fig:ex_fchlz}
\vspace{-0.8cm}
\end{figure}
\begin{figure*}[htb!]
\centering
\includegraphics[width=17cm]{arch_1.pdf}
\vspace{-0.8cm}
\caption{Schematic of X-ray imaging followed by CNN architecture for object detection in complex X-ray security imagery.}
\label{fig:arch}
\vspace{-0.5cm}
\end{figure*}
The advancement of deep Convolutional Neural Networks (CNN) has brought new insight to the automation of this X-ray imagery screening task \cite{akccay2016transfer,Akcay2018Xray,gaus2019evaluation} where the primary task is both to localise and classify the prohibited items. Prior works \cite{Akcay2018Xray,gaus2019evaluating} are concentrated on the shaped-based detection of prohibited items achieving both high detection performance with low false positive. The work of \cite{akccay2016transfer} uses a pre-trained GoogleNet model for classification task in X-ray baggage scans for detecting potentially prohibited items. Subsequently, the work of \cite{Akcay2018Xray} compares contemporary region-based and single forward-pass based CNN architectures (Faster R-CNN \cite{Ren2015fasterr-cnn}, YoloV2 \cite{Redmon2016yolo}) achieving $0.88$ and $0.97$ mean Average Precision (mAP) over six class and two class X-ray baggage security object detection problems respectively. Following these works, \cite{gaus2019evaluation} proposes a dual-stage CNN architecture for anomaly detection in a six class problem. Semi-supervised adversarial learning is used in the works of \cite{akcay2018ganomaly,akccay2019skip} for prohibited item detection. The availability of the large-scale X-ray baggage datasets (SIXray \cite{Miao2019SIXray}, and OPIXray \cite{wei2020occluded}) has provided further insight into the transferability and generalisation abilities of the CNN architectures \cite{gaus2019evaluating} across varying X-ray security scanners which all exhibit varying characteristics in terms of projection geometry common resolution and pseudo-colour mapping. While most prior work \cite{Akcay2018Xray,gaus2019evaluation,gaus2019evaluating} process each view of multi-view X-ray scanners independently, \cite{isaac20multiview} utilise the corresponding information between the views for a detection task achieving $0.91$ mAP.
Almost all of the prior work discussed here only use pseudo-colour/false colour ({\it rgb}) X-ray imagery that is itself generated from the `raw' {\it high/low/}effective-$z$ imagery obtained from the scanner. By contrast, in this study we consider the impact of using this `raw' imagery (Figure \ref{fig:ex_fchlz}(B)$\rightarrow$(D)) directly for the purposes of prohibited object detection. The objective of using two energy levels ({\it high} and {\it low}) for object detection task is to obtain both the density and atomic number $Z$ (effective-$z$) of the scanned materials \cite{rebuffel2007dual}, as the intensity values in the energy response may encode very valuable material information, which is not as readily identifiable within the pseudo-colour X-ray imagery.
Against this background, this paper introduces the following novel contributions: (a) an experimental evaluation of dual-energy X-ray imagery for joint object detection and segmentation task, via use of characteristically diverse end-to-end CNN architectures \cite{he2017maskrcnn,Bolya19:yolact,wang19:carafe,cai19:cascade}, (b) an investigation into the inter-scanner transferability of such CNN models, trained on dual-energy X-ray imagery, in terms of their generalisation across varying X-ray scanner characteristics.
\section{Proposed Approach} \label{s:proposal}
\vspace{-0.2cm}
In this study, we present dual-energy X-ray imaging technique (Figure \ref{fig:arch}, left) in Section \ref{ssec:xray_formation} and followed by object detection and segmentation strategies (Figure \ref{fig:arch}, right) in Section \ref{ssec:seg}.
\vspace{-0.4cm}
\subsection{Dual-Energy Projection X-ray Imaging} \label{ssec:xray_formation}
\vspace{-0.2cm}
The primary components of X-ray security scanner system are composed of an X-ray source emitter and detector (Figure \ref{fig:arch}, left). X-rays are emitted with photon energy ranging up to 150kV \cite{gilardoni_scanner640} from a X-ray source. Generally, the X-ray images are constructed by attenuating the signal on the material as the target object proceeds through the scanner tunnel, defined as $I(E)=I_0e^{-\mu t}$, where $I(E)$ is the captured intensity as a function of the thickness $t$, the emitted intensity $I_0$ and the absorption coefficient $\mu$. The absorption coefficient is defined by $\mu = \alpha(Z,E)\rho$, where $Z$ is the atomic number, $E$ is the energy, $\rho$ is the density, and $\alpha(Z,E)$ corresponds to the mass attenuation coefficient in terms of $Z$ and $E$ \cite{mery2020x}.
In the dual-energy source X-ray imaging, two intensity responses captured at two different energy levels, {\it low} and {\it high} ($E=\{l,h\}$) and are subsequently combined to construct {\it low} and {\it high} energy response images (Figure \ref{fig:arch}, left). Given the Compton scatter coefficient ($\mu_c$) and the photoelectric absorption coefficient ($\mu_p$) \cite{Mouton2015ARO}, material identification (approximate atomic number, effective-$z$; $Z\_eff$) can be calculated as:
\begin{equation}
Z\_eff = K^{'}(\frac{\mu_p}{\mu_c})^\frac{1}{n}
\end{equation}
where $K^{'}$ and $n$ are constant \cite{Mouton2015ARO}.
In this work, we evaluate the use of the pseudo-colour ({\it rgb}), dual-energy response ({\it h, l}) and effective-$z$ (Figure \ref{fig:ex_fchlz}) as alternative inputs imagery for CNN-based object detection.
\vspace{-0.3cm}
\subsection{Object Detection and Segmentation Strategy} \label{ssec:seg}
\vspace{-0.2cm}
We consider four contemporary CNN architectures of differing characteristics, spanning both single stage and multi stage detection approaches, and explore their applicability for prohibited item detection within varying configurations of dual-energy X-ray imagery inputs. \\
{\bf Mask R-CNN \cite{he2017maskrcnn}} is a two-stage detector for object instance segmentation, developed on top of Faster R-CNN \cite{Ren2015fasterr-cnn}.
Mask R-CNN \cite{he2017maskrcnn} uses the Faster R-CNN \cite{Ren2015fasterr-cnn} architecture for feature extraction, Region Proposal Network (RPN), and followed by region of interest alignment (RoIAlign) via bilinear boundary interpolation to produce higher resolution feature map boundaries suitable for input into a secondary classifier. The output from the RoIAlign layer is subsequently fed into a series of segmentation processing layers (mask head), that generate an additional image mask indicating pixel membership of a given detected object. \\
{\bf YOLACT \cite{Bolya19:yolact}} is an one-stage detector, based on RetinaNet \cite{lin2017retinanet}, that directly predicts boxes without a separate region proposal step. YOLACT \cite{Bolya19:yolact} generates a set of prototype masks, linear combination coefficients for each predicted instance, and associated bounding boxes. It combines the prototype masks using the corresponding predicted mask coefficients followed by cropping with a predicted bounding box to generate the final output. \\
{\bf CARAFE \cite{wang19:carafe}} is a two-stage architecture, which proposes effective feature up-sampling operators and integrates it into Feature Pyramid Network to boost the performance. For instance segmentation, a feature map, which represents the object shape accurately, is used to predict the final instance segmentation result. \\
{\bf Cascade Mask R-CNN \cite{cai19:cascade}}, a multi-stage detector, is a hybrid of Cascade R-CNN and Mask R-CNN \cite{he2017maskrcnn}. Similar to Mask R-CNN \cite{he2017maskrcnn}, each stage has a segmentation mask branch, a label prediction branch, and a bounding box detector branch. The current stage will accept RPN or the bounding box returned by the previous stage as an input. The second stage increases localisation performance accuracy, and subsequently, it further refines the output. This is repeated over multiple stages with increasingly refined criteria for discarding low-quality proposals from the previous stage such that it predicts precise bounding boxes and masks at the final stage.
In this study, we compare these four CNN architectures for object detection (Figure \ref{fig:arch}, right) using combination of different variants dual-energy X-ray imagery (Section \ref{ssec:xray_formation}). To assess the impact of dual-energy X-ray imagery variants on object detection we first use {\it rgb}, {\it high} ($h$), {\it low} ($l$), and effective-$z$ ($z$) imagery individually. Secondly, $h$, $l$ and $z$ are combined as three channels ({\it hlz}) images. Thirdly, we combine {\it rgb, high, low}, and effective-$z$ imagery for joint object detection and segmentation task.
Within the X-ray imagery security domain, imagery may be sourced using varying scanners \cite{gilardoni_scanner640,smithsdetection_scanner,rapiscan_scanner_620}, which have different X-ray energy spectra, spatial resolution and material colour profiles. In prior work \cite{Caldwell2017transfer, gaus2019evaluating} on transferability and generalisation ability, \cite{Caldwell2017transfer} focuses on transfer learning between cargo parcel scanning (different scanner equipment due to the differences in scale). The work of \cite{gaus2019evaluating} shows cross-scanner transferability of CNN architectures (using {\it rgb} X-ray imagery) in terms of their generalisation across varying X-ray scanner characteristics.
In this study, we further evaluate the effectiveness of using variants of dual-energy X-ray imagery (Section \ref{ssec:xray_formation}) on generalisation capabilities of the CNN architectures.
\section{Evaluation} \label{s:eval}
\vspace{-0.3cm}
We focus on three datasets that are sourced from different X-ray scanners \cite{gilardoni_scanner640,smithsdetection_scanner,rapiscan_scanner_620}. The {\it deei6} is created from a Gilardoni X-ray scanner \cite{gilardoni_scanner640}, and consists of {\it rgb}, {\it high, low}, and effective-$z$ imagery. The other two datasets, {\it dbs\_laptop} and {\it dbr\_laptop}, are generated by a Smith Detection \cite{smithsdetection_scanner} and Rapiscan X-ray scanner \cite{rapiscan_scanner_620} respectively and consist of {\it rgb} X-ray imagery.
The four CNN architectures (Section \ref{ssec:seg}) are trained using {\it rgb} and combinations of {\it rgb, high, low}, and effective-$z$ X-ray imagery from {\it deei6} dataset. Subsequently, we evaluate the model performance on {\it rgb} X-ray imagery of {\it dbs\_laptop} and {\it dbr\_laptop} datasets. \\
{\bf deei6:} Our dataset (Durham Electrical and Electronics Items) is constructed using a dual-energy Gilardoni FEP ME 640 AMX scanner \cite{gilardoni_scanner640} with associated pseudo-colour materials mapping. This dataset is composed of six-classes of consumer electronics, electrical and other items: \{{\it bottle, hairdryer, iron, toaster, phone-tablet, laptop}\}, totalling $7,022$ images (70:30 data split for experiments). We also access the {\it high, low}, and effective-$z$ imagery to construct {\it deei6$_{rgb}$}, {\it deei6$_{h}$}, {\it deei6$_{l}$} and {\it deei6$_{z}$} imagery as depicted in Figure \ref{fig:ex_fchlz}. \\
To investigate the generalisation capabilities of the CNN architectures, we also use the following two datasets: \\
{\bf dbs\_laptop:} comprises $488$ {\it laptop} class {\it rgb} X-ray image examples (with associated pseudo-colour materials mapping), which is sourced from a Smith Detection X-ray scanner \cite{smithsdetection_scanner}. \\
{\bf dbr\_laptop:} comprises $107$ {\it laptop} class X-ray {\it rgb} image examples (with associated pseudo-colour materials mapping). This dataset is sourced from Rapiscan 620DV X-ray scanner \cite{rapiscan_scanner_620}.
The CNN architectures (Section \ref{ssec:seg}) are implemented using MMDetection framework \cite{mmdetection}.
Through the transfer learning paradigm, training (using X-ray imagery variants) of all CNN architectures (Section \ref{ssec:seg}) are initialised with ImageNet \cite{deng2009imagenet} pretrained weights (which originate from training on colour RGB imagery). Our CNN architectures are trained using ResNet$_{50}$ \cite{He15:ResNet} backbone with following training configuration: backpropagation optimisation performed via Stochastic Gradient Descent, initial learning rate of $\num{2.5e-4}$ with decay by a factor of $10$ at 7$^{th}$ epoch, and a batch size of $4$.
The model performance is evaluated by MS-COCO metrics \cite{lin2014coco} (IoU of $0.50:.05:0.95$), using Average Precision (AP) for class-wise and mAP for overall performance.
\vspace{-0.4cm}
\subsection{Impact of Dual-energy X-ray Imagery} \label{ssc:baseline}
\vspace{-0.2cm}
In the first set of experiments (Table \ref{Table:mAP_impact}), exemplar items in X-ray security imagery are detected using the CNN architectures set out in Section \ref{ssec:seg}. We use variants of dual-energy X-ray imagery of the {\it deei6} dataset for training and evaluation denoted as {\it deei6$_{x}$} for $x = \{rgb, h, l, z, hlz\}$. The highlighted mAP signifies the maximal results obtained for overall performance. At first, the CNN architectures are trained and evaluated on {\it rgb} X-ray imagery (Table \ref{Table:mAP_impact}, {\it rgb}), in line with \cite{Akcay2018Xray,Miao2019SIXray,gaus2019evaluation}. The best performance is achieved by Cascade Mask R-CNN (CM RCNN) \cite{cai19:cascade} producing maximal mAP ($0.693$) and outperforming other three CNN architectures. When we train CNN architectures using {\it high}, {\it low}, and effective-$z$ imagery individually and together as three channels ({\it hlz}), the overall performance (Table \ref{Table:mAP_impact}) does not improve compared to {\it rgb} imagery. The lowest performing training set is {\it deei6$_{z}$} imagery achieving only $0.627$ of mAP (with Cascade Mask R-CNN \cite{cai19:cascade}). It is possibly due to the lack of contrast in the pixel intensity in effective-$z$ imagery where the target objects appear similar to the background, leading to inferior detection performance. The impact of dual-energy X-ray imagery can be observed while combining {\it rgb, high, low} and effective-$z$ ({\it deei6$_{rgb,hlz}$}) together. The maximal mAP of $0.7$ (Table \ref{Table:mAP_impact}, {\it rgb,hlz}) is achieved by CARAFE \cite{wang19:carafe} marginally outperforming {\it rgb} imagery (mAP: $0.693$).
Although YOLACT \cite{Bolya19:yolact} is the simplest architecture ($34.76$ million parameters), it outperforms Mask R-CNN \cite{he2017maskrcnn} while training using {\it rgb,hlz} X-ray imagery (mAP: $0.686$ vs $0.680$).
In the confusion matrices (Figure \ref{fig:conf}) of CARAFE \cite{wang19:carafe}, we observe strong true positive (diagonal) and low false positive (off-diagonal) occurrence. The advantage of combining {\it rgb, high, low}) and effective-$z$ can be seen in the class {\it phone-tablet} ($0.698$ to $0.729$, Figure \ref{fig:conf}(A)$\rightarrow$(B)), with improvement of confidence in localising small objects within cluttered X-ray security imagery.
\vspace{-0.2cm}
\input{tab_baseline}
\begin{figure}[htb!]
\vspace{-0.4cm}
\centering
\includegraphics[width=\linewidth]{conf_carafe.pdf}
\vspace{-0.9cm}
\caption{Confusion Matrix of the CARAFE \cite{wang19:carafe} trained on {\it rgb} (A) and combination of \{{\it rgb,hlz}\} (B) X-ray imagery.}
\label{fig:conf}
\vspace{-0.6cm}
\end{figure}
\vspace{-0.2cm}
\subsection{Cross-scanner Transferability}
\label{ssc:gen}
\vspace{-0.2cm}
In this set of experiments (Table \ref{Table:mAP_generalise}), we assess the CNN architecture performance across the X-ray imagery ({\it dbs$\_$laptop} and {\it dbr$\_$laptop}) from different scanner sources \cite{smithsdetection_scanner,rapiscan_scanner_620}. The CNN architectures are trained using variants of dual-energy X-ray imagery of {\it deei6} dataset but evaluated on a test set of only $rgb$ pseudo-colour imagery ({\it dbs$\_$laptop} and {\it dbr$\_$laptop}). The positive impact of combining \{{\it rgb,hlz}\} X-ray imagery is evident with all four CNN architectures (Table \ref{Table:mAP_generalise}). For {\it dbs$\_$laptop}, CARAFE \cite{wang19:carafe} produces the best performance (AP: $0.835$, Table \ref{Table:mAP_generalise}, lower) when trained using combination of {\it rgb, high, low} and effective-$z$ X-ray imagery, significantly outperforming {\it rgb} X-ray imagery (AP: $0.763$, Table \ref{Table:mAP_generalise}, upper). Similar significant performance improvement is noticeable on {\it dbr$\_$laptop} dataset with CARAFE \cite{wang19:carafe} achieving the highest AP of $0.611$ (Table \ref{Table:mAP_generalise}, lower). A plausible explanation for the performance improvement is that the variation in X-ray imagery by combining {\it rgb, high, low} and effective-$z$ imagery during training, leads the CNN architectures to learn meaningful image features, which alleviates to achieve a higher degree of model generalisation in object detection within X-ray imagery. Although CARAFE \cite{wang19:carafe} is a simpler architecture ($49.41$ million parameters) compared to the Cascade Mask R-CNN \cite{cai19:cascade} ($77.04$ million parameters), it offers a better generalisation ability by training on a more varied set of multiple X-ray imagery variants. In Figure \ref{fig:det_ex1}A the target {\it laptop} is missed in both test images when trained solely on {\it rgb} imagery, but successfully detected when trained with combined \{{\it rgb,hlz}\} X-ray imagery (Figure \ref{fig:det_ex1}B). Hence, we can deduce that although X-ray images are from differing scanners, the transferability of the trained CNN models is significantly improved by training over a more varied training set that includes both pseudo-colour {\it rgb} and variant dual-energy X-ray imagery.
\vspace{-0.2cm}
\input{tab_generalisation}
\vspace{-0.2cm}
\begin{figure}[htb!]
\vspace{-0.6cm}
\centering
\includegraphics[width=7.5cm]{det_gen_1.pdf}
\vspace{-0.6cm}
\caption{Detection examples from {\it dbs$\_$laptop} and {\it dbr$\_$laptop} using CARAFE \cite{wang19:carafe} trained on {\it rgb} (A) and \{{\it rgb,hlz}\} (B) X-ray imagery from {\it deei6} dataset. White dashed box in (A) fails to detect the target.}
\label{fig:det_ex1}
\vspace{-0.2cm}
\end{figure}
\section{Conclusion} \label{s:conclusion}
\vspace{-0.4cm}
This work examines the impact of X-ray imagery variants, i.e., dual-energy X-ray responses ({\it high, low}), effective-$z$ and pseudo-colour ({\it rgb}), via the use of CNN architectures for the object detection task posed within X-ray baggage security screening. We illustrate that the combination of {\it rgb, high, low} and effective-$z$ X-ray imagery produces maximal performance across all four CNN architectures for a six classes object detection problem, with CARAFE \cite{wang19:carafe} achieving the highest mAP of $0.7$. Furthermore, our results also demonstrate a remarkable degree of generalisation capability in terms of cross-scanner transferability (AP: $0.835/0.611$ with CARAFE \cite{wang19:carafe}) for a one class object detection problem by combining \{{\it rgb, hlz}\} X-ray imagery. This clearly illustrates a strong insight into the benefits of using a combination of dual-energy X-ray imagery for object detection and segmentation tasks, which could additionally useful for component-wise anomaly detection analysis. Future work will consider the use of dual-energy variant imagery for combined material discrimination and anomaly detection within cluttered X-ray security imagery.
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 9,598
|
package org.sleuthkit.autopsy.filesearch;
import java.awt.event.ActionEvent;
import java.awt.event.ActionListener;
import java.text.NumberFormat;
import javax.swing.JCheckBox;
import javax.swing.JComboBox;
import javax.swing.JFormattedTextField;
import javax.swing.JMenuItem;
import javax.swing.event.DocumentEvent;
import javax.swing.event.DocumentListener;
/**
*
* @author pmartel
*/
class SizeSearchPanel extends javax.swing.JPanel {
private static final long serialVersionUID = 1L;
/**
* Creates new form SizeSearchPanel
*/
SizeSearchPanel() {
initComponents();
customizeComponents();
setComponentsEnabled();
}
private void customizeComponents() {
sizeTextField.setComponentPopupMenu(rightClickMenu);
ActionListener actList = new ActionListener() {
@Override
public void actionPerformed(ActionEvent e) {
JMenuItem jmi = (JMenuItem) e.getSource();
if (jmi.equals(cutMenuItem)) {
sizeTextField.cut();
} else if (jmi.equals(copyMenuItem)) {
sizeTextField.copy();
} else if (jmi.equals(pasteMenuItem)) {
sizeTextField.paste();
} else if (jmi.equals(selectAllMenuItem)) {
sizeTextField.selectAll();
}
}
};
cutMenuItem.addActionListener(actList);
copyMenuItem.addActionListener(actList);
pasteMenuItem.addActionListener(actList);
selectAllMenuItem.addActionListener(actList);
this.sizeTextField.getDocument().addDocumentListener(new DocumentListener() {
@Override
public void insertUpdate(DocumentEvent e) {
firePropertyChange(FileSearchPanel.EVENT.CHECKED.toString(), null, null);
}
@Override
public void removeUpdate(DocumentEvent e) {
firePropertyChange(FileSearchPanel.EVENT.CHECKED.toString(), null, null);
}
@Override
public void changedUpdate(DocumentEvent e) {
firePropertyChange(FileSearchPanel.EVENT.CHECKED.toString(), null, null);
}
});
}
JCheckBox getSizeCheckBox() {
return sizeCheckBox;
}
JComboBox<String> getSizeCompareComboBox() {
return sizeCompareComboBox;
}
JFormattedTextField getSizeTextField() {
return sizeTextField;
}
JComboBox<String> getSizeUnitComboBox() {
return sizeUnitComboBox;
}
void setComponentsEnabled() {
boolean enabled = this.sizeCheckBox.isSelected();
this.sizeCompareComboBox.setEnabled(enabled);
this.sizeUnitComboBox.setEnabled(enabled);
this.sizeTextField.setEnabled(enabled);
}
/**
* This method is called from within the constructor to initialize the form.
* WARNING: Do NOT modify this code. The content of this method is always
* regenerated by the Form Editor.
*/
@SuppressWarnings("unchecked")
// <editor-fold defaultstate="collapsed" desc="Generated Code">//GEN-BEGIN:initComponents
private void initComponents() {
rightClickMenu = new javax.swing.JPopupMenu();
cutMenuItem = new javax.swing.JMenuItem();
copyMenuItem = new javax.swing.JMenuItem();
pasteMenuItem = new javax.swing.JMenuItem();
selectAllMenuItem = new javax.swing.JMenuItem();
sizeUnitComboBox = new javax.swing.JComboBox<>();
sizeTextField = new JFormattedTextField(NumberFormat.getIntegerInstance());
sizeCompareComboBox = new javax.swing.JComboBox<>();
sizeCheckBox = new javax.swing.JCheckBox();
cutMenuItem.setText(org.openide.util.NbBundle.getMessage(SizeSearchPanel.class, "SizeSearchPanel.cutMenuItem.text")); // NOI18N
rightClickMenu.add(cutMenuItem);
copyMenuItem.setText(org.openide.util.NbBundle.getMessage(SizeSearchPanel.class, "SizeSearchPanel.copyMenuItem.text")); // NOI18N
rightClickMenu.add(copyMenuItem);
pasteMenuItem.setText(org.openide.util.NbBundle.getMessage(SizeSearchPanel.class, "SizeSearchPanel.pasteMenuItem.text")); // NOI18N
rightClickMenu.add(pasteMenuItem);
selectAllMenuItem.setText(org.openide.util.NbBundle.getMessage(SizeSearchPanel.class, "SizeSearchPanel.selectAllMenuItem.text")); // NOI18N
rightClickMenu.add(selectAllMenuItem);
sizeUnitComboBox.setModel(new javax.swing.DefaultComboBoxModel<String>(new String[] { "Byte(s)", "KB", "MB", "GB", "TB" }));
sizeTextField.setValue(0);
sizeCompareComboBox.setModel(new javax.swing.DefaultComboBoxModel<String>(new String[] { "equal to", "greater than", "less than" }));
sizeCheckBox.setText(org.openide.util.NbBundle.getMessage(SizeSearchPanel.class, "SizeSearchPanel.sizeCheckBox.text")); // NOI18N
sizeCheckBox.addActionListener(new java.awt.event.ActionListener() {
public void actionPerformed(java.awt.event.ActionEvent evt) {
sizeCheckBoxActionPerformed(evt);
}
});
javax.swing.GroupLayout layout = new javax.swing.GroupLayout(this);
this.setLayout(layout);
layout.setHorizontalGroup(
layout.createParallelGroup(javax.swing.GroupLayout.Alignment.LEADING)
.addGroup(layout.createSequentialGroup()
.addComponent(sizeCheckBox)
.addPreferredGap(javax.swing.LayoutStyle.ComponentPlacement.RELATED)
.addComponent(sizeCompareComboBox, javax.swing.GroupLayout.PREFERRED_SIZE, javax.swing.GroupLayout.DEFAULT_SIZE, javax.swing.GroupLayout.PREFERRED_SIZE)
.addPreferredGap(javax.swing.LayoutStyle.ComponentPlacement.RELATED)
.addComponent(sizeTextField, javax.swing.GroupLayout.DEFAULT_SIZE, 119, Short.MAX_VALUE)
.addPreferredGap(javax.swing.LayoutStyle.ComponentPlacement.RELATED)
.addComponent(sizeUnitComboBox, javax.swing.GroupLayout.PREFERRED_SIZE, javax.swing.GroupLayout.DEFAULT_SIZE, javax.swing.GroupLayout.PREFERRED_SIZE)
.addGap(63, 63, 63))
);
layout.setVerticalGroup(
layout.createParallelGroup(javax.swing.GroupLayout.Alignment.LEADING)
.addGroup(layout.createParallelGroup(javax.swing.GroupLayout.Alignment.BASELINE)
.addComponent(sizeCompareComboBox, javax.swing.GroupLayout.PREFERRED_SIZE, javax.swing.GroupLayout.DEFAULT_SIZE, javax.swing.GroupLayout.PREFERRED_SIZE)
.addComponent(sizeTextField, javax.swing.GroupLayout.PREFERRED_SIZE, javax.swing.GroupLayout.DEFAULT_SIZE, javax.swing.GroupLayout.PREFERRED_SIZE)
.addComponent(sizeUnitComboBox, javax.swing.GroupLayout.PREFERRED_SIZE, javax.swing.GroupLayout.DEFAULT_SIZE, javax.swing.GroupLayout.PREFERRED_SIZE)
.addComponent(sizeCheckBox))
);
}// </editor-fold>//GEN-END:initComponents
private void sizeCheckBoxActionPerformed(java.awt.event.ActionEvent evt) {//GEN-FIRST:event_sizeCheckBoxActionPerformed
setComponentsEnabled();
firePropertyChange(FileSearchPanel.EVENT.CHECKED.toString(), null, null);
}//GEN-LAST:event_sizeCheckBoxActionPerformed
// Variables declaration - do not modify//GEN-BEGIN:variables
private javax.swing.JMenuItem copyMenuItem;
private javax.swing.JMenuItem cutMenuItem;
private javax.swing.JMenuItem pasteMenuItem;
private javax.swing.JPopupMenu rightClickMenu;
private javax.swing.JMenuItem selectAllMenuItem;
private javax.swing.JCheckBox sizeCheckBox;
private javax.swing.JComboBox<String> sizeCompareComboBox;
private javax.swing.JFormattedTextField sizeTextField;
private javax.swing.JComboBox<String> sizeUnitComboBox;
// End of variables declaration//GEN-END:variables
void addActionListener(ActionListener l) {
sizeTextField.addActionListener(l);
}
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 952
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Gangneung Airbase is an airbase holding the 18th fighter wing of the Republic of Korea Air Force. It is located in Gangneung, Gangwon-do. The airfield has one runway (8/26), and is ILS equipped on runway 23. In the past, this airfield also used to handle civilian air traffic. The passenger handling functions of this airfield were closed prior to the opening of Yangyang International Airport
History
During the Korean War, the USAF designated the base as K-18.
In 1969, Korean Air Lines YS-11 flying from Gangneung Airbase to Gimpo International Airport in Seoul was hijacked by a North Korean agent and forced to land in the North; seven of the passengers and all four crew members among them did not return to South Korea.
On 5 October 2022, due to the failed ballistic missile test, a major explosion occurred at the air base.
References
South Korean airbases
Korean War air bases
Buildings and structures in Gangneung
Airports established in 1958
1958 establishments in South Korea
20th-century architecture in South Korea
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 1,862
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John Watrous
Professor (on leave), Institute for Quantum Computing
and Cheriton School of Computer Science
The Theory of Quantum Information
Introduction to the Theory of Computing (2020)
Advanced Topics in Quantum Information Theory (2020)
Theory of Quantum Information (2011)
Introduction to Quantum Computing (2005)
Advanced Topics in Quantum Information Theory
John Bostanci and John Watrous. Quantum game theory and the complexity of approximating quantum Nash equilibria. Manuscript, 2021. [pdf, arXiv:2102.00512]
Bryan Coutts, Mark Girard, and John Watrous. Certifying optimality for convex quantum channel optimization problems. Quantum 5: 448, 2021. [pdf, arXiv:1810.13295]
Mark Girard, Debbie Leung, Jeremy Levick, Chi-Kwong Li, Vern Paulsen, Yiu Tung Poon, and John Watrous. On the mixed-unitary rank of quantum channels. Manuscript, 2020. [pdf, arXiv:2003.14405]
Soumik Ghosh and John Watrous. Complexity limitations on one-turn quantum refereed games. Manuscript, 2020. [pdf, arXiv:2002.01509]
Anne Broadbent, Zhengfeng Ji, Fang Song, John Watrous. Zero-knowledge proof systems for QMA. SIAM Journal on Computing 49(2): 245–283, 2020. (A preliminary version appeared in Proceedings of the 57th Annual IEEE Symposium on Foundations of Computer Science, pages 31–40, 2016.) [pdf, arXiv:1604.02804]
Colin Do-Yan Lee and John Watrous. Detecting mixed-unitary quantum channels is NP-hard. Quantum 4: 253, 2020. [pdf, arXiv:1902.03164]
Abel Molina and John Watrous. Revisiting the simulation of quantum Turing machines by quantum circuits. Proceedings of the Royal Society A 475 (2226): 0767, 2019. [pdf, arXiv:1808.01701]
Sanketh Menda and John Watrous. Oracle separations for quantum statistical zero-knowledge. Manuscript, 2018. [pdf, arXiv:1801.08967]
Yuan Su and John Watrous. Time-reversal of rank-one quantum strategy functions. Quantum 2: 98, 2018. [pdf, arXiv:1801.08491]
Vincent Russo and John Watrous. Extended nonlocal games from quantum-classical games. Chicago Journal of Theoretical Computer Science 2018: 4, 2018. [pdf, arXiv:1709.01837]
Daniel Puzzuoli and John Watrous. Ancilla dimension in quantum channel discrimination. Annales Henri Poincaré 18(4): 1153–1184, 2017. [pdf, arXiv:1604.08197]
Debbie Leung and John Watrous. On the complementary quantum capacity of the depolarizing channel. Quantum 1: 28, 2017. [pdf, arXiv:1510.01366]
Thomas Vidick and John Watrous. Quantum proofs. Foundations and Trends in Theoretical Computer Science 11(1&2): 1–215, 2016. [html, arXiv:1610.01664]
Nathaniel Johnston, Rajat Mittal, Vincent Russo, and John Watrous. Extended nonlocal games and monogamy-of-entanglement games. Proceedings of the Royal Society A 472(2189): 20160003, 2016. [pdf, arXiv:1510.02083]
Tom Cooney, Christoph Hirche, Ciara Morgan, Jonathan Olson, Kaushik Seshadreesan, John Watrous, and Mark Wilde. Operational meaning of quantum measures of recovery. Physical Review A 94(2): 022310, 2016. [pdf, arXiv.org 1512.05324]
Somshubhro Bandyopadhyay, Alessandro Cosentino, Nathaniel Johnston, Vincent Russo, John Watrous, and Nengkun Yu. Limitations on separable measurements by convex optimization. IEEE Transactions on Information Theory 61(6): 3593–3604, 2015. [pdf, arXiv:1408.6981]
Marco Piani and John Watrous. Necessary and sufficient quantum information characterization of Einstein-Podolsky-Rosen steering. Physical Review Letters 114(6): 060404, 2015. [pdf, arXiv:1406.0530]
Debbie Leung, Benjamin Toner, and John Watrous. Coherent state exchange in multi-prover quantum interactive proof systems. Chicago Journal of Theoretical Computer Science 2013: 11, 2013. [pdf, arXiv:0804.4118]
John Watrous. Simpler semidefinite programs for completely bounded norms. Chicago Journal of Theoretical Computer Science 2013: 8, 2013. [pdf, arXiv:1207.5726]
Abel Molina, Thomas Vidick, and John Watrous. Optimal counterfeiting attacks and generalizations for Wiesner's quantum money. Proceedings of the 7th Conference on Theory of Quantum Computation, Communication, and Cryptography, volume 7582 of Lecture Notes in Computer Science, pages 45–64, 2013. [pdf, arXiv:1202.4010]
Abel Molina and John Watrous. Hedging bets with correlated quantum strategies. Proceedings of the Royal Society A 468(2145): 2614–2629, 2012. [pdf, arXiv:1104.1140]
Tsuyoshi Ito, Hirotada Kobayashi, and John Watrous. Quantum interactive proofs with weak error bounds. Proceedings of the 3rd Innovations in Theoretical Computer Science Conference, pages 266–275, 2012. [pdf, arXiv:1012.4427]
Rahul Jain, Zhengfeng Ji, Sarvaghya Upadhyay, and John Watrous. QIP = PSPACE. Journal of the ACM 58(6): article 30, 2011. (A preliminary version appeared in Proceedings of the 42nd ACM Symposium on Theory of Computing, 2010.) [pdf, arXiv:0907.4737]
John Watrous. An introduction to quantum information and quantum circuits. ACM SIGACT News 42(2): 52–67, 2011. [pdf]
Salman Beigi, Peter Shor, and John Watrous. Quantum interactive proofs with short messages. Theory of Computing 7: 101–117, 2011. [pdf, arXiv:1004.0411]
William Matthews, Marco Piani, and John Watrous. Entanglement in channel discrimination with restricted measurements. Physical Review A 82(3): 032302, 2010. [pdf, arXiv:1004.0888]
Aram Harrow, Avinatan Hassidim, Debbie Leung, and John Watrous. Adaptive versus non-adaptive strategies for quantum channel discrimination. Physical Review A 81(3): 032339, 2010. [pdf, arXiv:0909.0256]
Richard Jozsa, Barbara Kraus, Akimasa Miyake, and John Watrous. Matchgate and space-bounded quantum computations are equivalent. Proceedings of the Royal Society A 446: 809–830, 2010. [pdf, arXiv:0908.1467]
Rahul Jain, Sarvaghya Upadhyay, and John Watrous. Two-message quantum interactive proofs are in PSPACE. Proceedings of the 50th Annual IEEE Symposium on Foundations of Computer Science, pages 534–543, 2009. [pdf, arXiv:0905.1300]
John Watrous. Semidefinite programs for completely bounded norms. Theory of Computing 5: 11, 2009. [pdf, arXiv:0901.4709]
Marco Piani and John Watrous. All entangled states are useful for channel discrimination. Physical Review Letters 102(25): 250501, 2009. [pdf, arXiv:0901.2118]
John Watrous. Zero-knowledge against quantum attacks. SIAM Journal on Computing 39(1): 25–58, 2009. (A preliminary version appeared in Proceedings of the 38th ACM Symposium on Theory of Computing, pages 296–305, 2006.) [pdf, arXiv:0511020]
Scott Aaronson and John Watrous. Closed timelike curves make quantum and classical computing equivalent. Proceedings of the Royal Society A 465(2102): 631–647, 2009. [pdf, arXiv:0808.2669]
Rahul Jain and John Watrous. Parallel approximation of non-interactive zero-sum quantum games. Proceedings of the 24th Annual IEEE Conference on Computational Complexity, pages 243–253, 2009. [pdf, arXiv:0808.2775]
John Watrous. Mixing doubly stochastic quantum channels with the completely depolarizing channel. Quantum Information and Computation 9(5&6): 406–413, 2009. [pdf, arXiv:0807.2668]
John Watrous. Quantum computational complexity. Encyclopedia of Complexity and System Science, Springer, 2009. [pdf, arXiv:0804.3401]
John Watrous. Distinguishing quantum operations having few Kraus operators. Quantum Information and Computation 8(9): 819–833, 2008. [pdf, arXiv:0710.0902]
Gus Gutoski and John Watrous. Toward a general theory of quantum games. Proceedings of the 39th ACM Symposium on Theory of Computing, pages 565–574, 2007. [pdf]
John Watrous. Bipartite subspaces having no bases distinguishable by local operations and classical communication. Physical Review Letters 95(8): 080505, 2005. [pdf]
Bill Rosgen and John Watrous. On the hardness of distinguishing mixed-state quantum computations. Proceedings of the 20th Annual IEEE Conference on Computational Complexity, pages 344–354, 2005. [pdf]
Chris Marriott and John Watrous. Quantum Arthur-Merlin games. Computational Complexity, 14(2): 122–152, 2005. (A preliminary version appeared in Proceedings of the 19th Annual IEEE Conference on Computational Complexity, pages 275–285, 2004.) [pdf]
Gus Gutoski and John Watrous. Quantum interactive proofs with competing provers. Proceedings of the 22nd Annual Symposium on Theoretical Aspects of Computer Science, volume 3404 of Lecture Notes in Computer Science, pages 605–616, Springer-Verlag, 2005. [pdf]
John Watrous. Notes on super-operator norms induced by Schatten norms. Quantum Information and Computation, 5(1): 58–68, 2005. [pdf]
Eric Bach, Susan Coppersmith, Marcel Paz Goldschen, Robert Joynt, and John Watrous. One-dimensional quantum walks with absorbing boundaries. Journal of Computer and System Sciences 69(4): 562–592, 2004. [pdf]
John Watrous. Many copies may be required for entanglement distillation. Physical Review Letters, 93(1): 010502, 2004. [pdf]
Richard Cleve, Peter Hoyer, Benjamin Toner, and John Watrous. Consequences and limits of nonlocal strategies. Proceedings of the 19th Annual IEEE Conference on Computational Complexity, pages 236–249, 2004. [pdf]
John Watrous. On the complexity of simulating space-bounded quantum computations. Computational Complexity, 12: 48–84, 2003. (A preliminary version appeared with the title "Quantum and classical space-bounded processes with algebraic transition amplitudes" in Proceedings of the 40th Annual IEEE Symposium on Foundations of Computer Science, pages 341–351, 1999.) [pdf]
Heath Gerhardt and John Watrous. Continuous-time quantum walks on the symmetric group. Proceedings of the 7th International Workshop on Randomization and Approximation Techniques in Computer Science, 2003. [pdf]
John Watrous. PSPACE has constant-round quantum interactive proof systems. Theoretical Computer Science, 292(3): 575–588, 2003. (A preliminary version appeared in Proceedings of the 40th Annual IEEE Symposium on Foundations of Computer Science, pages 112–119, 1999.) [pdf]
John Watrous. Limits on the power of quantum statistical zero-knowledge. Manuscript, 2003. (A preliminary version appeared in Proceedings of the 43rd Annual IEEE Symposium on Foundations of Computer Science, pages 459–468, 2002.) [pdf]
Niel de Beaudrap, Richard Cleve, and John Watrous. Sharp quantum vs. classical query complexity separations. Algorithmica, 34(4): 449–461, 2002. [pdf]
Andris Ambainis and John Watrous. Two-way finite automata with quantum and classical states. Theoretical Computer Science, 287(1): 299–311, 2002. [pdf]
Harry Buhrman, Richard Cleve, John Watrous, and Ronald de Wolf. Quantum fingerprinting. Physical Review Letters, 87(16): 167902, 2001. [pdf]
John Watrous. Quantum algorithms for solvable groups. Proceedings of the 33rd ACM Symposium on Theory of Computing, pages 60–67, 2001. [pdf]
Andris Ambainis, Eric Bach, Ashwin Nayak, Ashvin Vishwanath, and John Watrous. One-dimensional quantum walks. Proceedings of the 33rd ACM Symposium on Theory of Computing, pages 37–49, 2001. [pdf]
John Watrous. Quantum simulations of classical random walks and undirected graph connectivity. Journal of Computer and System Sciences, 62(2): 376–391, 2001. (A preliminary version appeared in Proceedings of the 14th Annual IEEE Conference on Computational Complexity, pages 180–187, 1999.) [pdf]
John Watrous. Succinct quantum proofs for properties of finite groups. Proceedings of the 41st Annual IEEE Symposium on Foundations of Computer Science, pages 537–546, 2000. [pdf]
Richard Cleve and John Watrous. Fast parallel circuits for the quantum Fourier transform. Proceedings of the 41st Annual IEEE Symposium on Foundations of Computer Science, pages 526–536, 2000. [pdf]
Alexei Kitaev and John Watrous. Parallelization, amplification, and exponential time simulation of quantum interactive proof systems. Proceedings of the 32nd ACM Symposium on Theory of Computing, pages 608–617, 2000. [pdf]
John Watrous. Space-bounded quantum complexity. Journal of Computer and System Sciences, 59(2): 281–326, 1999. (A preliminary version appeared with the title "Relationships between quantum and classical space-bounded complexity classes" in Proceedings of the 13th Annual IEEE Conference on Computational Complexity, pages 210–227, 1998.) [pdf]
Attila Kondacs and John Watrous. On the power of quantum finite state automata. Proceedings of the 38th Annual IEEE Symposium on Foundations of Computer Science, pages 66–75, 1997. [pdf]
John Watrous. On one-dimensional quantum cellular automata. Proceedings of the 36th Annual IEEE Symposium on Foundations of Computer Science, pages 528–537, 1995. [pdf]
John Watrous. A polynomial-time algorithm for the Artin-Whaples approximation theorem. Number Theory: Fourth Conference of the Canadian Number Theory Association, pages 397–407, 1995.
I am currently on leave from the University of Waterloo. I am not available to review papers, books, or proposals, and am not accepting new students or postdoctoral fellows at this time.
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 4,692
|
Items where Author is "Awang @Hashim, Nazratul Akmal"
Awang @Hashim, Nazratul Akmal (2015) Knowledge, attitude and the use of ICT among ESL lecturers in UiTM Terengganu / Nazratul Akmal Awang @Hashim. Masters thesis, Universiti Teknologi MARA.
This list was generated on Fri Apr 19 17:02:51 2019 +08.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 621
|
Europe and Russia
Clipper Russian space ship of the future
Thread starter jakojako777
jakojako777
Russia to start research into spacecraft nuclear engines in 2010
Russia will launch research into nuclear engines for spaceships from 2010, the head of the Federal Space Agency said on Sunday.
"Nuclear engines for spaceships are a very promising area. Such engines should be created to make flights to Mars and other planets, for example," Anatoly Perminov said.
Perminov earlier said that the development of Megawatt-class nuclear space power systems (MCNSPS) for manned spacecraft was crucial for Russia if the country wanted to maintain a competitive edge in the space race, including the exploration of the Moon and Mars.
Perminov said that the draft design of spacecraft powered by a nuclear engine would be finalized by 2012, and the financing for further development in the next nine years would require an investment of at least 17 billion rubles (over $580 million).
Anatoly Koroteyev, president of the Russian Academy of Cosmonautics and head of the Keldysh research center, earlier said that the key scientific and technical problem in sending manned missions to the Moon and Mars was the development of new propulsion systems and energy supplies with a high degree of energy-mass efficiency.
The current capabilities of the Russian space industry are clearly insufficient either to set up a permanent base on the Moon or accomplish an independent manned mission to Mars, he said.
BAIKONUR SPACE CENTER (Kazakhstan), December 20 (RIA Novosti)
Russia to start research into spacecraft nuclear engines in 2010 | Top Russian news and analysis online | 'RIA Novosti' newswire
Russia, Europe abandon joint space project - Roscosmos
MOSCOW, January 29 (RIA Novosti) - Russia and Europe will not continue the joint development of a new reusable manned spacecraft, an official from Russia's space agency (Roscosmos) said on Thursday.
The Federal Space Program for 2006-2015 stipulated the joint construction with European countries of a reusable "Clipper" spacecraft to service the International Space Station (ISS) and make journeys to the Moon.
"We planned to build a reusable manned spacecraft in cooperation with the European Space Agency [ESA], but our approaches to this project turned out to be very different," Alexei Krasnov, director of manned flight programs at Roscosmos, told a roundtable meeting in Moscow.
The official said Russia would launch a second tender for a new shuttle spacecraft because the first attempt had proved unsatisfactory. New design projects will be considered through 2010.
"The participants of a new tender may include the previous bidders - the Energia Rocket and Space Corporation, the Khrunichev State Research and Production Center and the Molniya Research and Production Association," Krasnov said.
He also said Russia was planning to build the project's first manned spacecraft by 2015-2018, along with a new carrier rocket with a payload capacity of at least 23 tons.
Various sources estimate the cost of the Russian reusable spacecraft project, including construction, will total $1-3 billion.
The launches of the future carrier rockets will be conducted from a new space center, Vostochny, in Russia's Far East, Krasnov said.
Russia currently uses two launch sites for space carrier rockets and ballistic missiles tests: the Baikonur space center in the Central Asian Republic of Kazakhstan, which it has leased since the collapse of the Soviet Union, and the Plesetsk space center in northwest Russia.
Russia, Europe abandon joint space project - Roscosmos | Top Russian news and analysis online | 'RIA Novosti' newswire
Kliper (Clipper) spacecraft
Designing the Soyuz replacement: 2000-2005
Since 1970s, Russian engineers pondered over possible configurations of a new spacecraft, which could replace the venerable but relatively small Soyuz. Before the collapse of the USSR, RKK Energia -- the developer of the Soyuz -- attempted to tackle the issue several times, however technical and financial problems kept all these efforts from coming to fruition. However, as soon as the Russian economy started emerging from the post-Soviet transition, developers renewed their search for the Soyuz replacement.
The 2006 configuration of the winged orbiter
By January 2006, when the Russian government launched a tender for the development of the next generation spacecraft to replace Soyuz, RKK Energia conceptualized a new configuration of the Kliper spacecraft. Along with the improved aerodynamic shape, RKK Energia returned to the use of the expendable habitation and propulsion module, since the federal tender required a single spacecraft design, rather than a "system."
Competitors: Alternative designs for the Kliper
According to the Russian law, federal funding for the development of the Kliper spacecraft could not be provided before the official tender of for the project had taken place. Although many considered the tender a formality and RKK Energia's design as the favorite, Khrunichev enterprise in Moscow submitted its proposals for the follow-on to the TKS spacecraft and NPO Molniya pushed the modified design of the MAKS mini-shuttle, it proposed in the 1990s. The closed tender was officially held from January 18 to July 19, 2006.
Into deep space
Early on in the program, RKK Energia advertised the Kliper, as a multifunctional vehicle, potentially capable of supporting missions into deep space. Develolpers proposed modifications of the spacecraft, which could play role in lunar exploration and even serve as a return vehicle in the expeditions to Mars.
Practically on a day the existence of the Kliper project was revealed to the public, Russian officials admitted that despite its pragmatic and cost-conscious design, the new orbiter had little chance getting off the ground without financial backing from abroad. No surprisingly, the Russian Space Agency, Roskosmos, and RKK Energia launched an aggressive marketing effort to sell the Kliper to international partners. However, they had little room to shop around.
The Kliper sported a reusable aerodynamically active fuselage, protected by special tiles, not unlike those on the US Space Shuttle and the Soviet Buran. The original design of the Kliper included so-called "lifting body," a wingless iron-shaped fuselage, which would enable the craft to maneuver in the Earth atmosphere during the reentry. However, by the end of 2004, engineers favored a winged body, which would increase the maneuverability of the vehicle, while reducing g-loads on the crew.
Cabin module
The main habitable volume onboard the Kliper would be contained inside a cone-shaped cabin structure. The lower half of the cabin would be enclosed within the main fuselage, while the top half would be covered with special protective shield. The cabin carried all avionics, flight control, and life-support systems.
Propulsion and habitation module
The original design of the Kliper spacecraft included a special detachable habitation and service module mounted behind the reentry glider. In its turn, the module would consist of two structural sections: a habitation module, closely resembling the one on the Soyuz spacecraft and the doughnut-shaped service module. The habitation module would contain docking port, toilet and other life-support systems. The In 2005, most functions of the habitation and propulsion module were transferred to a separately launched Parom space tug.
According to the original plans, the Kliper would be launched on top of a yet-to-be developed Onega booster -- a heavily modified Soyuz rocket. Given virtually nonexistent chances of obtaining funding for the Onega, RKK Energia considered the operational Zenit booster with similar capabilities, as well as yet-to-be built Angara-3 rocket. The Soyuz-3 rocket was also considered as the alternative. However, upon "spliting" the spacecraft into two independent vehicles in 2005, RKK Energia settled on the smaller Soyuz-2-3 launcher. However alternative options still remained on the table as of beginning of 2006.
Parom orbital tug
During 2005, RKK Energia embarked on another major revision of the Kliper. It would be the third significant re-shaping of the spacecraft configuration, since it was first unveiled to the public in February 2004. The latest design included not one but two vehicles: the Kliper reentry glider itself and the Parom (ferry) orbital tug -- a new element of the system, which would be launched by a separate rocket.
FLIGHT PROFILES
Nominal flight profile in Earth orbit
In its latest configuration, the Kliper would be launched on top of the three-stage Soyuz-2-3 rocket and upon reaching the orbit would wait for the arrival of the Parom orbital tug, which would boost the vehicle to the space station. The Parom would use its free port on the "tail" side of the vehicle to dock with the space station. After undocking, the Parom would remain in orbit for the next mission, while the Kliper would reenter and land on the runway as a glider.
Emergency escape profiles
In the original concept, the Kliper would be topped with the emergency escape rocket, which would pull the glider away from the failing booster during the launch, as it was done onboard the Soyuz spacecraft. However in the effort to save weight and simplify aerodynamic flow around the nose of the orbiter, engineers decided to move the escape rockets to the launch vehicle adapter on the tail of the spacecraft, where they could double as the orbital maneuvering system.
History of the Kliper (Clipper) spacecraft
During a press-conference at the ITAR TASS news agency on February 17, 2004, Yuri Koptev revealed that since 2000, RKK Energia had been working on a brand-new vehicle called Kliper (Clipper). In the following days, a flurry of reports in the Russian press provided the first details on the project.
At the time of Koptev's announcement, the project apparently had already evolved through several reincarnations, however from the outset it was a partially reusable "lifting-body" -- essentially a wingless orbiter, shaped in such a way that it could have an aerodynamic lift, when returning from orbit into the atmosphere. It would be launched by a medium class rocket.
The initial studies, which led to the Kliper concept, sought a modern vehicle capable of replacing the Soyuz, but built on existing manufacturing base as much as possible. One of the early concepts included an enlarged reentry capsule of the Soyuz spacecraft for as many as five or six people. However soon requirements for the precise landing dictated a vehicle, which would be capable of the controlled flight in the atmosphere.
In the second half of the 1990s, a leading aerodynamist of RKK Energia, Reshetin, proposed a reusable "lifting-body" spacecraft, which could carry up to six people and return up to 700 kilograms from orbit. In the following years, the aerodynamics of the vehicle was calculated and its mockup was tested in a wind tunnel. (259)
As of 2004, RKK Energia had submitted technical proposals for the new spacecraft to the Russian Aviation and Space Agency, Rosaviacosmos. The agency has apparently provided limited funding for further preliminary studies.
In April 2004, Nikolai Moiseev, First Deputy Director of the Russian Federal Space Agency, FKA, (formerly Rosaviacosmos) told Russian news agency that the Kliper project would be included in the federal space plan for 2005-2015.
On November 30, 2004, RKK Energia invited the press into its Checkout and Testing Station, KIS, to inspect a full-scale mockup of the Kliper spacecraft. The company also released revised technical information on the project, including details on a winged version of the spacecraft, developed in parallel with the work on the "lifting body."
Switch to wings
During 2004, RKK Energia apparently contacted its European partners on the feasibility of cooperative development of the Kliper. In 2005, RKK Energia displayed the spacecraft at EXPO-2005 in Japan and Le Bourget Air and Space Show, France.
However, the funding for the project was not forthcoming. In April 2005, in the interview with the Russian Novosti News Agency, Valeri Ryumin, Deputy designer General at RKK Energia said that the Russian federal budget did not earmarked any money for the program.
Upon completion of the preliminary evaluation of the lifting body for the Kliper, designers turned their attention to the concept of a winged vehicle. Although at one point both concepts were considered in parallel, soon RKK Energia focused on the winged version. At the time, Yuri Koptev still led the Russian Aviation and Space Agency, Rosaviacosmos, comprising both aviation and space industry. He apparently facilitated the involvement of the aviation industry into the Kliper project, which made the development of the winged orbiter both desirable and feasible.
Sukhoi's involvement
In March 2005, realizing new challenges of a winged design, RKK Energia leadership convinced OKB Sukhoi, a world-renown developer of military aircraft, to invest its own resources and expertise into the Kliper project. The agreement signed in March 2005 was reached after several months of negotiations between RKK Energia's chief Yuri Semenov and the head of the Sukhoi company Mikhail Pagasyan.
According to the agreement, RKK Energia would remain responsible for the overall design of the vehicle, including its aerodynamic shape, and RKK Energia would be responsible for ensuring the survivability of the aerodynamic shape of the vehicle at hypersonic speed. Sukhoi was expected to take RKK Energia's aerodynamic shape and conduct wind-tunnel tests according to their methodic for its temperature and stability characteristics.
Enter Europe
In search for partners in the development of the Kliper spacecraft, RKK Energia also looked outside Russia. With NASA out of the picture as a potential partner, Russians sought the cooperation with Europe and Japan.
Choosing the launcher
According to the original plans, the Kliper would be launched on top of a yet-to-be developed Onega booster -- a heavily modified Soyuz rocket -- with no payload fairing but with the emergency escape rocket attached to the nose section of the reentry capsule. The emergency escape system, resembling that of the Soyuz spacecraft, would be capable of pulling the crew capsule away from the launch vehicle at every stage of the launch and orbit insertion.
A successful development of the Onega booster and its launch infrastructure would be one of the most challenging and expensive aspects of the project. Also, the decision to base the project on the expendable booster would limit economic viability of the reusable spacecraft. The Onega booster, could be launched from upgraded Soyuz facilities in Baikonur, Plesetsk and, potentially, French Guiana.
Given virtually nonexistent chances of obtaining funding for the Onega, RKK Energia considered the Zenit booster with similar capabilities. The most advanced vehicle in the Soviet rocket fleet, the Zenit was essentially banished from the Russian space program, when the collapse of the USSR left its prime manufacturer in the newly independent republic of Ukraine. Yet, in the case of Kliper, technical pragmatism outweighed political considerations.
By August 2004, the company essentially committed to "re-tailor" the Kliper for the Zenit. The spacecraft had to shed around 1.5 tons from its total mass and around one ton from the mass of its reentry capsule. In addition, the emergency escape system was moved from the top of the spacecraft to the launch vehicle adapter. This way, during a nominal flight, emergency escape engines would be used for final orbital insertion maneuver, providing extra weight savings.
In 2005, the idea of using the Soyuz-derived vehicle re-surfaced again, however the Onega concept was replaced by the Soyuz-3 configuration. As of June 2005, Zenit, Soyuz-3 and Angara were all considered as launch vehicles.
Introduction of Parom
During 2005, RKK Energia embarked on another major revision of the Kliper design. The new configuration included not one but two vehicles: the Kliper reentry glider itself and the Parom (ferry) orbital tug -- a new element of the system, which would be launched by a separate rocket. Splitting the spacecraft into two independent segments would enable their launches onboard a modified version of the Soyuz rocket, which has been a workhorse of the Russian manned spaceflight for decades. The launch vehicle, designated Soyuz-2-3, would become a culmination of incremental upgrades then planned for the Soyuz-2 family of rockets.
As added bonus, the use of the Soyuz-2-3 rocket would allow launching the Kliper from the European Space Agency's facility in French Guiana, offering extra payload capabilities due to its geographical location.
Federal tender
Despite a setback in securing the European funding for the project in December of 2005, the Russian government said it had already committed to the development of the vehicle.
On October 22, 2005, the Russian government signed a decree No. 635, approving Federal Space Program for 2006-2015. It included planned funding for the new generation of reusable spacecraft. However in the accordance with the current Russian law, the prime developer of the vehicle had to be chosen in a tender. As a result, Khrunichev enterprise and NPO Molniya were invited to compete with RKK Energia in a closed tender, which opened at Roskosmos headquarters in Moscow on January 18, 2006.
Little details on the content of the proposals had been officially released at the beginning of the tender; although Roskosmos did state that the paperwork submitted by NPO Molniya had not met the requirements of the tender, since the cost of the proposal was calculated in "foreign currency" and the proper authorization was missing.
Competing proposals
Number of observers believed that Khrunichev came to the tender with a proposal for a follow-on to the TKS spacecraft, whose configuration had surfaced previously. However a drawing of a small winged vehicle with folding wings and launched by the Angara-3 rocket had also circulated.
NPO Molniya presented a slightly modified version of the MAKS space plane, which would be launched in mid-air from the An-225 Mriya transport aircraft.
Kliper in 2006 configuration
For obvious reasons, all eyes were on the latest reincarnation of the Kliper design submitted to the tender by RKK Energia, however details were emerging slowly. An officially released photo of RKK Energia's president Nikolai Sevastyanov holding an artist rendition of the "new" Kliper at the opening of the tender was analyzed to death, but it was too distorted by the perspective and low resolution to clearly visualize the vehicle.
First clear images of the latest configuration leaked from the Proceedings on the Cosmonautics held at Bauman school in Moscow on January 25-27, 2006. A redesigned shape of the Kliper, as well as modifications of the Parom orbital tug became apparent. At the time, RKK Energia kept all options on the table with respect to the launch vehicle. The Soyuz-2, Soyuz-2-3, Angara-3 and Zenit were all under consideration.
RKK Energia also returned to the use of the expendable habitation and propulsion module, since the tender required a single spacecraft design, rather than a "system." The Kliper with the habitation and propulsion module could still be launched by the Zenit-2 or the Soyuz-3 rockets, while the lighter vehicle could fly later on the Soyuz-2-3.
As required by the tender, the Kliper would be capable of lunar missions, (apparently, in a wingless configuration), and even had a potential for its use in the expeditions to Mars.
In the meantime, studies of Kliper's aerodynamics during 2005 resulted in drastic changes in the shape of its fuselage. In the effort to reduce heat loads on the underbelly of the vehicle during the reentry, engineers "rounded" a previously flat bottom of the vehicle. The wing structure was now attached to the fuselage at a higher position than before.
A somewhat flattened fuselage now held a cylindrical crew compartment and conical nose section. The crew members would now sit in pairs in three rows, instead of previous two rows with two pilots in front and four passengers behind.
Tender extends into 2006
Many observers saw the tender as a formality and RKK Energia a predetermined winner. They were proven wrong, when on February 3, 2006, when the tender was expected to be concluded, space officials announced the extension. According to Roskosmos, "none of the contenders was able to fully satisfy the requirements of the tender in respect to technical feasibility of the project within established timeframe and at the required level of safety." Representative of Roskosmos was quoted saying that the commission, which oversaw the tender, would clarify its requirements and deliver them to the participants within a month. On February 17, 2006, Deputy Head of Roskosmos Nikolai Moiseev said that the tender would be completed before the end of 2006. Moiseev added that the spacecraft should be able to function in space autonomously for no less than a month and be capable of lunar missions.
Then, it was widely anticipated that even if Khrunichev and NPO Molniya lose the competition to RKK Energia, the companies could still assume a role in the project as subcontractors.
Deferral of the program
On July 19, 2006, Russian space agency, Roskosmos, announced that it deferred the development of the new manned spacecraft until the next stage in the modernization of the nation's manned transport system. The agency's statement hinted that RKK Energia proposals for the Kliper spacecraft and Khrunichev's concept of the TKS-based capsule required the development of launch vehicles (Soyuz-2-3 and Angara-3 respectively), which Russian government would not be able to fund within 2006-2015 timeframe. The NPO Molniya's proposal for the development of an air-launched vehicle was rejected on the grounds that it involved the Antonov-224 Mriya carrier aircraft manufactured in the former Soviet republic of Ukraine, while Russian government wanted all system contractors to be located inside Russia.
In the meantime, the agency accepted alternative proposals from RKK Energia to conduct a radical upgrade of the Soyuz spacecraft, in order to give it the capabilities for circumlunar missions. Roskosmos said that the upgraded Soyuz would allow testing of prospective technologies, which could be later applied to the next-generation systems. According to Roskosmos, results of this work would pave the way to the decision on the design of the next generation spacecraft, "if such (spacecraft) would be required."
Evolution of the Kliper design
Distinctive characteristics Status
A wingless lifting body with emergency escape engines attached in the nose and solar panels on the service module. Would use parachute landing. Unveiled in February 2004
A wingless lifting body with emergency escape engines placed on the launch vehicle adapter, where they can double as orbital insertion system. Solar panels replaced with fuel cells. Unveiled in November 2004
A winged vehicle, presented as an alternative to the lifting body design. Orbital maneuvering engines moved inside of the service module from the external surface of the habitation module. Aerodynamic shape redesigned to accommodate wings. Number of attitude control thrusters reduced. Unveiled in November 2004
A winged vehicle without habitation and service modules, designed to dock with the Parom orbital tug. Developed during 2005
Aerodynamic shape of the vehicle is redesigned to reduce heat loads during reentry. Crew seats are arranged in three rows. Presented to the government tender in January 2006
A Soyuz-bssed vehicle, capable of circumlunar missions, employing new technologies, which could be potentially used in the development of a winged reusable orbiter. Declared as a preferred configuration in July 2006
Development plan (as of 2005)
As of 2005, the development plan for the Kliper project called for following milestones:
2007: Completion of the preliminary design
2008: Completion of the working documentation
2012: Completion of the experimental development
2013: First (unmanned) flight test
Primary developer
RKK Energia
Korolev
Aerodynamics OKB Sukhoi Moscow
Thermal protection Plastik Syzran
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|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 9,168
|
Saint Bartholomew
Kiribati Islands
L'hot-dog
wikipedia.org, lonelyplanet.com
Hot dog originali
For some thehot dog it's just a simple sandwich with a sausage very similar to sausage, for others it is one of the most delicious dishes in style street food that the American tradition has given us.
The history of the hot dog has its roots in several countries. Despite being a symbol of the United States of America, USA and Germany, contend for the authorship of the recipe. In fact, the German immigrants would have brought the sausage sandwich overseas.
The combination Wurstel with sauerkraut is actually one of the typical German dishes. It would therefore have been they, emigrated to the USA and nostalgic for home dishes, who would have made the recipe known to the Americans.
Because the hot dog is called that
According to a legend, a Bavarian butcher was the first to invent a so-called sausage in 1600 dachsund, what does it mean bass otto, just in honor of this canine race with a characteristic elongated shape.
Another tells and features a peddler of sandwiches. In 1867, to increase his sales at the stadium, he would have invented that his frankfurters were "dog sausages", a real Marketing Strategy to attract attention among buyers.
The sports version, on the other hand, refers to the games of the New York Giants: it seems to have been the designer who associated the sandwiches served during the disputes with the dachshund dogs (both long and German). PA Dorgan, with special vignettes. The third reconstruction is more etymological: the term dog was used to identify certain bridle used by railway workers on rails: the shape of the sandwich could recall those bridles.
You can create many different combinations of hot dogs, the most original are:
Hot dog with teryaki sauce (based on soy);
The lobster hot dog, for fish lovers and is enriched with sauces such as remoulade (based on mayonnaise);
Sesame hot dog, just add sesame seeds to the original recipe;
Hot dog with onion and bacon, which has bechamel sauce as an unusual and original ingredient;
Blueberry hot dog, its sweetness combined with balsamic vinegar and one of the most famous street food in the world.
Salse per hot dog
It is essential to choose the right combinations for the filling: hot dogs with sauerkraut, gherkins, vegetables, cheeses and what you love most.
But the real touch that creates a unique mix of flavors is the choice of hot dog sauce.
Usually the sauce to accompany the frankfurters is ketchup or mustard. The ideal white sausage sauce is always of German origin: pork and veal sausages, also known as Bavarian traditional weisswurst, are eaten only for breakfast and never after 12:00.
2 Panini da hot dog
2 Frankfurters
150 g Sauerkraut
30 g Cheese
sauces (to taste)
First, cook the frankfurters on the griddle or grill. With a knife cut the center of the sausage, lengthwise, and cook them inside as well.
As a second step, divide the sandwiches in half and heat them on the plate on both sides. Heat the sauerkraut in a saucepan with a drizzle of extra virgin olive oil. Finally, season the sandwiches with sauces of your choice, fill with the sausages, place the sauerkraut in the center of the sausages and finish with a grated cheese.
And here is some tasty hot dogs to share at the table with your loved ones. Bon appetit greedy!
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2023 / fortraveladvicelovers.com
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 6,623
|
require 'spec_helper'
module FluidSurveys
module Structure
describe SourceObservationV1 do
specify do
expect(SourceObservationV1.survey_id).to eq 51399
end
let(:v1) { SourceObservationV1.new(api) }
let(:deployment_code) { ' LR.CON.Q1.09.036.020 ' }
let(:flowing_water) { 'Yes' }
let(:maintenance_visit) { 'No' }
let(:notes) { 'Notes' }
let(:api) do
{
'icJ0bt2hs1' => deployment_code,
'qVreqGQpLA' => flowing_water,
'EbwEfSdETT' => 'Hand Pump: Afridev',
'hqSVwuhttr' => maintenance_visit,
'oDqhgFtgGQ' => notes,
'_id' => 11,
'_created_at' => '2011-02-11T00:01:02.005',
}
end
specify do
expect(v1.deployment_code).to eq 'LR.CON.Q1.09.036.020'
end
specify do
expect(v1.fs_response_id).to eq 11
end
specify do
expect(v1.fs_survey_id).to eq 51399
end
specify do
expect(v1.inventory_type).to eq 'Hand Pump: Afridev'
end
it 'strips the milliseconds off the submitted_at' do
expect(v1.submitted_at).to eq Time.zone.parse('2011-02-11T00:01:02')
end
describe '#status' do
context 'water is flowing' do
let(:flowing_water) { 'Yes' }
context 'maintenance is required' do
let(:maintenance_visit) { 'Yes' }
it 'returns needs_visit' do
expect(v1.status).to eq :needs_visit
end
end
context 'maintenance is not required' do
let(:maintenance_visit) { 'No' }
it 'returns flowing' do
expect(v1.status).to eq :flowing
end
end
end
context 'water is not flowing' do
let(:flowing_water) { 'No' }
context 'maintenance is required' do
let(:maintenance_visit) { 'Yes' }
it 'returns needs_maintenance' do
expect(v1.status).to eq :needs_maintenance
end
end
context 'maintenance is not required' do
let(:maintenance_visit) { 'No' }
it 'returns needs_maintenance' do
expect(v1.status).to eq :needs_maintenance
end
end
end
context 'water flow cannot be determined' do
let(:flowing_water) { 'Unable to Access' }
context 'maintenance is required' do
let(:maintenance_visit) { 'Yes' }
it 'returns needs_visit' do
expect(v1.status).to eq :needs_visit
end
end
context 'maintenance is not required' do
let(:maintenance_visit) { 'No' }
it 'returns needs_visit' do
expect(v1.status).to eq :needs_visit
end
end
end
end # describe #status
describe '#notes' do
let(:notes) { 'Some notes' }
specify do
expect(v1.notes).to eq 'Some notes'
end
end
describe '#valid?' do
context 'blank deployment code' do
let(:deployment_code) { '' }
specify do
expect(v1.valid?).to be_falsey
end
end
context 'present deployment code' do
let(:deployment_code) { 'LR.CON.Q1.09.036.020' }
specify do
expect(v1.valid?).to be_truthy
end
end
context 'present but non-matching code' do
let(:deployment_code) { 'LR.CON.Q1.09.XXX.020' }
specify do
expect(v1.valid?).to be_falsey
end
end
end
end
end
end
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 6,410
|
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